The Money You Actually Keep: Products, Costs and Taxes

Phase 0 · Orientation & Foundations · Week 4 · ~14 focused hours · Mastery gate ≥ 85%

Over two years a portfolio of six holdings earned a money-weighted return of 17.22% a year. Its owner kept 11.46% after tax, and 11.46% is before you ask what the rupees could still buy.

Nothing went wrong in that account. No fraud, no blown trade, no crisis. Between the 17.22% and what landed sit a distributor commission on one fund, the expense ratios on four of them, securities transaction tax on two share trades, a dividend taxed at the top slab, a capital gain taxed at 12.5%, and a currency that bought 4.9% less each year than the year before. Five leaks, every one of them legal, disclosed and findable, and together they took ₹1,36,700 out of a book that closed at ₹12,37,428.

Three of those five leaks account for 94.7% of the total. Only one of the three is the one people argue about.

An analyst who cannot do this arithmetic is not a worse investor than one who can. They are a worse analyst. The same machinery decides what a mutual fund's reported return means and what a management fee does to a fund's terminal wealth. It decides why an insurance policy sold as an investment returns 6.63% while a term policy plus an index fund returns 9.66% on the same outlay, and why a portfolio management service can charge nothing at all in a year the account rose 21%. Products are contracts. Costs are contract terms. Tax is a contract you did not sign and cannot renegotiate. All three are readable, and reading them is a skill with a very high wage per hour.

The subject also carries a hazard that no other topic in the programme carries so sharply: almost every specific number in it expires. A tax slab is set by a Finance Act and changed by the next one. A total-expense-ratio ceiling is set by a regulator's circular and amended by the following circular. A contribution limit is indexed annually. A statute gets rewritten and its section numbers move. Anything you memorise here has a half-life measured in months.

So the working rule is stated once here, under a name, and it governs every figure printed below.

Every rate, slab, threshold, limit, cap and section number below carries a verify flag in square brackets, and that marking is the perishable-number rule. The flag names the primary source that sets the figure and, where a dated instrument set it, names the instrument. It means the figure illustrates the structure and does not fix the level, so before you use it for anything real you open the named source, read the current number and write down the date you read it. The method is what you are being taught. The number is an example of the method's input, and it is disposable. An analyst who quotes a tax rate from memory in a client meeting is one Finance Act away from being wrong in public.

Learning objectives

You can:

1. Map any savings or investment product onto its wrapper, state whether the wrapper taxes the contribution, the growth or the withdrawal, and compute what each pattern does to one unit of pre-tax income over a stated horizon.
2. Read a mutual fund's total expense ratio against the regulatory ceiling for a fund of its size, compute the blended cap from the slab schedule by hand, and state what the gap between the cap and the charge tells you.
3. Compute what a distributor commission costs over a decade on a monthly investment plan, express it as a share of the terminal wealth and as a share of the total gain, and explain why the second number is the honest one.
4. Decide an exit-load question against a holding-period line, computing the break-even price move at which redeeming today beats waiting, and state which of the two costs is avoidable.
5. Extract the four facts that matter from a scheme information document and a factsheet: the benchmark and its variant, the expense ratio and its plan, the portfolio turnover, and the rolling rather than point-to-point return record.
6. Compute the arithmetic of a systematic investment, transfer and withdrawal plan, including the tax event that every transfer instalment creates and the sequence-of-returns exposure that a withdrawal plan carries.
7. Build the retail decision table for index exposure: index fund against exchange-traded fund, using tracking difference, tracking error, the premium or discount to indicative value, and the total cost of ownership at a stated holding size.
8. Price a retail fixed-income and gold decision by hand: a treasury bill's yield from its price, a deposit ladder against a single deposit including the premature-withdrawal penalty, and a sovereign gold bond against a gold fund against physical metal on holding period, coupon, tax and liquidity.
9. Separate insurance from investment and price the separation, computing an endowment policy's internal rate of return, the charge stack inside a unit-linked policy, the surrender loss at an early year, and the term-plus-index alternative on the same premium.
10. Compute a performance fee with a hurdle and a high-water mark across a losing year, state the value of the high-water mark in currency, and name the investor-level tax difference between a pass-through structure and a fund-level one.
11. Apply the capital-gains set-off ladder in both jurisdictions, in the correct order, including the carry-forward condition, the wash-sale rule and the annual ordinary-income offset limit, and quantify the cost of applying the ladder in the wrong order.
12. Compute the tax on equity compensation end to end: ordinary income at vest with the basis reset, a qualifying against a disqualifying purchase-plan disposition, and the perquisite-at-exercise plus capital-gain-at-sale sequence, including the reporting obligation a foreign holding creates.
13. Assemble cost, tax and inflation into one after-everything real return for a multi-holding portfolio, rank the three largest leaks in currency, and name one action per leak that is actually available to the holder.

Prerequisites & connections

Builds on. M0.02 gave you the market machinery: who the regulator is, what an exchange does, what a mutual fund legally is, and why a depository sits between you and your shares. M0.03 gave you the arithmetic this material runs on and owns it: the effective annual rate, the difference between nominal and real, the Fisher relation, and the fee-drag identity that turns a hundred basis points into a sixth of a terminal outcome. Every fee calculation here is that identity applied to a new contract. M0.04 gave you the transaction-cost stack and the contract note, and owns them; the rate card used in the worked examples below is M0.04's, cited rather than rebuilt. M0.05 taught you to find things inside a filing, which is the same muscle a scheme information document needs.

Feeds forward. M1.06 onward will make you read the notes to accounts where a company's own tax charge lives, and the deferred-tax note will make more sense once you have paid attention to your own. Phase 3's discount-rate work uses the after-tax, after-cost real return as the number a real investor actually earns. Phase 9's risk and position-sizing modules treat turnover and cost as first-class risks rather than housekeeping, and the arithmetic here is why. The private-wealth branch takes the tax-aware planning apparatus much further, and the fixed-income branch takes the government-securities material from a retail purchase to an institutional one.

The deliberate non-overlaps run to six neighbours. Each owns material that touches this one, and each is cited rather than rebuilt. M0.03 owns the fee-drag identity, the effective annual rate and the real-versus-nominal machinery; the compounding arithmetic below assumes it and does not re-derive it. M0.04 owns the transaction-cost stack, the contract note and the illustrative statutory rate card; the worked examples apply that card to a portfolio rather than teaching it again. PW1.01 owns the private-client investment policy statement, human capital, estate planning and the full tax-loss-harvesting and wash-sale treatment inside a planning engagement, and it keeps its India tax cluster; what follows carries only the product-level version a retail holder needs and points into PW1.01 for the planning version. M5.03 owns insurance from the insurer's side, meaning embedded value, the actuarial reserve and how a life company earns money; what follows treats a policy only as a product a buyer is deciding whether to buy. AA1.08 owns exchange-traded fund mechanics, creation and redemption baskets, the arbitrage band and replication method; what follows carries only the decision table a retail holder needs and hands the mechanism straight over. DV1.05 owns the taxation of exchange-traded derivatives, including the business-income treatment and the audit threshold; no futures or options tax appears below.

1. The wrapper map, and what a wrapper does to one unit of return

Two people earn the same salary, save the same fraction of it, buy the same underlying assets and hold for the same twenty-five years. One ends with half as much again as the other. The difference is not skill or luck. It is the container.

Take one concrete unit: $6,000 of pre-tax salary over a 25-year horizon, earning a 7.0% annual total return of which two points arrive as dividends. The holder faces a 22% marginal income-tax rate now and at withdrawal, and a 15% rate on long-term gains and qualified dividends [verify: rates and brackets under the Internal Revenue Code as published by the IRS at irs.gov; brackets are indexed annually and the rates themselves are set by statute]. Put that $6,000 through four containers and it becomes four different numbers.

The taxable account keeps 66.2% of what the health savings account keeps, on identical assets held for identical time by an identical investor. Worked example 7 builds every one of those four numbers line by line, including the year-by-year basis accretion inside the taxable account that most quick comparisons get wrong.

Three structural facts fall out of that table and they carry across both jurisdictions.

The first is that traditional and Roth are the same product when the tax rate does not move. Both arrive at $25,400.38 here, to the cent, and the identity behind that is worth committing to memory because it settles an argument that consumes an enormous amount of internet oxygen. Deferring tax at rate t and paying it later at the same rate t is arithmetically identical to paying it now, because multiplication commutes. Traditional wins only when your later rate is lower; Roth wins only when your later rate is higher. The ratio of Roth to traditional is exactly (1 − t now) ÷ (1 − t later), which is 0.9744 when you go from 24% to 22% and 1.0556 when you go from 24% to 28%. Everything else said about the choice is a claim about your future tax rate dressed up as a claim about a product.

The second is that a taxable account leaks even when you never sell. The $6,000 case above never realises a gain until the final day, yet it still ends 15% behind the deferred wrapper, because the dividends were taxed every year and the tax on them came out of a compounding base. The drag is small annually and enormous cumulatively, which is the shape of every cost in this material.

The third is that an exempt-exempt-exempt wrapper is not free money, it is a conditional promise. A health savings account is tax-free only against qualified medical spending, and it requires a high-deductible health plan to fund at all [verify: IRS Publication 969, irs.gov, current-year edition]. Its money is not the same liquid money as the brokerage account's. The comparison in the table holds the assets constant and lets the tax treatment vary, which is the right way to see the effect, and it is not a recommendation to fill an account you cannot spend from.

India's wrappers do not map one for one onto the American ones, and trying to force the mapping is how advisers get this wrong.

The Public Provident Fund is the closest thing to an exempt-exempt-exempt container: contributions attract a deduction, the credited interest is exempt, and the maturity proceeds are exempt, with a fifteen-year lock and an annual contribution ceiling [verify: the PPF Scheme as notified by the Ministry of Finance, and Section 80C of the income-tax statute; the rate is reset quarterly and the ceiling is set by notification]. The Employees' Provident Fund works similarly for salaried employees with an employer contribution alongside, and it has acquired a taxable band on employee contributions above a threshold, which is exactly the kind of amendment that turns a memorised rule into a wrong one [verify: EPF Scheme rules and the relevant Finance Act amendment]. The National Pension System is a deferred wrapper with a compulsory annuitisation leg at exit, treated below in its own section because that leg is where its arithmetic actually lives.

Set one rupee of return against one rupee of deposit interest and the wrapper effect shows in currency. Fifteen annual contributions of ₹1,50,000 growing at 7.1% inside a fully exempt wrapper reach ₹40,68,209. The same flows in a taxable deposit paying the same 7.1%, taxed each year at a 30% slab with 4% cess, reach ₹33,65,608, because the deposit is actually compounding at 4.8848% rather than 7.1%. The wrapper is worth ₹7,02,601 over fifteen years on ₹22,50,000 of contributions, and the investment decision inside both containers was identical.

Asset location is the name for using this deliberately: put the assets whose income is taxed worst inside the wrappers that shelter income, and keep the assets you can control the realisation timing on in the taxable account. The full planning treatment, with the constraint framework and the client conversation around it, belongs to the private-wealth branch and is not repeated here. What belongs here is the arithmetic that tells you how much the decision is worth, because an adviser who cannot compute the ₹7,02,601 cannot argue for it.

2. Mutual funds as products: categories, plans and the expense-ratio ceiling

A mutual fund is a legal wrapper around a portfolio, and almost everything a buyer needs to know about it is set by four choices the sponsor made: what the scheme is allowed to hold, whether you are buying it through a distributor, what it charges, and what it says it is trying to beat.

India's scheme categorisation was imposed by the regulator precisely because the first of those had become unreadable. Before it, a fund house could run eleven large-cap schemes with eleven different mandates and eleven marketing stories. The categorisation exercise forced every open-ended scheme into one of a fixed set of buckets with defined portfolio constraints, and forced one scheme per category per fund house [verify: SEBI circular on categorisation and rationalisation of mutual fund schemes, sebi.gov.in]. That one-scheme rule carries standing exceptions, for index funds and exchange-traded funds tracking different indices and for sectoral or thematic schemes covering different sectors, so a fund house running several of those is not breaching it. A large-cap fund must hold a stated minimum in the top hundred companies by market capitalisation. A mid-cap fund draws from a defined rank band. A flexi-cap fund may go anywhere but must keep a stated minimum in equity. The value of the exercise to you as a reader is that the category name now carries information, and the first thing to check about any scheme is whether its actual portfolio matches the category it is filed under.

The direct plan against regular plan distinction is the single largest avoidable cost in Indian retail investing and it is invisible unless you look for it. Both plans hold the identical portfolio, run by the identical manager, with the identical strategy. They differ in one thing. The regular plan pays a commission to the distributor who sold it to you and the direct plan does not, so the regular plan's expense ratio is higher by roughly the commission and its net asset value grows more slowly forever [verify: SEBI (Mutual Funds) Regulations require the direct plan's expense ratio to be lower to the extent of distribution expenses; confirm the current wording at sebi.gov.in].

Put a number on it. Fifteen thousand rupees a month for ten years, a portfolio returning 11.0% gross, a direct-plan expense ratio of 0.62% and a regular-plan ratio of 1.72%. Working in effective monthly rates, the direct plan compounds at 0.826386% a month and reaches ₹30,58,046; the regular plan compounds at 0.742268% and reaches ₹28,87,538. The gap is ₹1,70,509 on ₹18,00,000 invested.

Three ways to read the same gap, in ascending order of honesty. It is 1.10 percentage points a year, which sounds like nothing. It is 5.58% of the terminal wealth, which sounds like a rounding error. It is 15.68% of the entire gain the regular plan produced, which is what it actually is, because the ₹18,00,000 was never at risk of being lost to fees and only the ₹10,87,538 of gain was ever in play. Whenever somebody quotes a fee as a share of assets, convert it to a share of the expected gain before you decide whether it is small.

The total expense ratio itself is capped, and the cap is a slab schedule rather than a single number. For an open-ended equity scheme the schedule runs in tranches of daily net assets, each tranche carrying its own rate, with a step-down above a threshold and a floor at the top [verify: SEBI (Mutual Funds) Regulations 1996, Regulation 52(6)(a) as amended by the SEBI circular dated 22 October 2018, sebi.gov.in].

Compute the blended ceiling the way you would compute a progressive income tax, tranche by tranche, and never by looking up the marginal rate. A scheme with ₹12,000 crore of daily net assets is permitted ₹190.125 crore of annual expense, which is a blended ceiling of 1.5844%. Its marginal rate in the ₹10,000 to ₹15,000 crore band is 1.45%, and the difference between the two, 0.134 percentage points, is the amount by which the marginal rate understates what the fund may actually charge. Run the same arithmetic at other sizes and the ceiling falls as the fund grows: 1.9063% at ₹2,000 crore, 1.5844% at ₹12,000 crore, 1.4410% at ₹32,000 crore, 1.2935% at ₹60,000 crore.

Two readings follow, and the second is the useful one. The obvious reading is that scale is supposed to be passed on to the holder. The useful reading is that the ceiling is a ceiling and not a price: a fund charging 1.55% against a ceiling of 1.5844% is charging essentially the maximum, and a fund charging 0.62% against the same ceiling has made a competitive decision you should notice. Read the charge against the cap for the fund's size, not against the average of all funds.

3. Exit loads and the holding-period line

An exit load is a charge the scheme levies on you for redeeming inside a stated window, and it is paid to the scheme rather than to the fund house, which is a detail worth knowing because it means the load does not enrich the manager. Its practical importance is that it usually sits close to, but not exactly on, a tax boundary, and the two together make a decision that people get wrong by reflex.

