Institutional Investors: Objectives, Constraints and Allocation

Asset Allocation & Performance (Finance-Plus ring), Branch AA · Node AA1.05 · ~16 focused hours · Mastery gate >= 85%

A trustee of an Indian retirement trust opens the annual accounts and reads two figures. Assets, ₹640.00 crore. Present value of the promised benefits, ₹706.56 crore. The trust is 90.58% funded, which everyone in the room agrees is uncomfortable but survivable.

Nine months later the same two figures read ₹679.53 crore and ₹792.36 crore, and the funded ratio is 85.76%. Nothing was bought and nothing was sold. No company in the portfolio missed a forecast, no bond defaulted, and the equity index was flat. What happened is that the yield used to discount the promises fell by one percentage point, the promises are 11.18 years of modified duration long, and the assets are 6.18. The liability gained value nearly twice as fast as the assets did, and 4.82 points of funded ratio evaporated out of a decision nobody remembers making.

That is the institutional problem, and it is genuinely different from the one a person brings to an adviser. A person has a horizon that ends, a tax position, a spouse, and an opinion about volatility that moves with the market. An institution has a liability schedule, a board, a regulator, and in several cases a horizon that does not end at all. The seven-line skeleton looks the same on both sides, and every line in it means something different.

Six investor types run the institutional world and they agree about very little. A defined-benefit pension pays a schedule of promises, so its risk is measured against that schedule rather than against an index. A university endowment exists forever, which imposes a harder return requirement than any pension's. A private foundation looks like a small endowment until you notice its payout is set by statute rather than by its board. A bank holds securities as a liquidity and capital instrument, so a bond's accounting classification can matter more than the bond. A life insurer has written options it did not price as options. A casualty insurer has two liabilities, one paying out in months and one over a decade, and a tax code that reverses the ranking of two bonds.

The work here is not to memorise six templates. It is to read a mandate, find the constraint that is actually binding, price what it costs, and say so out loud. In the trust above, the mandate caps equity and equity-like assets at 20% of the portfolio, and against what the trustees would otherwise hold that cap costs 68.05 basis points of expected return every year, which compounds to ₹744.83 crore of forgone terminal value over twenty-five years on a ₹640 crore base. The duration hedge those same trustees argued about for two meetings costs 4.74 basis points. One of those numbers deserved the meeting time.

Sixteen hours, in that order: the constraint sets, the six types with their arithmetic, a comparison matrix that fits on one page, and the governance question that decides whether any of it can be implemented. Budget roughly six hours on the core content, three on the worked examples, three on the practice set, three on the mini-project and one on the cards and the gate.

Learning objectives

You can:

1. Rewrite the seven-line investment policy skeleton for an institution, stating for each line what changes when the client is a legal entity with a board rather than a person, and defend each change against the private-client version.
2. Compute a funded ratio, a liability duration and a currency-duration hedge ratio from a stated benefit schedule, and explain why matched durations under-hedge whenever assets are smaller than liabilities.
3. Solve for the asset duration a stated hedge ratio requires, test it against a mandate's investment limits, and state which of the two binds.
4. Run a ten-year spending-rule comparison across the simple, smoothed, hybrid and banded-inflation families, and report the distribution volatility and terminal real corpus each one produces.
5. Derive a foundation's required return from its payout floor, its fee load, its excise tax and its inflation assumption, and show why the additive shortcut understates it.
6. Classify a bank's securities book as held to maturity or available for sale, compute the capital consequence of each under a stated capital rule, and price the liquidity trap the safer-looking classification creates.
7. Diagnose spread compression on a guaranteed insurance block, computing the book yield after a stated share of assets rolls at a lower reinvestment rate, and identify the break-even reinvestment rate.
8. Compute a casualty insurer's blended payout duration and its after-tax yields under the proration rule, and show that the same two bonds rank in opposite orders for an insurer and for an ordinary taxpayer.
9. Classify a sovereign fund into the five-type taxonomy from its own stated mandate, and derive the horizon, the liquidity requirement and the risk tolerance that follow from the classification.
10. Price a binding constraint in basis points against a named alternative, including the constraint governance capacity imposes, and write the one-page finding a board can act on.

Prerequisites & connections

Builds on. AA1.01 supplies the frontier, the policy portfolio and the strategic-versus-tactical split; every policy portfolio derived here is a point on machinery that module built. AA1.02 supplies risk budgeting, the funded ratio and the surplus-volatility arithmetic, and its duration-gap example is the direct ancestor of the first worked example here, which extends it into the hedge-ratio decision rather than repeating it. FI1.02 supplies modified duration, convexity and the approximation's error term. M3.01 supplies present value and the annuity formulas used to discount every liability schedule below. PW1.01 supplies the private-client policy statement, the contrast case throughout. M1.12 supplies pension accounting, including how a discount rate is chosen and what a remeasurement does to reported equity.

