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 and the expense ratios on four of them. Securities transaction tax came off two share trades. A dividend was taxed at the top slab and a capital gain at 12.5%, and all the while the currency bought 4.9% less each year than the year before. Those are five leaks, every one of them legal, disclosed and findable. 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.

If you can't do this arithmetic, that doesn't make you a worse investor than someone who can. It makes you 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 course 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 here is the working rule, stated once and given a name. 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. Before you use it for anything real, 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. Quote a tax rate from memory in a client meeting and you're 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 base expense ratio (its total expense ratio less the statutory levies) 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 in the worked examples below is M0.04's, cited and not 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, 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 here, not 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, and the worked examples apply that card to a portfolio without 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. Here a policy is only 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, so no futures or options tax appears below.

Core teaching content

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 until the very 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. Don't subtract one percentage from another.

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. It produces this ladder:

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

Three habits fall out of that table, and they're what to take with you.

Rank in currency and leave percentages for later, 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. Treat the audit as a habit you keep.

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, never 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 wouldn't buy this stock today with the cash, you're 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 doesn't pay tax. You do. 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 transaction-cost toolkit, applied here and not rebuilt. On delivery equity, securities transaction tax is 0.10% each side, the exchange transaction charge 0.00297% each side, the regulator turnover fee ₹10 per crore each side, and stamp duty 0.015% on the buy side only. There's also 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, and leave the rounded ones in the table above for display. 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, meaning the money that actually left your pocket and came back to it, 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 instead of accruing it at year end changes the answer to 16.9119%, a difference of 1.00 basis point, so the year-end simplification is stated and then used.

Step 8, in real terms. Deflate, don't 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. Check the index fund's own tracking first. Its net asset value compounded at 11.5736% against the index's 12.15%, a tracking difference of 57.64 basis points. Its stated 20 basis points of expense explains a third of that. The other 37.64 basis points is unexplained, and it's 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. Pay attention to what the audit doesn't say, because it matters more than what it does. It doesn't 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 doesn't extrapolate either. Two years is a sample of one path, and the rolling-window arithmetic in the factsheet material is the corrective. And it doesn't 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, and it's set by contract, so no market can take it away. 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 arithmetic settles three of them. Sell the vested units unless you'd buy the stock with cash. Take the match to the cap, because 50% isn't 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. The remaining ₹95,500 goes each year into 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, and 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 really can't tolerate a falling statement, and an indefensible one for somebody who was never told the trade existed. The 6.63% isn't a bond yield either. Only the sum assured is contractual and the bonuses are discretionary, so you can't compare it against a government security. The surrender arithmetic makes the decision nearly irreversible, so get it right at the point of sale. Year three is too late.

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 one decision that changes the outcome is the withdrawal rate. A rate of 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, so the performance fee at 20% is ₹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, and a sample isn't 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 coupons reinvested at 6% net. Its redemption gain is exempt for an individual who subscribed at issue and holds to maturity, and from 1 April 2026 a bond bought on the exchange is taxed on that gain. 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. That's the feature of the instrument people misunderstand most. 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, and 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. The arithmetic can't tell you 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. The health savings account's advantage is real but conditional. It exists only against qualified medical spending and needs a particular health plan to fund it, so its dollars aren't 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 and 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 isn't tax-free income. It's 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 you read its solution. Peeking feels efficient and teaches you far less. 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 this tests the arithmetic and not 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 2.10% is ₹10.50 crore. Next ₹250 crore at 1.90% is ₹4.75 crore. Next ₹1,250 crore at 1.60% is ₹20.00 crore. Next ₹3,000 crore at 1.50% is ₹45.00 crore. Next ₹5,000 crore at 1.40% is ₹70.00 crore, taking the running total to ₹10,000 crore. Above that the rate steps down 0.05 points per ₹5,000 crore band: 1.35% on 10,000 to 15,000, 1.30% on 15,000 to 20,000, 1.25% on 20,000 to 25,000, 1.20% on 25,000 to 30,000, and 1.15% on the remaining ₹2,000 crore. Total permitted expense is ₹428.25 crore, a blended ceiling of 1.3383%, against a marginal band rate of 1.15%. They differ because the schedule is progressive: the fund keeps charging the higher tranche rates on the assets sitting in the lower tranches, just 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. Now convert it to a share of the gain, the figure that matters: 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 and not destroyed, and that's 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, and that's 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, and holders routinely fail to report them and so 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, so you don't get to choose it, 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 and never from memory.

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, as before: (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. Give yourself the full three hours the first time. 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. Don't subtract.

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 and have no 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. Each one 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 starts.

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 this entry is only worth something if it's about your money.

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. Points hide it.

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.