Take a real shape. You hold 4,000 units of an equity scheme bought at a net asset value of ₹62.50, now worth ₹79.12, a position of ₹3,16,480 on a cost of ₹2,50,000. You have held for 322 days. The scheme's exit load is 1% inside 365 days. Indian tax treats a gain on an equity-oriented unit held twelve months or less as short-term at 20%, and a longer holding as long-term at 12.5%. A 4% cess applies to the tax in both cases, and the long-term rate bites only above an annual exemption [verify: Sections 111A and 112A of the income-tax statute as amended by the Finance (No. 2) Act 2024, incometaxindia.gov.in; both the rates and the exemption are changed by Finance Acts, and India has since rewritten its income-tax statute, so confirm the current rate and the current section number before citing either].

Redeem today and you pay both charges. The load is 1% of ₹3,16,480, which is ₹3,164.80. The short-term tax on the ₹66,480 gain is ₹13,827.84. You keep ₹2,99,487.

Wait forty-four days and you pay neither the load nor the short-term rate. Assume for a moment the exemption has already been used on other gains, so the whole gain is taxed at 12.5% plus cess, which is ₹8,642.40. You keep ₹3,07,838.

Waiting is worth ₹8,350 at an unchanged price, on a decision that costs forty-four days. Then ask the question that turns this from arithmetic into judgment: how far would the price have to fall in those forty-four days for waiting to have been the wrong call? Solve for the net asset value at which the two routes tie and you get ₹76.72, a fall of 3.03%.

Read the number rather than the answer. Forty-four days of equity exposure with a 3.03% band around it is not a free option. An equity fund moves 3% in a fortnight often enough that this is a genuine gamble, not a rule. What the arithmetic gives you is the size of the prize, and the size of the prize is what tells you whether to take the risk. A holder whose entire reason for redeeming is that they need the money for a deposit next week should pay the ₹8,350 and stop thinking about it. A holder with no deadline has been handed a 3.03% cushion for forty-four days and should probably wait.

The general form applies far beyond mutual funds. Whenever a cost is triggered by a date, compute the price move that offsets it, and decide on the move rather than on the cost. People reliably over-weight the visible charge, which is the exit load here, and under-weight the invisible one, which is the seven-and-a-half-point difference between two tax rates. The load was ₹3,164.80. The tax difference was ₹5,185.44, or 62% of the total prize.

4. Reading a scheme document and a factsheet

Two documents carry everything a retail buyer is entitled to know, and both are written to be skimmed rather than read. The scheme information document is the constitutional text: mandate, asset allocation ranges, benchmark, load structure, risk factors and the fee schedule. The monthly factsheet is the operating report: current portfolio, current expense ratio, returns, and a small set of statistics.

Four things are worth extracting, in this order.

Start with the benchmark and its variant. A fund's benchmark is a claim about what it is trying to beat, and the variant is where the mischief lives. A price return index excludes dividends; a total return index includes them. Benchmarking an equity fund against a price index hands the manager the dividend yield as free alpha every year. India mandated total-return benchmarking for mutual funds precisely because the practice was widespread [verify: SEBI circular on benchmarking of mutual fund schemes, sebi.gov.in]. When you read any performance claim, in any market, the first question is whether the two sides of the comparison are the same kind of return. The full treatment of benchmark validity, including the seven properties a benchmark must satisfy, belongs to the performance-measurement material in the asset-allocation branch.

Then the expense ratio, and which plan it belongs to. Factsheets frequently print both plans' ratios in small type, so check that the one you are quoted is the one you would actually buy.

Portfolio turnover is third, and it is the line nobody reads. A ratio of 1.35 means the fund replaced the equivalent of 135% of its portfolio in the year, an average holding period of 8.9 months. Turnover costs money that does not appear in the expense ratio at all: brokerage, taxes and the spread are borne by the scheme and show up only as a slightly lower net asset value. At a round-trip cost of 35 basis points, a turnover of 1.35 implies a trading bill of 47.25 basis points a year, which on a ₹5,00,000 holding is ₹2,363 a year that no disclosure line will ever show you. Turnover is also information about the manager: a fund whose mandate is long-horizon quality and whose turnover is 1.35 is telling you something about itself that its marketing is not.

The fourth is the return record, which must be rolling rather than point-to-point. A point-to-point return is a single sample of a distribution, and a fund house choosing the two endpoints is choosing the sample. Take eight annual returns of +31%, −9%, +22%, +4%, −14%, +28%, +11% and +19%. The point-to-point compound return over the full eight years is 10.35%, which is the number that goes on the poster. Slice the same series into every three-year window and you get six windows returning 13.30%, 4.91%, 2.95%, 4.61%, 6.91% and 19.13%. The worst three-year window is 2.95% and the best is 19.13%, a spread of 16.18 percentage points, and every one of those windows was a real experience for somebody who invested on that day.

The point-to-point figure is not a lie. It is a summary of one path through a distribution whose width is the thing you actually needed to know, and the rolling view is how you recover the width. Ask for it, and where a fund does not publish it, build it yourself from the net-asset-value history.

The riskometer is the fifth item, and it deserves one paragraph of honest scepticism. It is a mandated pictogram placing a scheme on a scale from low to very high risk, computed from a defined methodology over the scheme's portfolio and reviewed monthly [verify: SEBI circular on product labelling in mutual fund schemes, sebi.gov.in]. It is genuinely useful as a floor, because it stops a fund selling credit-risk paper as a low-risk product. It is close to useless as a discriminator, because almost every equity scheme sits in the same bucket. Treat it as a check that the label is not fraudulent rather than as an input to a choice.

5. Investment, transfer and withdrawal plans, and the arithmetic under each

Three standing-instruction products dominate Indian retail investing, and each is a formula plus a tax consequence.

A systematic investment plan buys a fixed rupee amount at each interval. Its future value is the ordinary annuity formula from the numeracy work, applied at the effective rate for the interval rather than the annual rate divided by twelve. For a monthly plan, the monthly rate is i = (1 + R)^(1/12) − 1 where R is the annual net return, and the future value of n end-of-month contributions of P is P × [(1 + i)^*n* − 1] ÷ i. Using the annual rate divided by twelve instead overstates the answer, because it ignores that the twelve monthly credits themselves compound. On the ten-year, ₹15,000-a-month direct-plan case above, the effective monthly rate is 0.826386%; the naive 10.38 ÷ 12 = 0.865% would have added about ₹80,000 to a ₹30.6 lakh answer, all of it invented.

The behavioural claim usually made for these plans is that they buy more units when prices are low, which is arithmetically true and much less powerful than the marketing suggests. The genuine advantages are that the decision is made once rather than monthly, and that a plan running through a fall keeps buying when a discretionary investor would have stopped. Both are real. Neither is a return.

A systematic transfer plan moves a fixed amount at intervals from one scheme to another, typically from a liquid fund into an equity fund, and it carries a tax consequence that catches almost everybody. Each transfer is a redemption from the source scheme, and therefore a taxable event, and therefore a line the holder must report. Move ₹5,00,000 out of a liquid fund yielding 6.6% in ten monthly instalments of ₹50,000, the balance compounding at the effective monthly rate between transfers, and you realise ₹14,378 of gain across ten separate redemptions. The gain is taxed at the slab rate, because a debt-oriented scheme has no favourable long-term rate available to it [verify: the deemed-short-term treatment of specified mutual funds introduced by the Finance Act 2023 and refined by the Finance Act 2024, incometaxindia.gov.in]. At 30% plus cess that is ₹4,486 of tax and ten rows in a return. The liquid fund's 6.6% headline is really 4.5408% after tax to a top-slab holder, and the transfer plan generates the paperwork whether or not it generates the return.

A systematic withdrawal plan redeems a fixed rupee amount at intervals and pays it out. It is the decumulation mirror of the investment plan and it is far more dangerous, for a reason the arithmetic makes unarguable.

A fixed rupee withdrawal from a falling portfolio redeems more units. Those units are gone. When the market recovers, it recovers on a smaller unit count, and the recovery cannot undo the redemptions. This is sequence-of-returns risk, and it means that two investors with identical average returns can end with radically different outcomes purely because of the order in which those returns arrived.

Worked example 4 runs the numbers in full. The short version: a ₹1 crore corpus with a ₹60,000 monthly withdrawal, put through ten annual returns averaging 6.0%, ends at ₹48.05 lakh if the two bad years come first and ₹92.04 lakh if they come last. Same ten numbers, same mean, opposite order, and the bad-first investor ends with 52.2% of what the bad-last investor has. With no withdrawals at all, both orders end at exactly ₹1,69,05,914, because multiplication commutes when nothing is taken out. Withdrawals are what break the commutativity.

The tax side of a withdrawal plan is worth one line because it surprises people in a pleasant direction. Each redemption is matched against units on a first-in, first-out basis, so in a falling first year the redemptions realise losses rather than gains. In the bad-first sequence, the twelve first-year redemptions consumed 8,030.16 units bought at ₹100 and returned ₹7,20,000 of cash, an ₹83,016 short-term capital loss. That loss is useful, it can be set off, and it can be carried forward. The same first year in the bad-last sequence produced a ₹35,971 short-term gain. The withdrawal plan does not decide your tax; the market's order does.

6. Index funds and exchange-traded funds: the retail decision table

Both products track an index. The mechanism by which an exchange-traded fund keeps its price near its portfolio value, meaning the creation and redemption baskets, the authorised participants and the arbitrage band that closes a discount, belongs to the index and implementation material in the asset-allocation branch and is not rebuilt here. What belongs here is the decision a retail buyer actually faces, which turns on four things.

The first is the indicative net asset value. An exchange-traded fund publishes a continuously updated estimate of what its underlying basket is worth right now, computed by the fund house or the exchange during trading hours. The traded price can and does differ from it. A fund quoted at ₹248.30 against an indicative value of ₹244.10 is trading at a 1.7206% premium, and on a ₹5,00,000 order that premium costs ₹8,458 before any other cost. The discipline is to check the indicative value before placing the order and to refuse a wide premium rather than to pay it in a hurry.

Tracking difference and tracking error come second, and they are different objects. The confusion between them is one of the most common errors in retail commentary. Tracking difference is the realised gap between the fund's return and the index's return over a period: a level, signed, and directly interpretable as money. Tracking error is the standard deviation of that gap: a measure of how consistently the fund misses, saying nothing about which direction. Over five years, a fund whose annual tracking differences were −0.34, −0.41, −0.29, −0.55 and −0.38 percentage points has a mean tracking difference of −0.394 points and a standard deviation of 0.0878 points. The cumulative five-year shortfall is 1.955%, which on a ₹10,00,000 holding is ₹19,545.

Read those two numbers together. The tracking error of 0.09 points says this fund is extremely consistent. The tracking difference of −0.394 points says it consistently loses to its index by about four times its stated expense ratio, and the consistency is what makes the loss reliable rather than reassuring. A fund with a small tracking error and a large tracking difference is a well-run fund that is expensive; a fund with a small tracking difference and a large tracking error is a cheap fund with an operational problem. You need both numbers.

Third is a condition rather than a number: whether the arbitrage still works. The mechanism that keeps price near value depends on somebody being able to trade the underlying basket cheaply and immediately. It weakens when the underlying market is closed, when the underlying is illiquid, when there is a single authorised participant, and when regulatory limits stop new units being created. Indian holders have seen this in international funds, where inflow limits have at times forced schemes to stop accepting money and their exchange-traded versions to trade at large premiums [verify: the schemes' own addenda and the applicable overseas-investment limits, checked with the fund house]. A premium that persists for weeks is not an arbitrage opportunity; it is a sign the arbitrage is switched off, and paying it is paying for a number that will not survive the mechanism being switched back on.

Total cost of ownership is the fourth, and it is where the decision lands. The exchange-traded fund usually has the lower expense ratio; the index fund usually has zero trading cost and no premium risk. The crossover depends on how often you trade and how much you hold. For a monthly investment plan of a modest size, the index fund almost always wins, because twelve trades a year each carrying brokerage and a spread will beat any plausible expense-ratio saving. For a single large lump held for years, the exchange-traded fund usually wins. Compute it rather than asserting it, using the holding period and the order count as the inputs.

7. Retail fixed income and gold

Two asset classes that Indian retail investors buy badly, for the same reason: the accessible product is not the efficient one.

Government securities come first, bought through the retail route. A retail investor can hold central government securities, state loans and treasury bills directly, with no intermediary credit risk, through a retail participation platform run by the central bank [verify: RBI Retail Direct scheme terms, rbi.org.in]. The arithmetic to learn is the treasury bill's, because it is quoted as a price rather than a rate and the conversion trips people.

A 91-day bill priced at ₹98.42 per ₹100 of face returns ₹1.58 per ₹100 over 91 days, a simple 91-day return of 1.6054%. Annualise on India's actual/365 convention and the yield is 6.4391%. Two errors are common here. The first is quoting the 1.61% as though it were an annual number. The second is annualising on a 360-day basis, which is the American discount convention and gives a different answer; India quotes treasury bills on an actual/365 basis and the two conventions must never be mixed in one comparison. After tax at a 31.2% effective slab rate, that 6.4391% is 4.4301%, which is the number to compare against a bank deposit taxed the same way.

A deposit ladder splits a lump into rungs maturing in successive years, and each maturing rung is reinvested for a fresh term. The usual claim made for it is that it earns more. Test the claim. Split ₹10,00,000 into five rungs of ₹2,00,000 at a card rate curve of 6.65%, 6.90%, 7.10%, 7.05% and 7.00% for one to five years, quarterly compounded, rolling each maturing rung for its remaining tenor at that tenor's own rate. At year five the ladder is worth ₹14,14,500; a single five-year deposit of the whole ₹10,00,000 is worth ₹14,14,778. The ladder is ₹278 behind, or 0.028% of the deposit.

So the ladder does not earn more. What it earns is liquidity, and liquidity has a price you can compute. Suppose that at year two you need ₹2,00,000. With the ladder, the two-year rung matures on schedule and hands you ₹2,29,325. With the single deposit, you break it, the penalty applies, and the withdrawn slice earns the applicable rate for the run period less a penalty, here 6.90% less one point, so 5.90%, giving ₹2,24,855 [verify: the penalty and the applicable-rate rule are set by each bank's own deposit terms; read them]. The ladder is worth ₹4,470 on that single event.

The honest reading: a ladder costs about three basis points over five years and pays out about 2.2% of the amount the first time you need cash early. It is an insurance premium, priced sensibly, and it should be sold as one rather than as a yield trick.

Gold arrives in three containers. The metal is the same in all three; the containers are wildly different. Take ₹6,00,000 committed for eight years, gold at ₹6,000 a gram rising to ₹11,400, an implied compound growth of 8.354%.

A sovereign gold bond is a government obligation denominated in grams, paying a coupon on the issue price and redeeming at the prevailing gold price, with the capital gain on redemption at maturity exempt for an individual holder [verify: the Sovereign Gold Bond scheme terms as notified by the RBI and the exemption in the income-tax statute, rbi.gov.in and incometaxindia.gov.in]. ₹6,00,000 buys 100 grams. The 2.50% coupon is ₹15,000 a year gross, ₹10,320 after a top-slab tax, and rolled up at 6% over eight years the coupons come to ₹1,02,142. Redemption is ₹11,40,000 with no capital-gains tax. The route ends at ₹12,42,142.

A gold fund charging 0.50% a year, bought and sold with a 5 basis point spread each way, ends before tax at ₹10,94,095, pays ₹64,232 of long-term tax on the ₹4,94,095 gain, and lands at ₹10,29,863.

Physical gold at 8% making charges and 3% goods and services tax costs ₹6,674.40 a gram all in, so the same money buys only 89.90 grams rather than 100. Ten grams vanish at the counter before the price does anything. Sold at a 2% assay discount it fetches ₹10,04,315, pays ₹52,561 of tax, and carries eight years of locker charges worth ₹29,692 rolled up, landing at ₹9,22,062.