Feeds forward. AA1.04 builds the capital-market expectations a policy portfolio consumes, and the mini-project below takes its table as an input. AA1.06 and AA1.07 take the institutional mandate as given and ask how to fill it with managers. FI1.06 owns liability-driven investing as a fixed-income discipline, including cash-flow matching, immunisation and the derivative overlays a mandate-constrained trust reaches for when the cash bond market cannot deliver the duration. AL1.04 takes the allocation question into private markets and real assets, where the governance constraint developed here bites hardest.

Deliberate non-overlaps. PW1.01 owns the private-client policy statement in full: human capital, the ability-versus-willingness split, tax-aware location, estate transfer and the concentrated-position unwind. What appears here is the institutional contrast, line by line, and never the private-client derivation. AA1.02 owns risk budgeting, risk parity and the funded-ratio arithmetic at the allocation level, and it owns the goals-based bucket framework; both are cited and extended here, never rebuilt. AA1.01 owns mean-variance optimisation and the constrained frontier, so the policy portfolios below are stated and priced rather than optimised. M1.12 owns pension accounting, so the discount-rate choice, the service and interest cost, and the remeasurement mechanics live there and not here. M5.01 owns banks as businesses and M5.03 owns insurers as businesses, including underwriting analysis, reserve adequacy and embedded value; both appear below only as investors deploying a portfolio under a regulator's rules. ES1.02 owns the regulatory architecture itself, so every rule cited below carries a verify flag and a pointer to its primary source rather than a re-teaching of the regime.

Core teaching content

What changes when the client is an institution

Four things change, and each one lands on a different line of the policy statement.

The first is the liability. A person's spending is a preference that can be revised; a pension's benefit schedule is a promise that cannot. Once a liability exists, the portfolio's job stops being to earn a good risk-adjusted return and becomes to fund the schedule, and those point in different directions often enough to matter. A portfolio that maximises the Sharpe ratio and a portfolio that minimises the volatility of the funded ratio are different portfolios, and the second one holds more long-dated bonds than any Sharpe-maximising investor would tolerate. The trust in the opening lost 4.82 points of funded ratio in a period when its assets rose 6.18%. Its assets did well and its funding did badly, and only a liability makes those two statements compatible.

The second is the board. A private client can be persuaded in an afternoon. An institution decides through a committee that meets quarterly, whose members are volunteers with day jobs, whose composition turns over on a fixed cycle, and whose minutes are discoverable. Each of those facts is a constraint on strategy, and the governance section below prices them.

Third is the perpetuity. An endowment or a sovereign savings fund has no terminal date, which sounds like the most permissive constraint imaginable and is one of the tightest. It does not mean the portfolio can wait out anything. It means the portfolio must serve a claimant who does not yet exist, and intergenerational equity is a budget line that shows up as a return floor.

Fourth is the regulator. A person's legal constraints are mostly about what they may hold in which wrapper. An institution's are frequently quantitative: this share in government securities, that cap on equity, a single-issuer limit, a capital charge that varies with what you own. A quantitative constraint can be priced, which is the analyst's opening; a qualitative one cannot.

Hold those four apart. Most mistakes in institutional work come from treating a board problem as a portfolio problem, or a liability problem as a benchmark problem.

The institutional policy statement, line by line against the private-client version

The document has the same seven lines on both sides. Read them side by side and the differences are where the work is.

Two of those rows deserve a second look, because they are the ones authors get wrong.

The tax row is the one people wave away. An institution is described as tax-exempt and the analysis stops. A United States private foundation pays an excise tax on its net investment income; a property and casualty insurer loses part of a municipal bond's exemption to a proration rule; a cross-border holding suffers withholding at source that a treaty may or may not recover. Tax exemption is a claim about one tax, and there is always another one.

The willingness row is genuinely different rather than merely more complicated. A person's willingness to bear risk is a psychological fact you can measure, argue with and sometimes change. A committee's willingness is a political fact: the point at which a trustee starts asking, in a minuted meeting, why the fund owns what it owns. That threshold is real, it is usually lower than the fund's ability, and writing it into the policy statement as a maximum drawdown or a maximum funded-ratio fall is one of the more honest things a chief investment officer does.

The comparison, on one page

The matrix is a diagnostic rather than a summary. Run a new mandate across the seven columns, find the row it most resembles, and then find the one column where it does not fit that row. That column is almost always where the interesting work is.