The bond beats physical by ₹3,20,080, which is 53.3% of the entire original outlay, on identical exposure to identical metal over an identical period. Two of the three differences are structural and permanent: the coupon exists only in the bond, and the making charge exists only in the physical.

One caveat carries the whole example, and it is the perishable-number rule doing real work. The bond is a policy instrument and its issuance is a policy decision. New tranches are issued when the government chooses to issue them and not otherwise, and the secondary market in existing tranches is thin, so a buyer today may face a wide spread or no primary issue at all [verify: RBI press releases and the Union Budget documents for current issuance]. The arithmetic above is the structure of the comparison and it will hold whenever the product is available. Whether it is available on the day you want it is a separate question you must answer separately, and the same discipline applies to every government-set product in this material.

8. Insurance against investment, priced

The single most expensive decision an Indian household makes with a financial product is buying protection and investment bundled together, and the reason is that the bundle hides the price of each.

Start from what the two things are. Insurance transfers a risk you cannot afford to carry. Its correct price is small, because the event is unlikely. Investment compounds capital. Its correct price is also small, because compounding is done by the market rather than by the product. A bundled policy charges you as though both were expensive.

Price the bundle. A representative endowment policy takes ₹1,00,000 a year for twenty years, insures ₹20,00,000, and pays at maturity the sum assured plus accrued reversionary bonuses plus a terminal bonus. At a reversionary bonus of ₹45 per ₹1,000 of sum assured per year, the accrued bonus over twenty years is ₹18,00,000; add a ₹4,00,000 terminal bonus and maturity is ₹42,00,000 against ₹20,00,000 of premiums, a multiple of 2.10. The proceeds are exempt from tax where the premium stays inside the statutory proportion of the sum assured, which at 5% here it comfortably does [verify: Section 10(10D) of the income-tax statute and its premium-proportion conditions, incometaxindia.gov.in; these conditions have been amended repeatedly].

Two point one times your money over twenty years sounds respectable until you annualise it. The internal rate of return on that cash-flow series is 6.6326%.

Now unbundle. Buy the same ₹20,00,000 of cover as a term policy for ₹4,500 a year [verify: any insurer's published rate card for the buyer's age and health; term rates vary widely and change], and invest the remaining ₹95,500 a year in a direct index fund earning 11.0% gross less a 0.20% expense ratio. Twenty annual contributions at 10.80% reach ₹66,39,532 before tax. The gain is ₹47,29,532; long-term tax at 12.5% plus cess on the amount above the annual exemption is ₹5,98,589. The route ends at ₹60,40,943 after tax, with the same ₹20,00,000 of death cover in force throughout.

The unbundled route is worth ₹18,40,943 more on the same ₹1,00,000 a year, an internal rate of return of 9.6568% against 6.6326%, a gap of 3.02 percentage points a year.

Then do the thing that separates an analyst from an advocate: find the assumption the conclusion depends on and price it. The comparison assumed an 11.0% gross equity return. Solve for the gross return at which the two routes tie and you get 7.845%. Below that, the endowment wins. So the honest statement is not "endowment policies are bad"; it is "the endowment is buying you a guaranteed-ish 6.63% and you are giving up whatever equities return above 7.85% for it." That is a real trade and some people should take it. Most people taking it do not know they are taking it, which is the actual problem.

Three further facts belong to any conversation about these products.

The bonus is not guaranteed, and only the sum assured is contractual. Reversionary and terminal bonuses are declared at the insurer's discretion out of the participating fund's surplus, so the 6.63% is an illustration and not a promise, and it is not comparable with a government bond yield even though it is often presented that way.

The surrender schedule is brutal in the early years. Surrender at year three, having paid ₹3,00,000, and the guaranteed surrender value floor is a stated proportion of premiums paid excluding the first year, which at 30% is ₹60,000. You lose ₹2,40,000, or 80% of everything you paid [verify: the guaranteed and special surrender values are set by the policy document and by the current IRDAI product regulations, irdai.gov.in; the special surrender value regime was revised in 2024 and is materially more generous than the guaranteed floor, so read the policy's own table]. The lapse rate on these products is high, and a high lapse rate against a schedule like that is a transfer from the households who lapse to the ones who persist.

A unit-linked policy is an investment product with an insurance charge and four other charges. The stack, in the order it is deducted: a premium allocation charge taken off the top, a policy administration charge, a mortality charge for the cover, and a fund management charge on the assets. On a ₹2,00,000 annual premium with a 5% allocation charge, ₹6,000 of administration and ₹9,400 of mortality, only ₹1,74,600 reaches the fund in year one, a 12.70% drag before the fund management charge. Add 1.35% on the invested amount and the all-in first-year cost is ₹27,757, or 13.88% of premium [verify: every charge is set by the specific policy's benefit illustration, which the insurer must give you; read that document and not the brochure]. Charges typically fall in later years, which is why the product is sold on its long-run illustration and why the surrender schedule exists to stop you leaving before the charges taper.

The rule that survives all of this is to buy protection as protection and investment as investment. A product that will not tell you the price of each separately has already told you what you needed to know.

9. Portfolio management services and alternative funds as products

Above a regulatory minimum ticket, Indian investors are offered two structures that mutual funds are not: a portfolio management service, where the securities are held in the investor's own name, and an alternative investment fund, where they are pooled. Both charge differently from a mutual fund, and both tax differently. Neither difference is disclosed as clearly as a mutual fund's expense ratio.

The fee arithmetic is where the money is. A typical structure charges a fixed fee on assets plus a share of returns above a hurdle, subject to a high-water mark. All three terms have to be computed together, in the right order, and the order is: apply the gross return, deduct the fixed fee, compare the result against the high-water mark grown by the hurdle, and charge the performance share only on the excess.

Run one account through three years. ₹1,00,00,000 opening, a 1.00% fixed fee on average assets, a 20% performance fee above a 10% hurdle, an annual high-water mark, and gross returns of +24%, −8% and +21%.

Year three is the one to stare at. The account rose 21% gross and the manager earned no performance fee at all, because the high-water mark set in year one, grown by the 10% hurdle, sits at ₹1,32,33,440 and the account after its fixed fee reached ₹1,31,31,471. It missed by ₹1,01,969. Strip the high-water mark out and reset the hurdle to each year's opening value instead, and the same three years generate ₹4,74,350 of performance fees rather than ₹2,57,600. The high-water mark is worth ₹2,16,750 to this investor, which is 2.17% of the original account, earned entirely by a clause.

Over the three years the account compounds at 11.34% gross and 9.51% net, a drag of 1.84 percentage points a year, and the fees of ₹6,06,117 take 15.9% of the gross gain. Read that beside the mutual fund arithmetic above: a 1.10-point commission wedge took 15.7% of a regular plan's gain there, and a full performance-fee structure takes 15.9% here. The structures look completely different and cost almost exactly the same, which is not a coincidence. It is what a competitive market for distribution does.

Three terms decide whether a performance fee is fair, and they are the ones to read in the agreement rather than the headline rate.

A hard hurdle charges the performance share only on the excess over the hurdle. A soft hurdle with catch-up charges the share on the entire return once the hurdle is cleared, so clearing 10% by one rupee moves the fee from nil to 20% of everything. The headline "20% over 10%" describes both, and they are not remotely the same product.

A high-water mark means the manager must recover a previous loss before charging again, as year three above demonstrates. Without it, an investor pays twice for the same rupee of recovery.

The fee base matters: average daily assets, opening assets and closing assets give different answers, and a fee on closing assets in a rising year is materially larger than a fee on opening assets. The example above uses the average of opening and closing, which is a fair approximation of average daily assets and is stated so you can reproduce it.

The tax difference is structural and is the part most investors never see. In a portfolio management service the securities sit in the investor's own name, so every sale the manager makes is the investor's capital gain, taxed lot by lot in the investor's hands, in the year the manager chose to sell. A high-turnover manager therefore hands the client a tax bill the client did not decide to trigger, and the client's after-tax return can be far below the reported pre-tax one. Whether the performance fee itself is deductible against those gains has been contested rather than settled, and a fee that is not deductible is a cost paid out of after-tax money [verify: this position turns on case law and on the current wording of the deduction for expenditure in connection with a transfer; take current professional advice rather than relying on any summary].

Alternative investment funds split by category, and the split is a tax split. Categories I and II have pass-through status, so income other than business income is taxed in the investor's hands as though the investor had earned it directly. Category III does not have the same pass-through treatment and is generally taxed at the fund level, which changes both the rate and who reports it [verify: the pass-through provisions of the income-tax statute governing investment funds, incometaxindia.gov.in; this area has been amended repeatedly]. The practical consequence for a buyer is that two funds quoting the same gross return can deliver very different after-tax returns to the same person purely on structure, and the offering document is where that is stated.

10. The tax layer in India

Four rules carry most of what a retail Indian investor needs, and the fourth is the one that is worth actual money.

Start with listed equity and equity-oriented units. A gain on a listed share or an equity-oriented mutual fund unit on which securities transaction tax has been paid is short-term if the holding period is twelve months or less and long-term beyond that. The short-term rate is 20% and the long-term rate is 12.5%, both carrying a 4% cess on the tax. Long-term gains are exempt up to an annual threshold of ₹1,25,000 [verify: Sections 111A and 112A of the income-tax statute as amended by the Finance (No. 2) Act 2024, incometaxindia.gov.in; every one of these numbers is set by a Finance Act and India has since rewritten the statute, so confirm both the figure and the current section number].

Debt and specified funds are the second rule. A mutual fund that holds more than a stated proportion in debt and money-market instruments is a "specified" fund, and its gains are deemed short-term and taxed at the investor's slab rate however long the units were held. No long-term rate. No indexation. Ever, for that category [verify: the deeming provision introduced by the Finance Act 2023 and refined by the Finance Act 2024]. An investor who learned Indian debt-fund taxation before 2023 has a rule in their head that is now wrong, which is the clearest illustration in this material of why the perishable-number rule exists.

Dividends are taxed in the shareholder's hands at the slab rate, and the company withholds tax at source above an annual threshold per company. A holder at a 30% slab with 4% cess pays an effective 31.2% on dividend income and takes credit for the withholding when filing [verify: the withholding provision and its threshold, which was raised by a recent Finance Act, incometaxindia.gov.in].

The set-off ladder, which is rule four and the one worth money. Losses may be set off against gains, but not in any order you like:

• A short-term capital loss may be set off against both short-term and long-term capital gains.
• A long-term capital loss may be set off only against long-term capital gains.
• Whatever remains unabsorbed may be carried forward for eight assessment years, and the carry-forward is conditional on filing the return by the due date. Miss the due date and the loss is gone [verify: the set-off and carry-forward provisions and the filing condition, incometaxindia.gov.in].

The ladder is asymmetric, and the asymmetry has a price. A short-term loss is the more valuable instrument because it can reach both kinds of gain, so it should be spent against the highest-taxed gain available. Take a year with ₹2,40,000 of short-term gains, ₹3,10,000 of long-term gains, ₹95,000 of short-term losses and ₹1,40,000 of long-term losses. Set the short-term loss against the short-term gain first, where it saves tax at 20%, and the year's tax is ₹36,010. Set the short-term loss against the long-term gain instead, where it saves tax at 12.5%, and the tax is ₹49,920. The wrong order costs ₹13,910 on identical facts, and the return form will accept either.

A second, subtler timing error costs less but is more common. Set-off inside a year is compulsory rather than optional, so the year in which you realise a loss decides the rate at which it gets spent. Do not realise a loss in a year whose only available gain is taxed at the lower rate. In the portfolio audited in worked example 1, a short-term loss of ₹8,827 was realised in a year whose only gains were long-term. Absorbing it there saved ₹1,147 of tax at 12.5% plus cess. Held back to a year with short-term gains and spent at 20% plus cess, the same loss would have been worth ₹1,836. Realising it early destroyed ₹688 of its value, or 37.5%. A loss is an asset with a tax rate attached, and you spend it where the rate is highest.

India has no general wash-sale rule. Selling at a loss and repurchasing the same security immediately is not blocked by anything comparable to the American mechanism. What is policed, narrowly, is dividend stripping and bonus stripping, where a loss manufactured around a dividend or bonus record date is disallowed to the extent of the income received. The full treatment of both mechanisms, and the contrast with the American rule, belongs to the private-wealth branch's tax-aware investing material.

11. The tax layer in the United States

The American structure is different in shape and the differences are worth holding as contrasts rather than as a second list.

The holding-period line is one year, with none of the ambiguity people expect around it: a capital asset held more than one year produces a long-term gain. Short-term gains are taxed at ordinary income rates; long-term gains at a separate, lower schedule of brackets, with an additional net investment income tax above stated income thresholds [verify: the capital gain rate brackets and the net investment income tax thresholds published by the IRS at irs.gov; brackets are indexed annually].

Qualified dividends get the long-term rate rather than the ordinary rate, but only if a holding-period condition around the ex-dividend date is met and the payer qualifies. A dividend from a real estate investment trust is generally not qualified, which is why the trust distribution worked through later splits into four kinds of income rather than one. The condition catches people who buy just before an ex-date to capture a dividend and sell just after, which converts a favourable rate into an unfavourable one for no gain.

The wash-sale rule catches a repurchase. Sell a security at a loss and buy the same or a substantially identical security within 30 days before or after the sale, and the loss is disallowed for the current year. The disallowed loss is added to the basis of the replacement lot and the original holding period tacks on, so the benefit is deferred rather than destroyed, provided you eventually sell the replacement without repeating the mistake [verify: IRS Publication 550, irs.gov]. The trap that turns deferral into destruction is a repurchase inside a tax-advantaged account, where basis cannot be adjusted the normal way. Selling 200 shares bought at $61.00 for $47.50 realises a $2,700 loss; buying 200 back at $49.20 inside the window disallows the whole $2,700 and raises the replacement lot's basis from its $9,840 cost to $12,540, which is $62.70 a share.

The ordinary-income offset and the carry-forward come last. Capital losses first offset capital gains without limit. Whatever is left offsets ordinary income up to $3,000 a year, and the rest carries forward indefinitely [verify: IRC section 1211(b) and the current limit, irs.gov; the $3,000 figure is not indexed and has been unchanged for a very long time, which is itself worth noticing]. A $14,600 net capital loss with no gains to absorb it therefore takes five years to use up, at $3,000, $3,000, $3,000, $3,000 and $2,600. Its nominal value at a 24% rate is $3,504; discounted at 5%, it is worth $3,194 today. The deduction is not lost, it is stretched, and a loss you cannot use this year is worth less than one you can.

Set the two regimes side by side and the useful contrast is not the rates.

The rule that survives both columns: a realised loss is an asset, and its value depends on when and against what you can use it. Everything else in the table is detail you look up.

12. Equity compensation

More analysts lose money to a misunderstanding of their own pay package than to any investment decision they will make, and the misunderstanding is always the same one.

Restricted stock units are taxed as ordinary income when they vest, at the fair market value on the vest date, whether or not you sell. That value becomes your cost basis and the holding period starts that day. Three hundred units vesting at $84.60 produce $25,380 of ordinary income on the W-2. At a combined statutory withholding of 34.65%, the employer must remit $8,794.17, and because it withholds in whole shares it takes 104 shares worth $8,798.40, delivering 196 net.

Then read what happened. The employee received no cash at all, paid tax on $25,380 of income, and holds a $16,581.60 position in one company's stock with a basis of $84.60 a share. Sell at $71.30 and the loss is $2,606.80 short-term, of which only $3,000 a year can ever reach ordinary income. The tax on the vest is not refunded by the loss on the sale; they are different buckets.