Governance capacity as a constraint, and what it costs

An investment committee constrains strategy in the same way a regulatory cap does, and it can be priced the same way.

Three features decide what a committee can hold. How often it meets, which sets the fastest the portfolio can respond to anything. What it can underwrite, which is a function of staff rather than of members, since assessing a private-equity manager is a full-time skill and reading a quarterly report is not. And how long its members serve, because a strategy whose payoff arrives in year eight cannot be defended by a committee whose median tenure is four.

The delegation decision follows. A board that meets twice a year with no investment staff should not run a tactical overlay, should not select individual managers, and should not hold anything whose valuation it cannot independently challenge. Delegating to a discretionary manager or an outsourced chief investment officer costs a fee and buys decision speed the board does not otherwise have, and stating that as a price rather than as an admission of inadequacy is what gets it decided sensibly.

Price the constraint directly. Put private equity at 9.80% against public equity at 7.40%, an illiquidity premium of 2.4000 points, and suppose the fund would have held 15% in a private programme if it could govern one. Not holding it gives up 36.0000 basis points a year, which on $250 million over twenty-five years is $129.972456 million of terminal value, or 8.73%. At a 25% allocation the same arithmetic gives 60.0000 basis points and at 5% it gives 12.0000. The size of the programme the committee can supervise sets the price, so the honest question at a board meeting is not whether private markets are attractive but how large a programme this particular board can govern.

Two cautions. The number assumes the illiquidity premium is real and earned, which the alternatives work examines rather than grants. And it ignores manager dispersion in private markets, where the gap between a top-quartile and a bottom-quartile fund is wide enough that a badly governed programme can return less than the public index it replaced. A committee that cannot select managers does not earn the average of the asset class; it earns whatever it can access.

Two anchors: an Indian retirement mandate and a US university endowment

Institutional investing is a set of local rules wearing a common vocabulary, so end on two real anchors with their binding constraints identified.

Start in India. The Employees' Provident Fund Organisation manages retirement savings under a notified pattern of investment specifying permitted categories and their percentage bands, and it began investing in equity through exchange-traded funds in August 2015, at 5% of incremental flows, raised in later years. (Both facts are public record and are cited as history rather than current policy. Check the pattern in force, the equity share of incremental flows and the declared interest rate against the Ministry of Labour and Employment's notifications and the Central Board of Trustees' announcements.) The binding constraint on a mandate of that shape is not the equity cap that gets the headlines. It is that the pattern applies to incremental flows against an enormous corpus, so a change in the cap moves the portfolio slowly enough that its real cost is measured over a decade. The second is the declared rate credited to members, a liability with a floor set annually by a body that is not the investment manager, which attaches the life insurer's guarantee problem to the pension's schedule problem.

Now the United States. Yale University publishes its endowment spending policy in its annual endowment report, a hybrid of the family described above that weights prior-year spending most heavily and applies the target rate to market value at the remainder. (Check the weights and target rate for the year in question; both have been revised.) The NACUBO-Commonfund Study of Endowments publishes average effective spending rates across the US universe each year, which is where to check whether a stated policy rate and a realised effective rate agree. (Check the current year's figure.) The binding constraint on a large US endowment is neither the spending rate nor any regulation. It is the share of the portfolio in illiquid partnerships set against the share of the university's operating budget the endowment funds, because those two together decide what happens in a year when the distribution must be paid, capital calls arrive, and nothing can be sold at a price anyone will accept. The 2008 to 2009 episode made that visible across the sector, and the usual response was a stated liquidity policy expressed as years of distributions coverable from liquid assets, which is the endowment's version of the stabilisation fund's ninety-day sleeve.

Common mistakes & how experts think differently

1. Matching asset duration to liability duration and calling the plan hedged. Tempting because the two numbers are printed side by side and matching them looks like the obvious move. A plan at 90.58% funded that matches durations is hedged to 90.58% of its rate exposure, not to 100%. An expert works in currency duration, assets times duration against liabilities times duration, and treats underfunding as an unhedged rate position in its own right.

1. Reading the funded ratio as a solvency statement rather than as a quotient of two moving numbers. The trust in the first worked example loses 4.82 points of funded ratio in a period when its assets rise 6.18%. An expert asks what the ratio's own duration is before asking whether its level is comfortable.

1. Assuming tax exemption means no tax. A foundation pays excise tax; a casualty insurer loses part of a municipal exemption to proration; a cross-border position bleeds withholding. An expert asks which tax, at what rate, on what base, and whether the institution is currently a taxpayer at all, since a loss carry-forward turns a tax-driven allocation into a give-up.

1. Choosing a spending rule on its label rather than on its realised effective rate. A board adopts a hybrid believing it has adopted a 5% policy, and the ten-year mean effective rate comes out at 5.2841%. An expert computes the effective rate a rule produces on a realistic path before the board votes, and sets the budget-volatility column beside the terminal-corpus column so the trade is visible.

1. Treating a securities classification as an accounting decision. Held to maturity keeps a loss out of equity and out of capital right up to the moment the bank needs the cash, and then it protects nothing and taints the rest of the book. An expert prices the classification against the deposit base that can leave, which is the only variable deciding whether the protection is ever tested.

1. Hedging a guaranteed insurance block on duration alone. Duration handles the present-value hit and does nothing about the reinvestment hit arriving at the same instant, from the same move, against a floor that has not moved. An expert reports the break-even reinvestment rate and the share of the book that rolls before renewal, in basis points of margin rather than years of gap.

1. Arguing about the wrong constraint. In the first worked example the mandate's equity cap costs 68.05 basis points a year and the duration hedge costs 4.74, and committees reliably spend more time on the second. An expert prices every candidate constraint against a named alternative first, and lets the ranking set the agenda.

1. Building a strategy the governance cannot run. A twice-yearly committee with no staff cannot select private managers, supervise a derivative overlay or rebalance inside a band. An expert treats governance capacity as a hard constraint with a stated price and offers delegation as a priced trade rather than as a verdict on the board. The related error is importing the private-client framework wholesale: ability against willingness is a real distinction for a person and a category error for a committee, where the threshold belongs in the document as a stated maximum drawdown, decided in calm weather.

Worked examples

The figures come out of computation rather than from a retyped rounded display, and the full-precision values for all of them are collected at the end of the practice set.

Worked example 1: A funded ratio, a hedge ratio and a mandate that binds (India, ₹)

The Sahyadri Cements Employees' Retirement Trust (synthetic) owes a benefit schedule that pays ₹38.00 crore at the end of year one and escalates 5.00% a year for twenty-five years. The trust's stated actuarial discount rate is 7.10%. Assets are ₹640.00 crore, held as 52% government securities at a sleeve modified duration of 9.20, 30% corporate and public-sector debt at 4.60, 3% short-term debt at 0.40, 12% equity index units and 3% units of real-estate and infrastructure trusts, with the last two treated as carrying no direct rate sensitivity by convention. The mandate permits 45% to 65% in government securities, 20% to 45% in other debt, up to 5% short-term, 5% to 15% equity, and up to 5% in trust units. The longest available government bond is a forty-year issue priced at par to yield 7.10%.

Solution. Step 1, value and measure the liability. The final payment is ₹122.553798 crore and the undiscounted total ₹1,813.629755 crore. Discounting each payment at 7.10% gives a present value of ₹706.563187 crore, a Macaulay duration of 11.974452 years, a modified duration of 11.180627 and a convexity of 180.228826. Cross-check with the growing-annuity closed form, 38.00 / (0.071 - 0.05) x [1 - (1.05/1.071)^25], which returns ₹706.563187 crore to within 2.3 x 10^-12.

Step 2, the funded ratio. 640.00 / 706.563187 = 90.579302%, a deficit of ₹66.563187 crore.

Step 3, the asset duration and the currency-duration hedge ratio.

Asset currency duration is 640.00 x 6.176000 = ₹3,952.640000 crore per unit of rate move; liability currency duration is 706.563187 x 11.180627 = ₹7,899.819746 crore. The hedge ratio is 50.034559%. The duration ratio, 6.176/11.181 = 55.24%, would have overstated the hedge by more than five points.

Step 4, solve for the required asset duration. A 70% hedge needs 0.70 x (706.563187 / 640.00) x 11.180627 = 8.640428 years. A full hedge needs 12.343468 years, longer than the liability's own duration because the assets are the smaller pool.

Step 5, test it against the mandate. The forty-year par bond has a Macaulay duration of 14.114104 and a modified duration of 13.178435. At the mandate's limits, 0.65 x 13.178435 + 0.30 x 8.00 + 0.05 x 0 = 10.965983 years, a maximum hedge ratio of 88.840367%. The 70% target is reachable and a full hedge is not, at any permitted weighting, which is a finding about the mandate rather than about the portfolio.