The correct default therefore follows from the arithmetic rather than from a view on the stock. A vested restricted stock unit is economically a cash bonus that was handed to you already invested in your employer. If you would not use that cash to buy your employer's shares at today's price, sell them, because holding is an active decision to buy. The basis reset means selling at vest triggers essentially no additional tax, so the decision costs nothing to execute. Concentration risk in the same company that pays your salary is the risk you are actually carrying, and the position-sizing material in Phase 9 has the language for it.

Employee stock purchase plans are the most reliably mispriced benefit in American compensation, and the two dispositions are worth working once by hand.

A plan offers a 15% discount with a lookback, so the purchase price is 85% of the lower of the offering-date and purchase-date prices. With an offering-date price of $78.00 and a purchase-date price of $69.40, the purchase price is $58.99, and $7,500 of payroll contributions buy 127 shares for $7,491.73 with $8.27 refunded.

Sell inside the statutory holding requirement and the disposition is disqualifying. Ordinary income is the discount measured at purchase, which is (69.40 − 58.99) × 127 = $1,322.07; basis becomes $69.40; the remaining gain to $75.20 is $736.60 and is short-term. At a 24% ordinary rate, total tax is $494.08.

Sell after more than two years from the offering date and more than one year from purchase and the disposition is qualifying. Ordinary income is now the lesser of the discount computed on the offering-date price, 15% × $78.00 = $11.70 a share, and the actual gain, $75.20 − $58.99 = $16.21 a share. The lesser is $11.70, so ordinary income is $1,485.90, and the remaining $572.77 is a long-term gain at 15%. Total tax is $442.53 [verify: the qualifying-disposition ordering rules and the annual purchase limit, IRS Publication 525 and IRC section 423, irs.gov].

The qualifying disposition creates more ordinary income, not less, because the discount is measured on the higher price. It wins anyway, by $51.55, because the rest of the gain moves to the long-term rate. Then price what the win costs: sixteen extra months of undiversified exposure to a $9,550 single-stock position for $51.55, which is 0.54% of the position. A 1% move in the share price is worth nearly twice the tax saving. The tax tail should not wag this dog, and an analyst who can produce that comparison in ninety seconds is worth listening to.

India taxes the same economics in two stages, and the second stage is where the error lives. An employee stock option is taxed at exercise as a salary perquisite on the difference between the fair market value on the exercise date and the exercise price, with the employer withholding. It is taxed again at sale, as a capital gain measured from the fair market value on the exercise date, not from the exercise price [verify: the perquisite valuation rules and the cost-of-acquisition provision for such shares, incometaxindia.gov.in].

Exercise 500 options at ₹120 when the fair value is ₹640 and the perquisite is ₹2,60,000, taxed at 31.2% for a top-slab employee, or ₹81,120. Notice the cash position: the employee received nothing, paid ₹60,000 to exercise, and owes ₹81,120 of tax, so exercising required ₹1,41,120 of cash found from somewhere. Sell thirty months later at ₹910 and the capital gain is measured from ₹640, so it is ₹1,35,000, and long-term tax at 12.5% plus cess is ₹17,550.

The common error is computing the gain from the ₹120 exercise price, which gives ₹3,95,000 and a tax of ₹51,350. That is ₹33,800 of tax paid twice on income already taxed as a perquisite. It happens most often when the shares are foreign-listed and the employee is reconciling a foreign broker statement that knows nothing about Indian perquisite tax.

Which raises the last piece. An Indian resident holding foreign shares has a reporting obligation independent of whether any tax is due. Foreign assets, including vested shares and foreign broker accounts, must be disclosed in the return's foreign-asset schedule, and the penalty regime for non-disclosure is severe and is not proportionate to the amount [verify: the foreign-asset reporting requirement in the income-tax return and the black-money legislation's penalty provisions, incometaxindia.gov.in]. Nothing in this material will make you a tax adviser. Knowing that the obligation exists is what stops a competent professional walking into it.

``ai-augment-json { "skill": "Keeping a perishable rate, slab or limit current before it reaches a computation", "use": "Have an assistant produce a first-draft table of the rates, thresholds and section references a computation needs, together with the exact primary-source citation for each row, and then use it as a checklist of things YOU look up rather than as an answer. The value is the list of what to verify, never the values themselves.", "tools": ["Chat assistants with browsing or retrieval - Claude, ChatGPT, Gemini", "The primary sources themselves: incometaxindia.gov.in, sebi.gov.in, rbi.org.in, irdai.gov.in, irs.gov", "A spreadsheet holding one rate per row with a source column and a date-checked column"], "prompt": "I am computing the after-tax return on a resident Indian individual's listed-equity portfolio and on a US employee's restricted stock units. List every rate, threshold, exemption and holding-period line the computation needs. For each one give: the exact provision or circular that sets it, the URL of the primary source, the date it last changed, and a one-line note on how often provisions of that kind change. Do not give me the values. Give me the list of things I must look up and where each one lives.", "verify": "Treat every figure the model states as unverified until you have read it on the primary source yourself, because tax and regulatory figures change on an annual cycle that training data lags and a confidently wrong slab is invisible in a fluent answer. Open each named source, find the figure, record the date you read it, and put both into the spreadsheet's source and date-checked columns. Where the model cites a section number, confirm the number is still current: statutes get renumbered and a correct rate under a dead section number is a wrong citation. Then recompute the whole result with your verified figures and confirm the total moves the way the changed inputs say it should.", "diy": "You must be able to run the slab arithmetic, the set-off ladder and the blended expense-ratio ceiling by hand from stated inputs, because that is what the gate tests and it is the only thing that survives a rate change. A tool that hands you a rate cannot tell you that a short-term loss should be spent against the highest-taxed gain, or that a blended cap is not a marginal rate. Those are the judgments the arithmetic installs.", "market": "IN" } ``

13. Retirement mechanics in both systems

The employer match is the highest-return instrument most people will ever be offered, and it is not an investment. An employer matching 50 cents on the dollar up to 6% of pay hands an employee earning $145,000 who defers $8,700 a further $4,350, which is an immediate 50% return on the deferral before the market does anything. Where vesting is a three-year cliff, that 50% annualises to 14.47% a year, guaranteed by contract rather than by a market. Declining to defer forfeits $4,350 a year and $13,050 over the cliff.

Two honest limits sit beside that. The match is conditional on staying long enough to vest, so an employee who expects to leave within the cliff should discount it. And the deferral itself is locked in a retirement wrapper with its own withdrawal rules, so it is not the same money as cash.

Contribution and catch-up limits exist in both systems and are indexed, which makes them the most perishable numbers in this material. There is an annual elective deferral limit for workplace plans, a separate and smaller limit for individual retirement accounts, an additional catch-up amount from a stated age, and a further enhanced catch-up for a narrow age band introduced by recent legislation. Health savings accounts have their own self-only and family limits with their own catch-up [verify: the current-year limits are published by the IRS in an annual notice; read that notice at irs.gov rather than any secondary summary, because every one of these figures moves]. No computation in this material depends on a limit's exact value, and none of yours should either: state the contribution as a given and let the limit be a constraint you check separately.

Traditional against Roth was settled arithmetically by the wrapper table above and needs only the decision rule restated. The ratio of Roth to traditional is (1 − t now) ÷ (1 − t later). At 32% now and 24% later, Roth is 10.53% worse. At 12% now and 22% later, Roth is 12.82% better. At equal rates they are identical to the cent. Everything else in the argument is a forecast of your own future bracket, plus two second-order points that are real: a Roth has no required minimum distribution during the original owner's lifetime, and Roth contributions effectively shelter more because the tax was paid from outside the account.

Target-date funds are a glide path in a wrapper: an asset mix that shifts from equity toward bonds as a stated retirement year approaches, rebalanced by the fund. They are a genuinely good default for a person who will otherwise do nothing, and their cost varies by more than an order of magnitude between an index-built version and an actively built one. The whole decision is the expense ratio and the glide path's landing point, and both are printed. Read the glide path's equity share at the target date, because "2050" tells you nothing about whether that fund holds 30% or 55% equity when you get there.

India's National Pension System is structured differently and the difference is in the exit. Contributions go into a Tier I account, which is the retirement account with the withdrawal restrictions, or a Tier II account, which is a voluntary and liquid add-on with no lock and no deduction. Within Tier I, an active-choice subscriber allocates across equity, corporate debt, government securities and an alternatives sleeve, with the equity share capped and the cap tapering with age under the standard option [verify: the PFRDA investment guidelines and the current asset-class caps and taper schedule, pfrda.org.in].

The exit is the part to compute. At the normal exit age, up to 60% of the corpus may be taken as a lump sum and at least 40% must purchase an annuity from a registered life insurer [verify: the PFRDA exit regulations, pfrda.org.in]. On an ₹80,00,000 corpus that is ₹48,00,000 in hand and ₹32,00,000 compulsorily annuitised. At an annuity rate of 6.6% that buys ₹2,11,200 a year of income, which is taxable at slab in the year received. For a subscriber still in the 30% bracket with cess, the after-tax income is ₹1,45,306, an after-tax yield of 4.5408% on the annuitised corpus.

That last number is the honest summary of the product's exit, and it carries a live warning. The lump-sum share and the annuitisation share are set by regulation; the tax treatment of each has changed several times and the treatment of the annuity purchase and the annuity income are governed by different provisions. Any statement about the after-tax outcome of a National Pension System exit is a statement about a rule that has moved and will move again [verify: the exemption for the lump sum and the taxability of annuity income, incometaxindia.gov.in and pfrda.org.in, both read on the same day]. Compute the structure. Look up the rate.

14. Trusts that distribute: reading one payment as three payments

A real estate investment trust and an infrastructure investment trust hand the holder a single cash distribution that is legally several different kinds of income, each taxed differently. Reading the composition rather than the total is the whole skill.

Take 800 shares of a synthetic American trust bought at $42.50, a $34,000 position, receiving $2.60 a share in a year, or $2,080. The trust's own tax reporting splits that payment four ways: $1.72 of ordinary dividends, $0.18 of qualified dividends, $0.55 of return of capital and $0.15 of capital gain distribution.

Tax the four slices at a 24% ordinary rate and a 15% long-term rate, allowing the deduction available on qualified trust dividends [verify: the deduction for qualified business income as it applies to REIT dividends, IRC section 199A, irs.gov; this provision has a legislated life and its availability is not permanent]. The ordinary slice of $1,376 becomes $1,100.80 of taxable income and $264.19 of tax; the qualified slice is $21.60; the capital gain distribution is $18.00; the return of capital is nil. Total current tax is $303.79, an effective rate of 14.61% on the distribution. Treat the whole $2,080 as ordinary income, which is the naive default, and you would compute $499.20. The decomposition is worth $195.41 in a single year on a single holding.

Then do the part almost everybody skips. The return of capital was not tax-free. It was tax-deferred, and it changed the rate. The $440 reduces basis from $34,000 to $33,560, or $41.95 a share. Sell later at $46.20 and the gain is $3,400 rather than the $2,960 it would have been, so the tax at sale is $66 higher. Had the same cash arrived as an ordinary trust dividend it would have carried the same 20% deduction the ordinary slice above carried, so the tax deferred is 24% of 80% of $440, which is $84.48. Set the $66 against it and the net benefit is $18.48: a genuine gain, from deferral plus the conversion of ordinary-rate income into long-term-rate gain, and 21.9% of what the naive "return of capital is not taxed" reading would suggest.

The Indian analogue works the same way with different labels. A trust's distribution to a unitholder splits into interest, dividend and repayment of the unit's cost, and each is taxed under its own rule, with the repayment component reducing the cost of acquisition of the unit rather than escaping tax [verify: the taxation of business trust distributions in the income-tax statute as amended, incometaxindia.gov.in]. The trust publishes the split. Read it, apply three rates, and never take the yield at face value.

15. The full leak audit

Put the whole thing together on one page and it becomes a procedure you can run on any portfolio in an hour.

Start from the money-weighted return, because it is what the holder actually earned given when they put money in. Then subtract, in order, and keep every figure in currency rather than percentages until the last step.

1. Transaction costs. Every contract note, both sides, plus stamp duty on fund purchases. Visible, small, and the one people obsess over.
2. Fund expenses. Average holding value multiplied by the expense ratio multiplied by the time held, for each fund. Invisible, because it is netted into the net asset value and never appears on a statement.
3. Avoidable distribution costs. The wedge between the regular plan and the direct plan of the same scheme. Invisible for the same reason, and entirely a choice.
4. Tax. Realised gains at the correct rate, dividends at slab, with the set-off ladder applied in the right order.
5. Inflation. Deflate the final number rather than subtracting a percentage from a percentage.

Then compare against the benchmark on the same basis, meaning after the same fees and the same tax. Comparing an after-tax portfolio return against a pre-tax index return is the most common error in this whole area and it flatters the index by whatever the tax was.

Worked example 1 runs the procedure end to end on a six-holding rupee portfolio. Its answer, and the reason this material exists, is the ladder it produces:

The top three account for 94.7% of a total of ₹1,36,700, and the two leaks a holder could have closed with a single decision each, the commission at ₹5,851 and the ₹688 destroyed by realising a loss in a year that could only absorb it at the lower rate, come to ₹6,539 over two years on a book of about twelve lakh.

Three habits fall out of that table and they are what to carry away.

Rank in currency, not in percentages, because a 1.10-point commission and a 4.9% inflation rate are not comparable until both are rupees.

Separate the avoidable from the unavoidable before you act, because attention spent on the ₹1,345 of transaction costs is attention not spent on the ₹5,851 that one form would have fixed.

Rerun it annually, because the leaks move. The commission is fixed until you switch. The tax depends on what you realised. Inflation depends on the year. The audit is a habit rather than a calculation.

Common mistakes & how experts think differently

1. Comparing a fee to assets instead of to the expected gain. A 1.10-point commission is 5.58% of terminal wealth and 15.68% of the gain that terminal wealth represents, because the contributed capital was never the thing at risk from fees. Novices quote the first number because the industry does. An expert converts every recurring charge to a share of expected gain before deciding whether it is small, and does the same to a performance fee, an insurance charge and an advisory retainer.

1. Reading the marginal expense-ratio rate as the cap. The slab schedule is progressive, so a fund at ₹12,000 crore is permitted a blended 1.5844% while its marginal band rate is 1.45%. Quoting the marginal rate understates the permitted charge by 0.134 points and makes a fund look closer to its ceiling than it is. Experts compute the blended cap the way they compute a progressive tax bill, tranche by tranche.

1. Treating an exit load as the decision. The load is visible and small; the tax rate difference on either side of the holding-period line is invisible and usually larger. In the exit-load case above, the load was ₹3,164.80 and the tax difference ₹5,185.44. An expert prices the whole decision as a break-even price move, gets 3.03%, and then decides whether that cushion is worth forty-four days of exposure.

1. Harvesting a loss into the lower rate. Realising a short-term loss in a year whose only gains are long-term forces it to be absorbed at 12.5%, converting an asset worth ₹1,836 at a future 20% rate into one worth ₹1,147 today. Experts treat a realised loss as an asset with a rate attached and spend it against the highest-taxed gain available, which sometimes means not realising it at all this year.

1. Believing the reported return is the investor's return. A fund's published return is time-weighted and assumes one rupee left alone; the investor's return is money-weighted and depends on when they added. In the audited portfolio the two differ, and every leak below the headline widens the gap further. Experts never quote a fund return to a client without asking what that client actually earned.

1. Assuming an insurance-plus-investment bundle can be evaluated on its maturity multiple. Two point one times the premiums over twenty years annualises to 6.63%, and the alternative on the same outlay annualises to 9.66%. Experts annualise before forming a view, then find the break-even assumption, which here is a 7.85% gross equity return, and state the conclusion as a trade rather than as a verdict.