Step 6, build the policy portfolio. Hold equity at its 15% cap and trust units at their 5% cap, keep short-term at 3%, and split the remaining 77%:

w_gsec x 13.178435 + w_corp x 4.60 + 0.03 x 0.40 = 8.640428,   w_gsec + w_corp = 0.77
w_gsec = 59.293192%   w_corp = 17.706808%   asset modified duration = 8.640428 (exact)
expected return 7.950094%, against the current portfolio's 7.859000%

Step 7, shock it. Rates fall 100 basis points to 6.10%. Revaluing the liability exactly, by re-discounting all twenty-five payments, gives ₹792.357030 crore, a rise of 12.142416%. The duration-only approximation gives +11.180627% and ₹785.561384 crore; adding convexity gives +12.081772% and ₹791.928537 crore, still ₹0.428494 crore short of exact, which is what a second-order approximation on a long liability at a large move looks like.

Funded ratio falls from 90.579302% to 85.760128% unhedged and to 87.750687% hedged, so the hedge protects ₹15.772338 crore of surplus and 1.99 points of funded ratio.

Step 8, price the constraints. The trustees, unconstrained, would hold 30% equity, 8% trust units, 40% government securities, 20% corporate debt and 2% short-term, for an expected return of 8.678000%. The best the mandate permits is 15% equity, 5% trust units, 52%, 25% and 3%, for 7.997500%. The cap costs 68.0500 basis points a year, ₹744.8308 crore of terminal value over twenty-five years on ₹640 crore. The hedge, inside the mandate, costs 4.7406 basis points. The cap costs 14.35 times what the hedge costs.

Read it. The trust's exposure was never a market view. It was the arithmetic gap between an 11.18-year promise and a 6.18-year portfolio, and closing 70% of it was affordable while 100% sat outside the mandate. Two numbers should reach the trustees: the mandate costs 68 basis points a year, and full immunisation needs either a rule change or a swap. What the analysis does not say is that the hedged portfolio is better in every state. Rates rising instead of falling would have made the unhedged book look clever. A hedge is not a forecast; it is a decision to stop being paid for a risk nobody chose to take.

Worked example 2: Four spending rules over one ten-year path (US, $)

The Cascade Ridge University Endowment (synthetic) opens at $1,200.0 million with a 5.00% target spending rate. Distributions are taken at the start of each fiscal year out of the prior year-end market value; the remainder earns that year's return. No gifts arrive, and returns are net of investment expense. The ten-year nominal return path is +14.2%, +8.6%, -18.4%, +22.1%, +6.3%, +11.0%, -6.5%, +15.8%, +4.2%, +9.4%. Inflation is 2.1%, 2.4%, 3.8%, 5.9%, 3.2%, 2.6%, 2.2%, 2.5%, 2.3%, 2.4%. For the smoothed rule, the three-year history before year one is flat at $1,200.0 million.

The four rules: simple, S = 5.00% x MV(t-1); three-year smoothed, S = 5.00% x mean of the last three year-end values; hybrid, S = 0.70 x S(t-1) x (1 + inflation) + 0.30 x 5.00% x MV(t-1), with year one at 5.00% of the opening value; banded, S = S(t-1) x (1 + inflation) clipped so the effective rate stays between 4.25% and 5.75% of the prior market value.

Solution. Step 1, the path's own statistics. Geometric mean 6.051379%, arithmetic mean 6.670000%, standard deviation 11.624978% at ddof=1. Cumulative inflation 33.535403%, a deflator of 1.335354.

Step 2, run the four rules. Distributions, in $ million:

Step 3, verify the accounting identity. Year one: (1200.000000 - 60.000000) x 1.142 = 1301.880000, which is the recorded corpus exactly. Year three: (1343.149596 - 67.157480) x 0.816 = 1041.209567, exact. Year ten: (1244.054991 - 62.202750) x 1.094 = 1292.946353, exact. If that identity does not hold to machine precision, the distribution has been taken from the wrong base and every column below it is wrong.

Step 4, the summary statistics.

Read it. The hybrid protects the operating budget best, holding the worst single-year cut to 2.35% against the simple rule's 22.48%, and it pays for that with $25.30 million more distributed over the decade and $38.25 million less nominal corpus at the end. The simple rule protects the spending discipline perfectly, at a mean effective rate of exactly 5.0000%, and hands the university a cut no institution absorbs gracefully. Smoothing behaves in the year after the crash exactly as its reputation predicts, distributing $9.5294 million more than the simple rule out of a corpus that has just fallen 18.4%, and then very nearly gives it back over the following six years, ending $0.2556 million behind on $1.29 billion.

The table does not license a general claim about which rule preserves capital. This is one path: the budget-volatility ranking is a property of the rules and holds anywhere, while the terminal-corpus ranking is a property of this path's shape. Every column also loses about 20% of the corpus in real terms across the decade, because a 5% rule on a 6.05% geometric return against 2.9% average inflation does not preserve purchasing power. That is the finding a board should take away, and no choice among the four rules fixes it.

Worked example 3: A foundation's required return, and its half-life (US, $)

The Halden Foundation (synthetic), a US private non-operating foundation, holds $250.0 million. It faces a 5.00% minimum qualifying distribution, pays 0.62% in investment management and custody, pays the 1.39% excise tax on net investment income, and assumes 2.40% long-run inflation. (The payout minimum and the excise rate are statutory; check both against the current Code text and the foundation's tax counsel. The excise rate has been amended.)

Solution. Step 1, the shortcut, and why it is wrong. Adding payout, fee and inflation gives 8.020000%. It omits the excise tax, which resists being added as a flat cost because it is charged on the investment income the portfolio produces, and that is the quantity being solved for.

Step 2, solve it properly. Require that the corpus end the year worth 1 + inflation times its opening value after all outflows:

R - [ 0.0500 + 0.0062 + 0.0139 x (R - 0.0062) ] = 0.0240
R x (1 - 0.0139) = 0.0240 + 0.0500 + 0.0062 - 0.0139 x 0.0062 = 0.08011382
R = 8.124310%

The excise tax adds 10.4310 basis points to the requirement.

Step 3, verify by simulating one year. On $250.0 million at 8.124310%: gross $270.310775 million; less $12.500000 million of qualifying distribution, $1.550000 million of investment expense and $0.260775 million of excise tax; closing corpus $256.000000 million. The corpus needed to hold purchasing power is 250.0 x 1.024 = $256.000000 million. The difference is zero to machine precision.

Step 4, the half-life at realised returns.

The third row is a check rather than a scenario. At the required return the real corpus neither grows nor shrinks, which is what solving for it meant, and a row that came back with any drift in it would mean the solution was wrong.

Read it. One percentage point of realised return moves the foundation's half-life from thirty-three years to sixty-two, and nothing else on its balance sheet has that leverage. The number bites harder here than at an endowment because the payout floor is statutory: an endowment whose returns disappoint can cut its distribution and a foundation cannot. Set a comparable endowment beside it, board policy 4.50% and fees 0.70% against 2.50% inflation, requiring 7.700000% against the foundation's 8.305720%, and the statutory floor costs 60.5720 basis points a year.

One limit is worth stating. The 2.40% inflation assumption is doing as much work as any statutory number here, and it is the input nobody verifies. A foundation using 2.4% while its grant-making sector inflates at 4% has an intergenerational-equity problem no allocation solves.

Worked example 4: Held to maturity against available for sale, and the trap (US, $)

Cordillera National Bank (synthetic) holds $9,500.0 million of common equity tier 1 against $95,000.0 million of risk-weighted assets, a ratio of exactly 10.00%. Its securities book is $20,000.0 million par of ten-year US Treasuries bought at par with a 3.20% annual coupon. Deposits are $85,000.0 million and cash is $4,000.0 million. The tax rate is 21%. Yields rise 200 basis points.

Solution. Step 1, the bond mathematics. At a 3.20% yield the bond prices at 100.000000, as it must, with a Macaulay duration of 8.713995, a modified duration of 8.443794 and a convexity of 85.756363. At 5.20% the exact price is 3.20 x [1 - 1.052^-10]/0.052 + 100/1.052^10 = 84.705432, a fall of 15.294568%. The duration-plus-convexity approximation gives -8.443794 x 0.02 + 0.5 x 85.756363 x 0.0004 = -15.172460%, an error of 12.2107 basis points, which is the second-order term running out of road at a 200 basis point move.

Step 2, the loss. 20,000.0 x (100 - 84.705432)/100 = $3,058.913505 million pre-tax, x 0.79 = $2,416.541669 million after tax.

Step 3, the three treatments. Treasuries carry a zero risk weight, so risk-weighted assets stay at $95,000.0 million throughout.

Common equity under generally accepted accounting principles is $7,083.4583 million in the first two rows alike, a fall of 25.437281%.

Step 4, spring the trap. Deposits fall 12%, which is $10,200.0000 million. Cash covers $4,000.0 million, leaving $6,200.0000 million to be raised from the securities book. At 84.705432 that requires selling 6,200.0000 / 0.84705432 = $7,319.483319 million of par, 36.597417% of the book. Check the proceeds: 7,319.483319 x 0.84705432 = $6,200.000000 million, exact. The realised loss is $1,119.483319 million pre-tax and $884.391822 million after tax, so CET1 falls to $8,615.6082 million and the ratio to 9.069061%.