1. Holding vested stock because selling "feels like a decision". The basis reset at vest means selling costs essentially no extra tax, so holding is the active choice and selling is the neutral one. Experts state the test in one line: if you would not buy this stock today with the cash, you are holding it out of inertia and concentration risk in your employer is the risk you are least able to diversify.

1. Optimising the tax tail on a small amount while carrying a large undiversified position. Waiting sixteen months for a qualifying disposition saved $51.55 on a $9,550 position, which one percent of price movement erases nearly twice over. Experts size the tax saving against the risk being carried before recommending the wait.

1. Comparing an after-tax portfolio return with a pre-tax benchmark. The index does not pay tax; the investor does. Putting the two side by side awards the index a free win equal to the tax rate. Experts put both sides through the same fees and the same tax before drawing any conclusion, and say explicitly what basis they used.

1. Memorising a rate instead of a source. Every slab, cap, limit and section number in this area moves, and an analyst who quotes a rate from memory is one Finance Act or one annual notice away from being confidently wrong. Experts memorise where the number lives and how often it changes, and look it up every time it matters.

Worked examples

Each figure here comes out of an arithmetic you can reproduce, and the verify block after the last example restates the key ones at full precision so you can check your own working against them. Currencies are marked in each heading. All companies and funds named are synthetic composites; all rates are illustrative and carry the verify flags they were introduced with.

Worked example 1: The full leak audit on a six-holding rupee portfolio (India, ₹)

Setup. A resident individual at a 30% slab with 4% cess ran the following account from 5 April 2024 to 31 March 2026, a window of 725 days or 1.986301 years. All fund names and share names are synthetic.

Two realisations occurred. On 20 November 2025 the holder sold 300 Kaveri shares at ₹1,850. On 10 February 2026 the holder sold all 100 Konkan shares at ₹412. Kaveri paid a dividend of ₹28 a share on 400 shares on 14 August 2025. Closing prices on 31 March 2026: Nilgiri ₹186.4500, Sahyadri ₹79.1200, Kaveri ₹1,905, Deccan ₹27.8600, Bharat Gold ₹84.2000. The benchmark total return index compounded at 12.15% over the window, and average consumer price inflation over the window was 4.9% [verify: MoSPI consumer price index releases, mospi.gov.in, and the index provider's own published total return series].

The statutory cost card is the one from the toolkit module, applied rather than rebuilt. On delivery equity: securities transaction tax 0.10% each side, exchange transaction charge 0.00297% each side, regulator turnover fee ₹10 per crore each side, stamp duty 0.015% on the buy side only, a depository charge of ₹13.50 per scrip on the sell, goods and services tax at 18% on the exchange, regulator and depository charges, and zero brokerage. Mutual fund purchases attract stamp duty at 0.005% deducted before units are allotted [verify: the applicable rates are set by the Finance Act, the exchanges, the depositories and the GST Council; read your own broker's tariff sheet].

Solution. Step 1, the transaction costs, both sides of both share trades.

Securities transaction tax is excluded from the deductible column because it is specifically not allowed as a cost of acquisition or transfer. Everything else is.

Step 2, the two realisations, lot by lot. Work from the unrounded charges rather than the rounded ones in the table above. Kaveri's cost of acquisition per share is (5,00,000 + 93.1130) ÷ 400 = ₹1,250.232783. For 300 shares that is ₹3,75,069.83. Consideration is ₹5,55,000 less ₹36.0354 of deductible transfer expenses, so the long-term capital gain is ₹1,79,894.13, the holding period being 19.5 months.

Konkan's cost is 50,000 + 9.3113 = ₹50,009.31. Consideration is ₹41,200 less ₹17.4225, so the short-term capital loss is ₹8,826.73, the holding period being 7.7 months.

Step 3, the set-off ladder. A short-term loss may be set against either kind of gain. There is no short-term gain in the year, so it goes against the long-term gain: ₹1,79,894.13 − ₹8,826.73 = ₹1,71,067.40. Apply the ₹1,25,000 annual exemption and ₹46,067.40 is taxable at 12.5% plus 4% cess, which is ₹5,988.76.

Step 4, the dividend. ₹28 × 400 = ₹11,200 gross; the company withheld 10%, so ₹1,120, and credited ₹10,080. At a 31.2% effective slab the full liability is ₹3,494.40, leaving ₹2,374.40 payable on filing. Total tax accrued on the year is 3,494.40 + 5,988.76 = ₹9,483.16, of which ₹8,363.16 is still to pay after the withholding credit.

Step 5, the closing value.

The rounded rows in that column add to ₹12,37,427.66 while the unrounded total is ₹12,37,427.651. The one-paisa gap is display rounding, and it is worth seeing once here so you never chase it in your own working: round for display, and carry full precision through every intermediate step.

Step 6, the money-weighted return. Lay out the pocket-level cash flows and solve for the rate that sets their present value to zero.

The pre-tax money-weighted return is 17.2238% a year.

Step 7, after tax. Deduct the ₹8,363.16 still owed from the terminal value, giving ₹12,29,064.49, and re-solve: 16.9219%. The tax drag is 0.3019 percentage points. Placing the capital-gains tax at the advance-tax instalment date of 15 December 2025 rather than accruing it at year end changes the answer to 16.9119%, a difference of 1.00 basis point, which is why the year-end simplification is stated and then used.

Step 8, in real terms. Deflate rather than subtract: (1.169219 ÷ 1.049) − 1 = 11.4604% real, after tax and after all costs.

Step 9, the benchmark on the same basis. Take ₹10,00,000 in the index at 12.15% for 1.986301 years, gross ₹12,55,788.13. Inside a 0.20% index fund it becomes ₹12,51,343.76. Tax the whole ₹2,51,343.76 gain at 12.5% plus cess, since the exemption was already consumed, and it lands at ₹12,18,669.07, an after-fee after-tax annualised 10.4687%, or 5.3085% real. The portfolio beat that benchmark by 6.45 percentage points on a like-for-like basis.

Step 10, the leaks, in rupees. The index fund's own tracking is worth checking first: its net asset value compounded at 11.5736% against the index's 12.15%, a tracking difference of 57.64 basis points, of which its stated 20 basis points of expense explains a third and 37.64 basis points is unexplained and worth a question to the fund house.

Read it. The three largest leaks are 94.7% of the total and only one of them, the commission, is fully avoidable. The commission also has a second, larger expression: because 1.04 points was charged every year on a growing base, holding 2 is worth ₹5,832 less at the end than the direct plan of the identical scheme would have been. What the audit does not say is more important than what it does. It does not say the portfolio was well constructed; a 17.22% money-weighted return over two years says as much about the market as about the holder. It does not extrapolate: two years is a sample of one path, and the rolling-window arithmetic in the factsheet material is the corrective. And it does not price the largest cost of all, which is the return on the money that was never invested, because that cost does not appear on any statement.

Worked example 2: Restricted stock, an employee purchase plan, the match and the Roth line (US, $)

Setup. An employee of a synthetic US company earns $145,000. Three hundred restricted stock units vest on 15 March 2025 at a fair market value of $84.60. The employer withholds at a combined statutory 34.65%, being 22% federal supplemental, 7.65% payroll tax and 5% state, and withholds in whole shares. The employee sells all net shares on 20 January 2026 at $71.30. Separately, an employee stock purchase plan ran from 1 July 2025 to 31 December 2025 with a 15% discount and a lookback; the offering-date price was $78.00 and the purchase-date price $69.40, and the employee contributed $7,500. The employer matches 50% of deferrals up to 6% of pay with a three-year cliff. Ordinary rate 24%, long-term rate 15% [verify: withholding rates, the supplemental rate and the rate brackets are IRS-published and change; irs.gov].

Solution. Step 1, the vest. Ordinary income is 300 × $84.60 = $25,380.00, reported on the W-2 whether or not anything is sold. Required withholding is 34.65% × $25,380 = $8,794.17. In whole shares that is ceiling(8,794.17 ÷ 84.60) = 104 shares worth $8,798.40, over-withheld by $4.23. 196 shares are delivered, with a basis of $84.60 each and a holding period starting 15 March 2025.

Step 2, the sale. 196 × ($71.30 − $84.60) = −$2,606.80, short-term because the sale is 311 days after vest. The employee has paid $8,794.17 of tax on income that arrived entirely as stock and now holds a realised loss of which only $3,000 a year can reach ordinary income.

Step 3, the purchase plan. The purchase price is 85% × min($78.00, $69.40) = $58.99. $7,500 buys floor(7,500 ÷ 58.99) = 127 shares costing $7,491.73, with $8.27 refunded.

Step 4, the disqualifying disposition. Sold on 2 March 2026 at $75.20, inside both holding requirements. Ordinary income is the discount measured at purchase: ($69.40 − $58.99) × 127 = $1,322.07. Basis becomes $69.40, so the capital gain is ($75.20 − $69.40) × 127 = $736.60, short-term. Tax at 24% on both is $494.08.

Step 5, the qualifying disposition, same exit price. Ordinary income is the lesser of 15% of the offering-date price, being $11.70 a share, and the actual gain of $16.21 a share. The lesser is $11.70, so ordinary income is $1,485.90 and the residual $572.77 is a long-term gain. Tax is 1,485.90 × 0.24 + 572.77 × 0.15 = $442.53.

Step 6, price the wait. The qualifying route saves $51.55. It costs sixteen additional months of exposure to a $9,550.40 single-stock position, so the saving is 0.54% of the position. A 1% move in the share price is worth nearly twice the entire tax advantage.

Step 7, the match. A 6% deferral is $8,700; the match is $4,350, an immediate 50% return. Over the three-year cliff that annualises to 1.50^(1/3) − 1 = 14.4714% a year, contractual rather than market-dependent. Deferring nothing forfeits $13,050 across the cliff.

Step 8, the traditional-against-Roth line. At 7% for 25 years the growth factor is 5.427433.

Read it. Four separate decisions sit in one pay package and three of them are settled by arithmetic rather than opinion. Sell the vested units unless you would buy the stock with cash; take the match to the cap because 50% is not available anywhere else; and choose the wrapper on your expected future bracket, since the ratio (1 − t now) ÷ (1 − t later) is the entire answer. The fourth decision, whether to hold for a qualifying disposition, is the only one that needs judgment, and the judgment is that $51.55 does not justify sixteen months of concentration. What none of this tells you is whether the shares are worth holding on the merits. That is a valuation question, and this arithmetic must not be mistaken for one.

Worked example 3: An endowment policy against term cover plus an index fund (India, ₹)

Setup. A twenty-year participating endowment policy on a synthetic insurer's rate card: annual premium ₹1,00,000, sum assured ₹20,00,000, reversionary bonus ₹45 per ₹1,000 of sum assured a year, terminal bonus ₹4,00,000. Premiums are paid at the start of each year and maturity is at the end of year twenty. The alternative is a term policy for the same ₹20,00,000 of cover at ₹4,500 a year, with the remaining ₹95,500 invested annually in a direct index fund earning 11.0% gross against a 0.20% expense ratio [verify: term premiums vary with age, health and insurer and must be quoted; bonus rates are declared annually and are not guaranteed].

Solution. Step 1, the endowment's maturity. Accrued reversionary bonus is 45 × 2,000 × 20 = ₹18,00,000. Add the sum assured and the terminal bonus: ₹42,00,000, against ₹20,00,000 of premiums, a multiple of 2.10. Proceeds are exempt where the premium stays inside the statutory proportion of the sum assured, which at 5% it does.

Step 2, the endowment's internal rate of return. Solve Σ 1,00,000 × (1 + r)^(20 − t) for t = 0 to 19, set equal to 42,00,000. The answer is 6.6326%.

Step 3, the alternative. Twenty annual contributions of ₹95,500 at 10.80% net reach ₹66,39,532.16. Total invested is ₹19,10,000, so the gain is ₹47,29,532.16; long-term tax at 12.5% plus cess on the amount above the ₹1,25,000 exemption is ₹5,98,589.18; after tax the route holds ₹60,40,942.98, with ₹20,00,000 of cover in force the whole time.

Step 4, like for like. The alternative is ₹18,40,942.98 ahead on the same ₹1,00,000 a year, and solving the same annuity for its rate gives an internal rate of return of 9.6568% against 6.6326%, a gap of 3.02 percentage points a year.

Step 5, find the assumption that carries the conclusion. Solve for the gross equity return at which the two routes tie, holding everything else fixed. It is 7.845%. Below that, the endowment wins.

Step 6, the exit. Surrender at the end of year three, having paid ₹3,00,000. The guaranteed floor is 30% of premiums paid excluding the first year, so ₹60,000, a loss of ₹2,40,000, which is 80% of everything paid in.

Read it. The endowment is buying a bonus-dependent 6.63% and selling the equity return above 7.85%. That is a defensible trade for somebody who genuinely cannot tolerate a falling statement, and an indefensible one for somebody who was never told the trade existed. The 6.63% is also not a bond yield: only the sum assured is contractual and the bonuses are discretionary, so the comparison against a government security is not available. The surrender arithmetic is what makes the decision nearly irreversible, and it is the reason to get it right at the point of sale rather than in year three.

Worked example 4: A withdrawal plan through a bad start (India, ₹)

Setup. A ₹1,00,00,000 corpus in an equity fund at a net asset value of ₹100.0000, so 1,00,000 units. The holder withdraws ₹60,000 a month, which is 7.2% of the opening corpus a year, for ten years. Two annual return sequences, identical in content and opposite in order: bad-first is −18%, −11%, +4%, +14%, +16%, +9%, +12%, +11%, +13%, +10%; bad-last is that reversed. Both have an arithmetic mean of 6.00% and a compound rate of 5.3911%. Within each year the return is applied evenly as a monthly factor of (1 + R)^(1/12), and the withdrawal redeems units at the prevailing value.

Solution. Step 1, the no-withdrawal case, as the control. Both orders end at exactly ₹1,69,05,914.45, because multiplication commutes. Nothing about the order matters when nothing is taken out.

Step 2, bad-first, year by year.

Step 3, bad-last, same table.

Step 4, the gap. Both holders withdrew ₹72,00,000 of cash. The bad-first holder ends with ₹48,04,619 and the bad-last holder with ₹92,03,523, a difference of ₹43,98,903. The bad-first corpus is 52.20% of the bad-last one.

Step 5, why, in units. Bad-first redeemed 71,580.25 of the original 1,00,000 units and is left holding 28,419.75 at a terminal net asset value of ₹169.06; bad-last redeemed fewer units at higher prices and is left holding 54,439.66. The falling first years forced the withdrawal to consume more units per rupee, and those units were not there to recover.

Step 6, the tax side of year one. Bad-first's twelve redemptions in year one consumed 8,030.16 units with a cost of ₹8,03,015.88 and returned ₹7,20,000, an ₹83,015.88 short-term capital loss available for set-off and carry-forward. Bad-last's twelve redemptions consumed 6,840.29 units at a cost of ₹6,84,029.27 for the same ₹7,20,000, a ₹35,970.73 short-term gain.

Read it. The mean return told you nothing. Both sequences average 6.00%, and one holder ends with almost twice the other's money. The single decision that changes the outcome is the withdrawal rate: 7.2% of the opening corpus was survivable in one order and close to ruinous in the other. What this example does not establish is a safe withdrawal rate, because two hand-built sequences are not a distribution. The retirement-decumulation material in the private-wealth branch runs the same question properly with simulation. What it does establish is that a plan quoting an average return and a withdrawal rate together, without saying anything about order, has not answered the question.

Worked example 5: A performance fee with a hurdle and a high-water mark (India, ₹)

Setup. A ₹1,00,00,000 discretionary account. Fixed fee 1.00% a year on average assets, taken as 1% of the mean of the opening and closing gross values. Performance fee 20% of the excess over a 10% hurdle applied to the high-water mark, charged annually, hard hurdle. Gross returns of +24%, −8% and +21%.