Step 5, the second-order consequence. Selling from the held-to-maturity category calls the whole category's stated intent into question. The remaining $12,680.5167 million of par carries a further $1,532.1498 million of after-tax loss, and if the category is reclassified, CET1 lands at $7,083.4583 million and the ratio at 7.456272%, exactly where the marked available-for-sale case sat from the first day.

Read it. The classification never changed the economics. It changed when the economics became visible, which made the bank's crisis arrive as news rather than as a trend. Silicon Valley Bank announced on 8 March 2023 the sale of about $21 billion of available-for-sale securities at an after-tax loss of about $1.8 billion, and was closed within two days; verify those figures against the company's filing of that date. The rule the arithmetic supports is narrower than the anecdote: the size of an unrealised loss matters far less than the size of the deposit base that can force its realisation, and no accounting election changes that ratio.

Worked example 5: A guaranteed block, and where the margin actually goes (India, ₹)

Sanchay Life Assurance (synthetic) runs a non-participating guaranteed-savings block paying ₹640.0 crore a year for twenty-five years, valued at a 6.40% discount rate. Backing assets are ₹8,900.0 crore with a book yield of 6.90% and a modified duration of 7.60. The guaranteed credited rate is 4.50% and maintenance and administration cost 0.55% of assets.

Solution. Step 1, the block. Present value 640.0 x [1 - 1.064^-25]/0.064 = ₹7,879.397344 crore, which the term-by-term discounting confirms to within 6.4 x 10^-12. Macaulay duration 9.896685 years, modified 9.301396, convexity 136.144455.

Step 2, the mismatch, read correctly. Assets over the block's present value is 112.952801%. The asset duration is 1.701396 years shorter than the liability's, which looks like a serious under-hedge. In currency terms the hedge ratio is 8,900.0 x 7.60 / (7,879.397344 x 9.301396) = 92.291663%, and the asset duration needed for a full hedge is 7,879.397344 x 9.301396 / 8,900.0 = 8.234763 years, well short of the liability's own 9.30. Being over-assets is a partial hedge in exactly the way being under-assets was a leak.

Step 3, the spread, and what happens to it. The spread over the guarantee is 2.4000 points, ₹213.600000 crore a year. Roll 22% of the book, yielding 7.80%, at a reinvestment rate of 5.90%. The untouched 78% must be yielding (6.90 - 0.22 x 7.80)/0.78 = 6.646154%. The new book yield is 0.22 x 5.90 + 0.78 x 6.646154 = 6.482000% and the spread is 1.9820 points, ₹176.398000 crore. Roll a further 26% that was yielding 7.15% at the same 5.90% and the book yield falls to 6.157000%, the spread to 1.6570 points, ₹147.473000 crore. Two tranches have cost 74.3000 basis points, which is 30.958333% of the original spread.

Step 4, the break-even. Charge the 0.55% expense and the block breaks even when the fully rolled book yields 4.50 + 0.55 = 5.050000%. At the 5.90% on offer, a fully rolled book leaves 85.0000 basis points of margin, ₹75.650000 crore a year. Today's book yield of 6.90% covers guarantee plus expense with 185.0000 basis points to spare, so the entire exposure is the 100 basis point gap between 6.90% and 5.90%, multiplied by whatever share of the book rolls before the block runs off.

Step 5, the double hit. Rates fall 100 basis points. The block's present value rises 10.025335% to ₹8,669.333313 crore; the assets rise 7.600000% to ₹9,576.400000 crore; the funded ratio slips from 112.952801% to 110.462935%. At the same moment the reinvestment rate on every new rupee falls 100 basis points against a floor that has not moved.

Read it. Duration reports the first hit and is silent about the second, which is why matching duration does not hedge a guaranteed block. The number to put in front of a board is 85 basis points of margin at the current reinvestment rate, with the share of the book that rolls in the next three years. What the analysis cannot tell you is where reinvestment rates go, so the honest form of the finding is a break-even rather than a forecast: the block survives at any reinvestment rate above 5.05%, and the market is 85 basis points above that today.

Worked example 6: A casualty book's two liabilities and a tax rule that reverses an answer (US, $)

Blue Ridge Mutual Casualty (synthetic) holds $4,200.0 million of loss reserves, 62% short-tail at a payout duration of 1.15 years and 38% long-tail at 6.40 years. Policyholders' surplus is $2,100.0 million, net earned premium is $3,600.0 million, and the investment book yields 4.30% on $6,300.0 million of invested assets. The federal rate is 21% and the proration percentage is 25%.