Solution. Year 1. Gross ₹1,24,00,000. Fixed fee 1% × (1,00,00,000 + 1,24,00,000) ÷ 2 = ₹1,12,000, leaving ₹1,22,88,000. The high-water mark is the opening ₹1,00,00,000, so the hurdle level is ₹1,10,00,000. Excess ₹12,88,000; performance fee 20% = ₹2,57,600. Closing ₹1,20,30,400, which becomes the new mark.

Year 2. Gross ₹1,10,67,968. Fixed fee ₹1,15,491.84, leaving ₹1,09,52,476.16. Hurdle level is 1,20,30,400 × 1.10 = ₹1,32,33,440, far above. No performance fee. Closing ₹1,09,52,476.16, and the mark stays at ₹1,20,30,400.

Year 3. Gross ₹1,32,52,496.15. Fixed fee ₹1,21,024.86, leaving ₹1,31,31,471.29. The hurdle level is still ₹1,32,33,440. The account is ₹1,01,968.71 short. No performance fee, in a year the account rose 21% gross.

Step 4, the totals. Gross terminal value with no fees at all would be ₹1,38,03,680; the account ends at ₹1,31,31,471.29. Fixed fees total ₹3,48,516.70 and performance fees ₹2,57,600, so ₹6,06,116.70 of fees. Gross compound return 11.3435%, net 9.5060%, a drag of 1.8376 percentage points a year, and the fees took 15.94% of the gross gain.

Step 5, what the high-water mark was worth. Rerun the three years with the hurdle reset to each year's opening value and no mark. Performance fees become ₹4,74,349.50 rather than ₹2,57,600, and the account ends at ₹1,29,14,721.79. The clause is worth ₹2,16,749.50, or 2.17% of the original account.

Read it. The headline "1 and 20 over a 10% hurdle" is not a price until you know three more things: whether the hurdle is hard or soft with catch-up, whether there is a high-water mark, and what the fixed fee is computed on. Change any one and the same three years produce a materially different bill. The comparison against a mutual fund is also worth making explicitly: a 1.10-point distribution wedge took 15.68% of a fund investor's gain in the direct-plan arithmetic, and this full performance structure took 15.94% here. Two very different-looking contracts, almost the same price. What this example cannot tell you is whether the manager was worth it, because 11.34% gross over three years is a sample, not evidence.

Worked example 6: One kilogram of the same metal, three containers (India, ₹)

Setup. ₹6,00,000 committed for eight years. Gold at ₹6,000 a gram at the start and ₹11,400 at the end, an implied compound growth of 8.3538%. Route A is a sovereign gold bond paying 2.50% a year on the issue price with the redemption gain exempt for an individual at maturity, coupons reinvested at 6% net. Route B is a gold fund charging 0.50% a year, bought and sold with a 5 basis point spread each way. Route C is physical metal at 8% making charges and 3% goods and services tax on purchase, sold at a 2% assay discount, with ₹3,000 a year of locker charges rolled up at 6%. The holder is at a 31.2% effective slab; long-term gains on the fund and the metal are taxed at 12.5% plus cess [verify: every one of these treatments is statutory and has changed; incometaxindia.gov.in and rbi.org.in].

Solution. Route A, the bond. ₹6,00,000 at ₹6,000 buys 100 grams. The coupon is 2.50% × ₹6,00,000 = ₹15,000 a year, on the issue price and not on the market price, which is the single most misunderstood feature of the instrument. After slab tax it is ₹10,320 a year, and eight such receipts rolled at 6% come to ₹1,02,141.87. Redemption is 100 × ₹11,400 = ₹11,40,000, with no capital-gains tax at maturity. Total ₹12,42,141.87.

Route B, the fund. Buying costs 5 basis points, so ₹5,99,700 is at work; it tracks gold less 0.50% a year, giving ₹10,94,642.47 before exit, and ₹10,94,095.15 after the exit spread. The gain of ₹4,94,095.15 attracts ₹64,232.37 of tax. Total ₹10,29,862.78.

Route C, the metal. Each gram costs 6,000 × 1.08 × 1.03 = ₹6,674.40, so ₹6,00,000 buys 89.8957 grams rather than 100. Ten grams disappear at the counter. Sold at a 2% discount the metal fetches ₹10,04,314.99; tax on the ₹4,04,314.99 gain is ₹52,560.95; eight years of locker charges rolled up are ₹29,692.40. Total ₹9,22,061.64.

Read it. The bond beats the metal by 53.3% of the original outlay over eight years on identical exposure to the identical commodity. Two of the three drivers are structural and permanent: only the bond pays a coupon, and only the physical route pays a making charge that is never recovered. The third, the tax exemption at maturity, is statutory and could be withdrawn. What the arithmetic cannot tell you is whether the instrument is available: new tranches are issued at the government's discretion, and the secondary market in existing tranches is thin enough that a buyer today may face a wide spread [verify: RBI press releases and the Budget documents]. The structure of the comparison is durable. Its availability is a separate question you answer on the day.

Worked example 7: Four containers, one unit of pay (US, $)

Setup. $6,000 of pre-tax salary, a 25-year horizon, a 7.0% total return of which two points arrive as dividends and five as price appreciation, a 22% ordinary rate now and at withdrawal, and a 15% rate on long-term gains and qualified dividends. The health savings account assumes qualified medical spending at withdrawal [verify: all rates and the account rules are IRS-published and change annually; irs.gov].

Solution. Route 1, taxable brokerage. Income tax takes 22% first, so only $4,680 is invested. Each year the dividend of 2% of the balance is taxed at 15%, and the after-tax remainder is reinvested, adding to basis. Run twenty-five years: the account grows at 1.05 + 0.017 = 1.067 a year and reaches $23,678.62, with a basis that has accreted from $4,680 to $9,500.54. The embedded gain of $14,178.07 is taxed at 15%, which is $2,126.71, leaving $21,551.91. The implied net annual rate on the $4,680 is 6.2991%, against a 7.0% gross.

Route 2, traditional workplace plan. The full $6,000 goes in. At 7% for 25 years it reaches $32,564.60, and withdrawal at 22% leaves $25,400.38.

Route 3, Roth. Income tax first, so $4,680 goes in, grows to $25,400.38, and comes out untaxed.

Route 4, health savings account. The full $6,000 goes in, reaches $32,564.60, and comes out untaxed for qualified medical spending.

Read it. Routes 2 and 3 agree to the cent because the rate did not move, which is the identity worth carrying. The taxable account's 15% shortfall against the deferred wrappers came entirely from dividends taxed annually out of a compounding base, with no trading at all. And the health savings account's advantage is real but conditional: it exists only against qualified medical spending, requires a particular health plan to fund, and its dollars are therefore not the same dollars as the brokerage account's. The table holds the assets constant and varies only the container, which is the right way to isolate the effect and the wrong way to choose an account. Liquidity, eligibility and what you will actually need the money for decide that.

Worked example 8: One distribution, four kinds of income (US, $)

Setup. 800 units of a synthetic American real estate investment trust bought at $42.50, a $34,000 position. During 2025 the trust distributes $2.60 a unit, and its own tax reporting splits the payment into $1.72 of ordinary dividends, $0.18 of qualified dividends, $0.55 of return of capital and $0.15 of capital gain distribution. The holder is at a 24% ordinary rate and a 15% long-term rate and can claim the 20% deduction on qualified trust dividends. The units are sold on 1 March 2027 at $46.20 [verify: the deduction on qualified REIT dividends has a legislated life; confirm current availability at irs.gov].

Solution. Step 1, the four slices in dollars. Ordinary $1,376.00; qualified $144.00; return of capital $440.00; capital gain distribution $120.00. They sum to the $2,080.00 distributed.

Step 2, the current-year tax. The ordinary slice takes the 20% deduction first, so $1,100.80 is taxable at 24%, which is $264.19. The qualified slice is taxed at 15%, $21.60. The capital gain distribution is taxed at 15%, $18.00. The return of capital attracts nil. Total $303.79, an effective 14.61% on the distribution.

Step 3, the naive answer. Treating the whole $2,080 as ordinary income at 24% gives $499.20. The decomposition is worth $195.41 in one year on one holding.

Step 4, the basis. The $440 return of capital reduces the position's basis from $34,000 to $33,560, or $41.95 a unit.

Step 5, the sale. Proceeds 800 × $46.20 = $36,960. Against the reduced basis the long-term gain is $3,400 and the tax is $510.00. Had there been no return of capital the gain would have been $2,960 and the tax $444, so the return of capital cost $66 extra at sale.

Step 6, the net. Measure the deferral against the treatment the same cash would have carried as an ordinary trust dividend, which is the 20% deduction and then 24%: 440 × 0.80 × 0.24 = $84.48 of tax deferred, against $66 of long-term-rate tax paid later. The net benefit is $18.48. Using the full 24% and ignoring the deduction gives $105.60 and overstates the benefit by $21.12, which is the error of applying a deduction to one slice of a distribution and not to the counterfactual for another.

Read it. Return of capital is not tax-free income; it is tax deferred and rate-converted, and here that conversion was worth 21.9% of what the naive reading would have credited it with. The distribution yield on this holding, $2.60 on a $42.50 cost, is 6.12% before tax and 5.22% after, and a screen sorting trusts by headline yield cannot see that difference. Every trust publishes the split annually. Read it, apply three rates, adjust the basis, and keep the adjusted basis somewhere you will find it years later, because the sale is where the omission finally shows up.

Verify block

Every figure the worked examples turn on, at the precision the computation produced. Reproduce these before trusting any answer of your own.

Worked example 1. Kaveri cost per share ₹1,250.232783. Long-term gain ₹1,79,894.129820. Short-term loss −₹8,826.733811. Gain after set-off ₹1,71,067.396009. Taxable after exemption ₹46,067.396009. Capital-gains tax ₹5,988.761481. Dividend tax ₹3,494.40, withheld ₹1,120.00. Total tax accrued ₹9,483.161481. Closing value ₹12,37,427.651. Money-weighted return 17.223838%; after tax 16.921932%; with the advance-tax timing 16.911883%. Real after tax 11.460374%. Benchmark after fee and tax 10.468652%, real 5.308533%. Tracking difference 57.643065 basis points. Leaks: inflation ₹1,12,166.214152; tax ₹9,483.161481; fund expenses ₹7,855.751686; commission ₹5,850.747448; transaction costs ₹1,344.582240. Total ₹1,36,700.457007, top three 94.736428%. The two avoidable leaks come to ₹6,539.232685, being the ₹5,850.747448 commission plus the ₹688.485237 destroyed by spending the loss at the lower rate. The commission's terminal-value expression is ₹5,832.037041.

Worked example 2. Ordinary income at vest $25,380.00; withholding required $8,794.17; 104 shares withheld worth $8,798.40; 196 delivered. Sale loss −$2,606.80. Purchase price $58.99; 127 shares for $7,491.73; $8.27 refunded. Disqualifying: ordinary $1,322.07, gain $736.60, tax $494.0808. Qualifying: ordinary $1,485.90, gain $572.77, tax $442.5315. Saving $51.5493, being 0.539761% of a $9,550.40 position. Match $4,350.00 on an $8,700.00 deferral, 14.471424% annualised over three years. Growth factor 5.427433; traditional at 22% later $36,830.557896; Roth $35,886.184616.

Worked example 3. Maturity ₹42,00,000, internal rate of return 6.632555%. Alternative before tax ₹66,39,532.155529, tax ₹5,98,589.180219, after tax ₹60,40,942.975310, internal rate of return 9.656754%. Advantage ₹18,40,942.975310. Break-even gross equity return 7.845176%. Surrender at year three: floor ₹60,000, loss ₹2,40,000, 80.0%.

Worked example 4. No-withdrawal terminal value ₹1,69,05,914.448863. Bad-first ₹48,04,619.364435 with 28,419.754394 units left; bad-last ₹92,03,522.767497 with 54,439.662494 units left; gap ₹43,98,903.403062; ratio 52.204134%. Year-one units redeemed 8,030.158769 and 6,840.292698; year-one result −₹83,015.876945 and +₹35,970.730240. Terminal net asset value ₹169.059144 in both orders.

Worked example 5. Fixed fees ₹1,12,000.00, ₹1,15,491.84, ₹1,21,024.861568. Performance fees ₹2,57,600.00, nil, nil. Closing values ₹1,20,30,400.00, ₹1,09,52,476.16, ₹1,31,31,471.292032. Year-three shortfall against the hurdle level ₹1,01,968.707968. Gross compound 11.343524%, net 9.505970%, drag 1.837554 points. Fees ₹6,06,116.701568, being 15.935008% of the gross gain. Without the mark, performance fees ₹4,74,349.503206 and terminal ₹1,29,14,721.788826; the mark is worth ₹2,16,749.503206.

Worked example 6. Gold compound growth 8.353813%. Bond: coupons ₹1,02,141.868819, redemption ₹11,40,000, total ₹12,42,141.868819, annualised 9.522284%. Fund: ₹10,94,095.153404 before tax, tax ₹64,232.369942, total ₹10,29,862.783461, annualised 6.986385%. Physical: ₹6,674.40 a gram, 89.895721 grams, proceeds ₹10,04,314.994606, tax ₹52,560.949299, locker ₹29,692.403727, total ₹9,22,061.641581, annualised 5.517888%.

Worked example 7. Taxable terminal value $23,678.617316 on a basis of $9,500.544692, exit tax $2,126.710894, after everything $21,551.906422, implied rate 6.299101%. Traditional and Roth both $25,400.384756. Health savings account $32,564.595841. Taxable is 66.182017% of the best.

Worked example 8. Current tax $303.792000, effective 14.605385%. Naive $499.20, difference $195.408. Basis after return of capital $33,560.00, being $41.95 a unit. Gain at sale $3,400.00, tax $510.00; extra tax caused by the return of capital $66.00; tax deferred on the same cash treated as an ordinary trust dividend $84.48; net benefit $18.48, being 21.875% of the deferred tax.

Section figures, in the order they appear. Blended expense ceilings: 1.906250% at ₹2,000 crore, 1.584375% at ₹12,000 crore, 1.441016% at ₹32,000 crore, 1.293542% at ₹60,000 crore. Ten-year investment plan: direct ₹30,58,046.165403 at a monthly 0.826386%, regular ₹28,87,537.583272 at 0.742268%, gap ₹1,70,508.582131, being 15.678408% of the regular plan's gain. Exit-load case: redeem now ₹2,99,487.36, wait ₹3,07,837.60, advantage ₹8,350.24, break-even net asset value ₹76.720506 or a 3.032728% fall. Transfer plan: gain ₹14,377.533685 across ten redemptions, tax ₹4,485.790510. Exchange-traded fund premium 1.720606%; mean tracking difference −0.394 points, standard deviation 0.087772 points, five-year shortfall 1.954537%. Rolling windows: point-to-point 10.353351%, worst 2.950993%, best 19.131507%, spread 16.180514 points. Turnover 1.35 implies 8.888889 months and 47.25 basis points. Treasury bill at ₹98.42 yields 6.439100% on actual/365 and 4.430101% after tax. Deposit ladder ₹14,14,499.748285 against ₹14,14,778.195756 single, behind by ₹278.447471, and worth ₹4,470.134067 on one early need. Employee stock option: perquisite ₹2,60,000, tax ₹81,120, cash needed at exercise ₹1,41,120, capital gain ₹1,35,000, tax ₹17,550, and the double-count error costs ₹33,800. Exempt wrapper against taxable deposit over fifteen years: ₹40,68,209.220288 against ₹33,65,608.063449, a gap of ₹7,02,601.156839.

Practice set

Work each problem fully before reading its solution. A calculator is assumed. Numeric answers within ±1% of the printed figure score as correct unless the problem demands an exact reconciliation. Every rate given in a problem is a given: use it, and do not substitute a rate you believe is current, because the skill being tested is the arithmetic rather than the lookup. Problems 1 to 3 are guided, 4 to 11 are independent, and 12 to 14 are timed at eight minutes each.

P1 (guided). The blended expense ceiling. An open-ended equity scheme has ₹32,000 crore of daily net assets. Using the slab schedule from the teaching content, compute the blended ceiling, the rupees of annual expense it permits, and the marginal rate in the scheme's own band. Then state why the two rates differ.

Solution. Walk the tranches. First ₹500 crore at 2.25% is ₹11.25 crore. Next ₹250 crore at 2.00% is ₹5.00 crore. Next ₹1,250 crore at 1.75% is ₹21.875 crore. Next ₹3,000 crore at 1.60% is ₹48.00 crore. Next ₹5,000 crore at 1.50% is ₹75.00 crore, taking the running total to ₹10,000 crore. Above that the rate steps down 0.05 points per ₹5,000 crore band: 1.45% on 10,000 to 15,000, 1.40% on 15,000 to 20,000, 1.35% on 20,000 to 25,000, 1.30% on 25,000 to 30,000, and 1.25% on the remaining ₹2,000 crore. Total permitted expense is ₹461.125 crore, a blended ceiling of 1.4410%, against a marginal band rate of 1.25%. They differ because the schedule is progressive: the fund keeps charging the higher tranche rates on the assets sitting in the lower tranches, exactly as a taxpayer keeps paying the lower slab rates on the first part of their income.

P2 (guided). A decade of commission. ₹10,000 a month for ten years, a portfolio returning 11.5% gross, a direct-plan expense ratio of 0.55% and a regular-plan ratio of 1.50%. Compute both terminal values and the cost of the commission, in rupees and as a share of the direct-plan outcome.

Solution. Net returns are 10.95% and 10.00%. Effective monthly rates are 1.1095^(1/12) − 1 = 0.869672% and 1.10^(1/12) − 1 = 0.797414%. The future value of 120 end-of-month contributions is P × [(1 + i)^120 − 1] ÷ i, giving ₹21,00,397 direct and ₹19,98,639 regular. The commission cost ₹1,01,759, which is 4.84% of the direct-plan outcome. Convert it to a share of the gain for the honest version: the regular plan's gain over ₹12,00,000 invested was ₹7,98,639, so the commission took 12.74% of everything the investor made.

P3 (guided). A vest, in whole shares. 450 restricted stock units vest at a fair market value of $56.80. The employer withholds at a combined 33% and withholds in whole shares. Compute the ordinary income, the shares withheld, the net shares delivered, the basis, and the gain if the net shares are sold at $61.40.

Solution. Ordinary income is 450 × $56.80 = $25,560.00. Withholding required is 33% of that, $8,434.80. In whole shares that is ceiling(8,434.80 ÷ 56.80) = ceiling(148.50) = 149 shares, so 301 shares are delivered. Basis is $56.80 a share. Selling at $61.40 gives 301 × $4.60 = $1,384.60 of capital gain, short-term unless the sale is more than a year after vest. The employee's cash position at vest was zero; the entire tax was settled in stock.

P4. Load against line. A holder has ₹4,80,000 of an equity fund bought for ₹4,00,000, held for 340 days, with a 1% exit load inside 365 days. Short-term gains are taxed at 20% plus 4% cess, long-term at 12.5% plus 4% cess, and assume the annual exemption is already used. Compute the net proceeds of redeeming today and of waiting past the line at an unchanged price, and the fall in value that would wipe out the advantage of waiting.

Solution. The gain is ₹80,000. Redeeming today costs a load of ₹4,800 and short-term tax of 80,000 × 0.20 × 1.04 = ₹16,640, leaving ₹4,58,560. Waiting costs no load and long-term tax of 80,000 × 0.125 × 1.04 = ₹10,400, leaving ₹4,69,600. Waiting is worth ₹11,040, which is 2.30% of the position. The break-even is not that 2.30%, because the tax falls with the value too: solve 0.87 × V + 52,000 = 4,58,560 and the two routes tie at a value of ₹4,67,310, a fall of 2.64% over the remaining 26 days. The load was ₹4,800 and the tax difference ₹6,240, so the invisible cost was the larger one.

P5. The disallowed loss. An American investor bought 200 shares at $61.00, sold them at $47.50, and bought 200 of the same shares back at $49.20 eleven days later. Compute the loss claimed, the loss allowed, and the basis of the replacement lot.

Solution. The realised loss is 200 × ($47.50 − $61.00) = −$2,700.00. The repurchase falls inside the 30-day window on the after side, so the entire $2,700 is disallowed for the current year. It is added to the replacement lot's basis: the lot cost 200 × $49.20 = $9,840, and the adjusted basis is 9,840 + 2,700 = $12,540.00, or $62.70 a share. The original holding period tacks on. The benefit was deferred rather than destroyed, which is only true because the repurchase happened in a taxable account.

P6. Spend the loss where the rate is highest. An Indian resident's year contains ₹2,40,000 of short-term capital gains, ₹3,10,000 of long-term capital gains on listed equity, ₹95,000 of short-term capital losses and ₹1,40,000 of long-term capital losses. Short-term is taxed at 20% plus cess, long-term at 12.5% plus cess above a ₹1,25,000 exemption. Compute the tax with the ladder applied correctly, and the tax if the short-term loss is applied to the long-term gain instead.

Solution. The long-term loss can only reach long-term gains, so it goes there: 3,10,000 − 1,40,000 = ₹1,70,000. The short-term loss can reach either, so spend it where the rate is 20%: 2,40,000 − 95,000 = ₹1,45,000 of short-term gain, taxed at 20% × 1.04 = ₹30,160. The long-term slice of ₹1,70,000 less the ₹1,25,000 exemption leaves ₹45,000 taxed at 12.5% × 1.04 = ₹5,850. Total ₹36,010. Apply the short-term loss to the long-term gain instead and the short-term gain is taxed in full at ₹49,920 while the long-term slice falls to zero after the exemption, for a total of ₹49,920. The wrong order costs ₹13,910 on identical facts.

P7. A loss you cannot use quickly. An American investor ends the year with a $14,600 net capital loss and no gains to absorb it. The annual offset against ordinary income is $3,000 and the marginal rate is 24%. Compute how long the loss takes to use, its nominal tax value, and its present value discounted at 5%.

Solution. At $3,000 a year the loss takes five years: $3,000 in each of years one to four and $2,600 in year five. Nominal value is $14,600 × 0.24 = $3,504.00. Discounting each year's deduction at 5%, with the first taken immediately, gives $3,194.10. The deduction lost $309.90, or 8.8% of its value, purely to the queue. A loss you can use against a gain this year is worth more than one that has to wait, which is why realising a loss is worth more in a year with gains than in a year without.

P8. What a withdrawal plan realises in a falling year. A holder starts a withdrawal plan with units bought at a net asset value of ₹100.0000, withdrawing ₹40,000 a month. Over the first twelve months the value stands at 102.0, 99.5, 97.0, 95.5, 96.0, 94.0, 93.0, 95.0, 98.0, 101.0, 103.5 and 105.0 on the redemption dates. Compute the units redeemed, the cost of those units, the cash received and the taxable result.

Solution. Units redeemed each month are 40,000 divided by that month's value; summing the twelve gives 4,890.373635 units. Their cost at the ₹100.0000 purchase value is ₹4,89,037.36. Cash received is 12 × ₹40,000 = ₹4,80,000. The result is a short-term capital loss of ₹9,037.36, and the tax is nil. The loss is an asset: it may be set against short-term or long-term gains this year and carried forward for eight assessment years if the return is filed on time. A withdrawal plan in a falling market generates losses, not gains, and holders routinely fail to report them and thereby lose them.

P9. Which wrapper wins. For each pair of marginal rates, state whether a Roth or a traditional contribution ends larger and by what percentage: (a) 32% now, 24% later; (b) 12% now, 22% later; (c) 24% now, 24% later.

Solution. The ratio of Roth to traditional is (1 − t now) ÷ (1 − t later), and the growth rate and horizon cancel entirely. (a) 0.68 ÷ 0.76 = 0.894737, so traditional wins by 10.53%. (b) 0.88 ÷ 0.78 = 1.128205, so Roth wins by 12.82%. (c) 0.76 ÷ 0.76 = 1, so they are identical. Every argument about these two products that is not an argument about your future marginal rate is a distraction, with two real exceptions: the absence of a required minimum distribution, and the fact that paying tax from outside the account effectively shelters more.

P10. The charge stack. A unit-linked policy takes a ₹2,00,000 annual premium with a 5% premium allocation charge, a ₹6,000 policy administration charge, a ₹9,400 mortality charge and a 1.35% fund management charge on the invested amount. Compute the amount reaching the fund in year one, the drag before the fund management charge, and the all-in first-year cost as a share of premium.

Solution. The allocation charge takes ₹10,000, leaving ₹1,90,000. Administration takes ₹6,000 and mortality ₹9,400, so ₹1,74,600 reaches the fund, a drag of ₹25,400 or 12.70% of premium before any investment charge. The fund management charge is 1.35% × ₹1,74,600 = ₹2,357.10, so the all-in first-year cost is ₹27,757.10, or 13.88% of premium. Compare that against the 0.62% a direct index fund would have charged on the same money and the product has to outperform by more than thirteen points in year one just to draw level.

P11. The coupon is on the issue price. A sovereign gold bond was issued at ₹5,100 a gram with a 2.50% annual coupon. It now trades at ₹6,890. Compute the annual coupon per gram, the current yield to a buyer at today's price, and the gap against the headline rate.

Solution. The coupon is 2.50% × ₹5,100 = ₹127.50 a gram a year, fixed for the life of the bond because it is computed on the issue price and never on the market price. A buyer paying ₹6,890 receives ₹127.50, a current yield of 1.8505%, which is 0.6495 percentage points below the headline 2.50%. Anybody quoting the headline coupon to a secondary-market buyer is quoting a rate that buyer will not receive.

P12 (timed, 8 minutes). Three containers, twenty years. $4,000 of pre-tax salary, 20 years, a 6.5% total return of which 1.8 points arrive as dividends, a 24% ordinary rate now, a 22% rate at withdrawal, and a 15% rate on qualified dividends and long-term gains. Compute the after-everything value in a health savings account, a traditional workplace plan and a taxable brokerage account.

Solution. The health savings account takes the full $4,000, which at 6.5% for 20 years reaches $14,094.58, withdrawn free for qualified medical spending. The traditional plan also takes $4,000 and reaches $14,094.58, then pays 22% on withdrawal, leaving $10,993.77. The taxable account starts with $4,000 × 0.76 = $3,040 after income tax; each year the 1.8% dividend is taxed at 15% and the remainder reinvested, so the balance grows at 1.047 + 0.0153 = 1.0623 and the basis accretes; after 20 years the balance is $10,181.63 on a basis of $4,793.88, and the 15% exit tax of $808.16 leaves $9,373.47. The health savings account keeps $4,721.11 more than the taxable account on identical assets.

P13 (timed, 8 minutes). The exit that is not yours to choose. A subscriber reaches the normal exit age with an ₹80,00,000 corpus. Regulation permits up to 60% as a lump sum and requires at least 40% to buy an annuity. The annuity rate available is 6.6% and the subscriber remains in the 30% slab with 4% cess. Compute the lump sum, the annuitised amount, the gross and after-tax annual income, and the after-tax yield on the annuitised corpus.

Solution. Lump sum ₹48,00,000; annuitised ₹32,00,000. Gross annual income is 6.6% × ₹32,00,000 = ₹2,11,200, taxable at slab in the year received, so tax of 31.2% is ₹65,894.40 and the after-tax income is ₹1,45,305.60. The after-tax yield on the annuitised corpus is 4.5408%. Two facts to carry: the annuity is compulsory rather than chosen, and its income is taxed at slab while the lump sum's treatment is set by a separate provision that has been amended more than once, so the after-tax outcome of an exit must be computed with current rules rather than remembered.

P14 (timed, 8 minutes). The whole ladder. A portfolio returned 11.80% nominal before costs. Its funds charged 1.25%; transaction costs ran to 0.30%; tax took 0.92 points of the return; inflation over the year was 5.2%. Compute the return after costs, after tax and after inflation, the share of the gross return that survived, and rank the three leaks.

Solution. After the expense ratio and transaction costs the return is 11.80 − 1.25 − 0.30 = 10.25%. After tax it is 10.25 − 0.92 = 9.33%. Deflate rather than subtract: (1.0933 ÷ 1.052) − 1 = 3.9259% real. Only 33.27% of the gross return survived. Ranked, the leaks are inflation at 5.40 points, cost at 1.55 points and tax at 0.92 points. The ranking is the point: the largest leak is the one no product disclosure mentions, the second largest is the one the investor controls most directly, and the smallest is the one that generates all the anxiety.

Applied mini-project

Audit your own money, or a supplied portfolio, end to end, in about three hours. The deliverable is a three-page working file plus a one-page verdict, and everything in it must reconcile.

Use your own holdings if you have them. If you do not, or would rather not, build a synthetic portfolio of at least five holdings across at least three product types, with at least six dated cash flows across at least eighteen months, one realised gain and one realised loss. A synthetic portfolio must be labelled synthetic on every page.

Step 1: assemble the facts (about 35 minutes). For every holding record the purchase date, the amount, the units or shares, the plan (direct or regular, where the distinction exists), the current expense ratio, the current value and its date, and the source of each figure with the date you read it. For every fund, record the benchmark including its variant, the portfolio turnover and the current-year expense ratio. For every realisation, record the contract note or the transaction statement.

Step 2: the cost stack (about 25 minutes). Build one table of every cost actually borne: transaction charges and taxes on both sides of every trade, stamp duty on every fund purchase, and, for each fund, the expense ratio applied to the average value over the time held. Where a holding is in a regular plan, find the direct plan of the identical scheme and compute the commission wedge separately, so it does not double-count against the fund's own expense line.

Step 3: the money-weighted return (about 30 minutes). Lay out every pocket-level cash flow with its date, add the current value as a terminal inflow, and solve for the annualised rate. State the day-count convention you used. Then compute the time-weighted return over the same window if you can, and explain in two sentences why the two differ for your account.

Step 4: the tax layer (about 35 minutes). Compute every realised gain and loss lot by lot, applying the correct holding-period line, the correct rate and any annual exemption. Apply the set-off ladder in the order that minimises tax and show the order you rejected and what it would have cost. Compute dividend or distribution income at the correct rate, taking credit for any tax withheld. Every rate carries its source and the date you read it, without exception.

Step 5: inflation and the real number (about 15 minutes). Deflate the after-cost, after-tax nominal return by a published inflation series for the same window, naming the series and its source. Deflate rather than subtracting.

Step 6: the benchmark, on the same basis (about 20 minutes). Choose one benchmark, state its variant, and put it through the same fee and the same tax treatment your portfolio faced before comparing. A comparison against a pre-tax index return does not count and scores zero on that row.

Step 7: the verdict (about 20 minutes). One page, no more than 500 words. Rank the leaks in currency, largest first. For each of the three largest, state one action available to you, what it would be worth per year, and what it would cost to execute. Close with one paragraph naming every place your numbers rest on an assumption rather than a source.

Rubric (20 points; pass at 16 with no zero on any row)

Any row whose underlying computation does not reconcile scores zero regardless of how well it is written. A cost stack that misses a category, a set-off that cannot be reproduced from the numbers shown, or a benchmark comparison on the wrong basis is not a presentation problem. It is a wrong answer wearing a table.

Reading & resources

Primary sources first, because everything in this area is a rule somebody wrote down and the rule is the only authority. Free unless marked.

1. The mutual fund regulations and the circulars amending them, at sebi.gov.in (free, intermediate). The expense-ratio schedule, the categorisation framework, the direct-plan requirement and the benchmarking rules all live here. Read one scheme information document alongside one circular and the document becomes legible.
2. A live scheme information document and the matching monthly factsheet, from any Indian asset manager's own site (free, beginner). Pick a fund you might actually buy. Find the expense ratio for both plans, the benchmark variant, the exit load table and the portfolio turnover, and time yourself.
3. The income-tax department's site, incometaxindia.gov.in (free, intermediate). The Act, the Finance Acts that amend it, the return forms and their instructions. The instructions to the capital-gains schedule of the return form are the most underrated tax teaching material available anywhere, because they show the ladder as an actual worksheet.
4. IRS Publication 550, Investment Income and Expenses, at irs.gov (free, intermediate). The wash sale, the holding period, the qualified-dividend condition and the loss limitation, written by the people who administer them.
5. IRS Publication 525, Taxable and Nontaxable Income, at irs.gov (free, intermediate). The equity-compensation sections cover restricted stock and employee purchase plans with the ordering rules worked out.
6. IRS Publication 969, at irs.gov (free, beginner). The health savings account rules, including what "qualified" spending means and what changes at 65.
7. The Reserve Bank's retail participation pages and the sovereign gold bond scheme notifications, at rbi.org.in (free, beginner). Government-security auction results, treasury bill cut-offs and the bond scheme's terms, from the issuer.
8. The pension authority's exit regulations and investment guidelines, at pfrda.org.in (free, intermediate). The asset-class caps, the taper and the annuitisation requirement, stated by the regulator that sets them.
9. The insurance regulator's product regulations and any insurer's benefit illustration, at irdai.gov.in and the insurer's own site (free, intermediate). The benefit illustration is the document that shows the charge stack year by year, and insurers must give it to you. Ask for it before buying anything.
10. **John C. Bogle, *Common Sense on Mutual Funds*** (paid, beginner to intermediate). The cost argument made at book length by the person who built the industry that proved it. Read the chapters on cost and on the arithmetic of active management, and skip nothing in them.
11. **William J. Bernstein, *The Four Pillars of Investing*** (paid, beginner). The clearest short treatment of why product choice and cost dominate security selection for a household, with the history that makes the argument stick.
12. Your own contract note, factsheet, benefit illustration, tax return and pay slip (free, essential). Every document this material teaches you to read is one you already receive and probably file unread. Pull the last twelve months of all five, and do it before the mini-project rather than during it.

Flashcards

This module's flashcards and mastery quiz are wired into the app: see the node's Quiz and Reviews.

Mastery check

Two parallel forms. Closed book, calculator allowed, about 40 minutes per form. Numeric answers within ±2% score as correct except where an exact reconciliation is asked for. Pass threshold: ≥ 85%, which with twelve one-point items is eleven of twelve. Every rate needed is given in the question, because the gate tests the arithmetic and the judgment rather than your memory of a slab that will have changed by the time you sit it. If you score nine or ten, redo the related practice problems and sit the other form after a break.

Form A

A1 (MCQ). A regular plan and a direct plan of the same scheme differ in: (a) the portfolio held (b) the fund manager (c) the expense ratio, by roughly the distributor commission (d) the exit load

A2 (short). State in one sentence why quoting a fee as a share of assets understates it, and give the alternative denominator.

A3 (numeric). An open-ended equity scheme has ₹8,000 crore of daily net assets. Using the schedule 2.25% / 2.00% / 1.75% / 1.60% / 1.50% on tranches of ₹500 / ₹250 / ₹1,250 / ₹3,000 / ₹5,000 crore, compute the blended expense-ratio ceiling to four decimal places.

A4 (numeric). ₹25,000 a month for eight years, 12.0% gross, direct-plan expense ratio 0.50% and regular-plan 1.50%. Compute both terminal values and the commission cost.

A5 (numeric). A holder has ₹2,50,000 of an equity fund bought for ₹2,10,000, held 300 days, with a 1% exit load inside 365 days. Short-term 20% plus 4% cess; long-term 12.5% plus 4% cess with the exemption already used. Compute the net proceeds of redeeming today and of waiting past the line at an unchanged price.

A6 (numeric). 220 restricted stock units vest at a fair market value of $48.00. Compute the ordinary income at vest, and the capital gain or loss if all shares delivered were sold at $41.25 (ignore share withholding and treat all 220 as delivered).

A7 (numeric). An Indian resident's year contains ₹1,20,000 of short-term gains, ₹4,00,000 of long-term gains on listed equity and ₹1,50,000 of short-term losses. Short-term 20% plus 4% cess; long-term 12.5% plus 4% cess above a ₹1,25,000 exemption. Compute the tax with the ladder applied optimally.

A8 (numeric). An employer matches dollar for dollar on the employee's deferral, with a four-year cliff. State the immediate return on the deferral and annualise it over the cliff.

A9 (numeric). A twenty-year endowment takes ₹1,00,000 a year at the start of each year, with a sum assured of ₹20,00,000, a reversionary bonus of ₹40 per ₹1,000 of sum assured a year, and a ₹3,00,000 terminal bonus. Compute the maturity proceeds and the internal rate of return.

A10 (numeric). A ₹50,00,000 discretionary account returns +18% gross in year one. The fixed fee is 1.00% of the mean of opening and closing gross values; the performance fee is 20% of the excess over a 10% hurdle applied to the opening high-water mark. Compute the fixed fee, the hurdle level, the performance fee and the closing value.

A11 (numeric). A trust distributes $1,900 to a holder, split 70% ordinary dividends, 10% qualified dividends and 20% return of capital. The ordinary slice carries a 20% deduction; the ordinary rate is 24% and the long-term rate 15%. Compute the current-year tax and the reduction in basis.

A12 (short). A colleague says a portfolio returned 14.2% while its index returned 12.9%, so the manager added 1.3 points. Name the three things you would check before agreeing, and say which one is most likely to reverse the conclusion.

Form A key. A1: c. Same portfolio, same manager, same strategy; the plans differ only in whether a distributor is being paid, and the regulations require the direct plan's ratio to be lower to the extent of distribution expenses. A2: Contributed capital was never at risk from fees, so the fee should be measured against the expected gain rather than against assets; on the ten-year worked case 1.10 points was 5.58% of terminal wealth and 15.68% of the gain. A3: 11.25 + 5.00 + 21.875 + 48.00 + 45.00 = ₹131.125 crore on ₹8,000 crore = 1.6391%. The last tranche is only ₹3,000 crore of the ₹5,000 crore band, which is where most errors happen. A4: net returns 11.50% and 10.50%; effective monthly rates 0.911247% and 0.835516%; direct ₹38,10,453, regular ₹36,58,786, commission ₹1,51,667. A5: gain ₹40,000; load ₹2,500 and short-term tax ₹8,320, so ₹2,39,180 now; long-term tax ₹5,200, so ₹2,44,800 if held; waiting is worth ₹5,620. A6: ordinary income 220 × 48.00 = $10,560.00; the loss is 220 × (41.25 − 48.00) = −$1,485.00, short-term, and only $3,000 a year of it can reach ordinary income. A7: the ₹1,50,000 short-term loss goes first against the ₹1,20,000 short-term gain, taxed at the higher rate, wiping it out and leaving ₹30,000; that reduces the long-term gain to ₹3,70,000, less the ₹1,25,000 exemption leaves ₹2,45,000 at 12.5% × 1.04 = ₹31,850. A8: an immediate 100%, annualised over four years as 2^(1/4) − 1 = 18.9207% a year, contractual rather than market-dependent. A9: accrued bonus 40 × 2,000 × 20 = ₹16,00,000, so maturity is 20,00,000 + 16,00,000 + 3,00,000 = ₹39,00,000, and the internal rate of return on twenty beginning-of-year premiums is 6.0016%. A10: gross ₹59,00,000; fixed fee 1% × (50,00,000 + 59,00,000)/2 = ₹54,500; after it ₹58,45,500; hurdle level 50,00,000 × 1.10 = ₹55,00,000; excess ₹3,45,500, performance fee ₹69,100; closing ₹57,76,400. A11: ordinary $1,330 less the 20% deduction is $1,064 at 24% = $255.36; qualified $190 at 15% = $28.50; return of capital $380 attracts nil. Total $283.86, and basis falls by $380.00. A12: whether the index is a total-return or price variant, whether the portfolio return is after fees and the index is not, and whether both are on the same tax basis. The variant is most likely to reverse it, because a dividend yield of well over 1.3 points is common and benchmarking against a price index hands the manager exactly that as free alpha.

Form B

B1 (MCQ). A fund's tracking difference is −0.39 points a year with a standard deviation of 0.09 points. The correct reading is: (a) the fund is poorly run and erratic (b) the fund is consistent and reliably behind its index by more than its stated fee (c) the fund beat its index (d) tracking difference and tracking error are the same measure

B2 (short). State what a systematic transfer plan does to the holder's tax position, and why the effect surprises people.

B3 (numeric). An open-ended equity scheme has ₹20,000 crore of daily net assets. Using the same tranche schedule as Form A, with 0.05 points off per ₹5,000 crore band above ₹10,000 crore, compute the blended ceiling to four decimal places.

B4 (numeric). ₹20,000 a month for ten years, 10.5% gross, direct-plan expense ratio 0.45% and regular-plan 1.65%. Compute both terminal values and the commission cost.

B5 (numeric). A holder has ₹3,60,000 of an equity fund bought for ₹3,00,000, held 350 days, with a 1% exit load inside 365 days. Same rates as Form A. Compute the net proceeds both ways and the advantage of waiting.

B6 (numeric). 150 restricted stock units vest at a fair market value of $92.40. Compute the ordinary income at vest and the capital gain or loss on selling all 150 at $88.10.

B7 (numeric). An Indian resident's year contains ₹2,00,000 of short-term gains, ₹2,60,000 of long-term gains on listed equity and ₹80,000 of short-term losses. Same rates as Form A. Compute the tax with the ladder applied optimally.

B8 (numeric). An employer matches 50 cents on the dollar with a five-year cliff. Annualise the match over the cliff.

B9 (numeric). A fifteen-year endowment takes ₹75,000 a year at the start of each year, with a sum assured of ₹15,00,000, a reversionary bonus of ₹42 per ₹1,000 of sum assured a year, and a ₹2,50,000 terminal bonus. Compute the maturity proceeds and the internal rate of return.

B10 (numeric). A ₹80,00,000 discretionary account returns −6% gross in a year. The fixed fee is 1.00% of the mean of opening and closing gross values; the performance fee is 20% over a 10% hurdle on the high-water mark, which equals the opening value. Compute the fixed fee, the performance fee and the closing value.

B11 (numeric). A trust distributes $2,400 to a holder, split 60% ordinary dividends, 15% qualified dividends and 25% return of capital, with the same deduction and rates as Form A. Compute the current-year tax.

B12 (short). A friend is about to spend ₹8,00,000 on gold jewellery as an investment, at ₹6,000 a gram plus 10% making charges and 3% goods and services tax on the total. Compute the grams that buys, compute how many grams the same ₹8,00,000 would buy in a form carrying neither charge, and state in two sentences what you would tell them.

Form B key. B1: b. A small tracking error means the fund misses consistently; a large tracking difference means it misses by a lot. Together they describe a well-run fund whose shortfall of 0.39 points is about four times its stated expense ratio, which is a question for the fund house. B2: Every transfer instalment is a redemption from the source scheme and therefore a reportable taxable disposal; ten monthly transfers create ten separate gains rather than one, and holders are surprised because the money never left the fund house and felt like an internal movement. B3: 11.25 + 5.00 + 21.875 + 48.00 + 75.00 on the first ₹10,000 crore, then ₹5,000 crore at 1.45% = 72.50 and ₹5,000 crore at 1.40% = 70.00. Total ₹303.625 crore on ₹20,000 crore = 1.5181%. B4: net returns 10.05% and 8.85%; direct ₹40,07,722, regular ₹37,64,902, commission ₹2,42,820, which is 6.06% of the direct outcome and 17.79% of the regular plan's gain. B5: gain ₹60,000; load ₹3,600 and short-term tax ₹12,480, so ₹3,43,920 now; long-term tax ₹7,800, so ₹3,52,200 if held; waiting is worth ₹8,280, being 2.30% of the position, and there are 16 days to run. B6: ordinary income 150 × 92.40 = $13,860.00; loss 150 × (88.10 − 92.40) = −$645.00. The tax on $13,860 is not refunded by the $645 loss; they are different buckets. B7: the ₹80,000 short-term loss goes against the short-term gain at 20%, leaving ₹1,20,000 taxed at 20% × 1.04 = ₹24,960; the long-term gain of ₹2,60,000 less the ₹1,25,000 exemption leaves ₹1,35,000 at 12.5% × 1.04 = ₹17,550. Total ₹42,510. B8: 1.5^(1/5) − 1 = 8.4472% a year, still better than any risk-free rate available, but 44.7% of the four-year 100% case because both the multiple and the wait are worse. B9: accrued bonus 42 × 1,500 × 15 = ₹9,45,000, so maturity is 15,00,000 + 9,45,000 + 2,50,000 = ₹26,95,000 on ₹11,25,000 of premiums, and the internal rate of return is 10.3137%. That is a good endowment, and the point of the item is that the arithmetic tells you so rather than the brochure. B10: gross ₹75,20,000; fixed fee 1% × (80,00,000 + 75,20,000)/2 = ₹77,600; performance fee nil, since the account is far below the hurdle level of ₹88,00,000; closing ₹74,42,400. The fixed fee is charged in full in a losing year, which is what "fixed" means. B11: ordinary $1,440 less the 20% deduction is $1,152 at 24% = $276.48; qualified $360 at 15% = $54.00; return of capital $600 attracts nil. Total $330.48. B12: each gram costs 6,000 × 1.10 × 1.03 = ₹6,798, so ₹8,00,000 buys 117.68 grams against 133.33 grams at the bare metal price. Nearly sixteen grams disappear at the counter before the price moves, and jewellery is also sold back at a discount for purity, so if the purpose is investment rather than wearing it, buy the metal in a paper form and buy the jewellery separately when you want jewellery.

This module's flashcards and mastery quiz are wired into the app: see the node's Quiz and Reviews.

Teach it back & journal

Feynman prompt. Write two pages, no jargon, for a working adult who has money in a bank account and has never bought a fund. Answer these four, in order.

1. The difference between the return a product advertises and the money that reaches you.
2. Why one percent a year matters when it sounds like nothing.
3. The one question to ask before buying any investment product that also promises insurance.
4. Why every number in your explanation needs a date attached to it.

Two rules for the page. Every time you use a term the reader would not know, either explain it in the same sentence or delete the sentence and try again. And put one number in each answer, computed rather than recalled, showing your working in a line the reader could redo on a phone calculator.

Journal prompt. Open your own statements before answering, because the value of this entry is that it is about your money rather than the module's.

Write down the total expense ratio of every fund you hold and the plan each one is in. If any is a regular plan whose scheme also offers a direct plan, compute what the wedge is costing you a year at your current holding, and write that number down in rupees or dollars rather than in points.

Then write down the three largest leaks in your own arrangements, ranked in currency, and for the largest one write a single sentence naming the action available to you, what it would be worth, and what has stopped you taking it so far. The last clause is the one that matters, and it is the only part of the entry nobody else will ever see.

Finally, list every rate you used in this exercise and, beside each, the source you would go to if you had to defend it and the date you last read it there. Any rate with a blank in either column is a rate you do not actually know. Put a date in your calendar, one year out, to check the blanks.