Solution. Step 1, the two liabilities. Short-tail reserves $2,604.0000 million, long-tail $1,596.0000 million, blended payout duration 0.62 x 1.15 + 0.38 x 6.40 = 3.145000 years. Reserves are exactly 2.00 times surplus.

Step 2, the cycle. At a 95.5% combined ratio the underwriting result is 3,600.0 x (1 - 0.955) = $+162.0000 million, 7.714286% of surplus. At 112.0% it is $-432.0000 million, 20.571429% of surplus. Investment income is 6,300.0 x 0.043 = $270.9000 million, so the pre-tax operating result swings from $+432.9000 million to $-161.1000 million. The combined ratio at which investment income exactly offsets the underwriting loss is 1 + 270.9000/3,600.0 = 107.525000%.

Step 3, the proration arithmetic. The insurer's effective tax on municipal interest is 0.25 x 0.21 = 5.250000%.

The municipal's taxable-equivalent yield for the insurer is 4.074250 / 0.79 = 5.157278% against the corporate's 5.30%, and the municipal would need to yield 4.418997% to break even. Proration alone is worth a 22.5750 basis point swing, which is what turns an 11.3 basis point municipal advantage into an 11.3 basis point disadvantage. On a $1,000 million allocation the annual difference to the insurer is $1.127500 million.

Read it. The break-even combined ratio of 107.53% sets the portfolio's risk budget, because underwriting risk and investment risk draw on one pool of surplus and the cycle moves the draw without asking. The tax rows catch people out: two bonds, one tax rate, and the ranking reverses on a rule that lives in a single subsection of the code. The third row is the most important and the one an analyst forgets. A tax-driven allocation held by an institution that is not currently paying tax is a straight 100 basis point give-up, and casualty insurers cross in and out of that state with a cycle they do not control.

Worked example 7: Three sovereign mandates, classified and costed (US $bn, and a general obligation)

Three synthetic mandates arrive on the same desk.

Mandate A. "To insulate the annual budget from movements in the hydrocarbon price, maintaining sufficient resources to cover the budget deficit arising at a price below the fiscal break-even for a period of not less than three years." The country exports 1,850,000 barrels a day; the fiscal break-even is $68.00 a barrel; the fund holds $92.0 billion.

Mandate B. "To convert the nation's non-renewable resource wealth into a permanent financial endowment, transferring a real return to the budget annually while preserving the fund's purchasing power for future generations."

Mandate C. "To pre-fund the state pension scheme's projected deficit, with no withdrawals permitted before the eighteenth year and a projected run-off of forty years thereafter."

Solution. Step 1, classify. A is a stabilisation fund: short horizon, severe liquidity requirement, low risk tolerance. B is a savings fund: multi-generational horizon, minimal liquidity requirement beyond the annual transfer, the highest risk tolerance of the three. C is a pension reserve fund: long, finite and deferred, which is not the same as long.

Step 2, cost mandate A. Annual exports are 1,850,000 x 365 = 675.25 million barrels. At $46.00 against a $68.00 break-even the shortfall is $22.00 a barrel, so the annual revenue shortfall is $14.855500 billion.

The mandate's three-year promise therefore requires 48.441848% of the fund in instruments sellable inside ninety days without moving their own price. Total cover at this shortfall is 6.192992 years, and the oil price at which three years of cover exactly exhausts the fund is $22.584722 a barrel.

Step 3, measure mandate C's horizon. Nothing for eighteen years, then a level payment for forty, discounted at 5.00%. The present value per unit of annual payment is 7.129955 and the Macaulay duration is 32.377471 years. The same forty payments starting immediately have a Macaulay duration of 14.377471 years, so deferral adds exactly 18.000000 years. That equality is the check: shifting every cash flow by eighteen years must shift the weighted-average time by eighteen, so any other answer means the discounting is wrong.

Read it. Mandate A's allocation is decided by one line of arithmetic: half the fund is a liquidity sleeve because the mandate says three years, and the risk budget is whatever remains. Mandate B, on identical oil revenue in the same country, faces an annual transfer instead of a three-year draw and can carry a majority in growth assets. Mandate C cannot immunise at all, because a 32-year obligation is longer than any bond it can buy.

Two limits. The three-year cover requirement rests entirely on a $46.00 price assumption, so the honest presentation is the price at which cover fails, $22.58, rather than the cover at one assumed price. And the classification is a claim about purpose rather than behaviour: a fund whose stated mandate is stabilisation and whose practice is to accumulate has been reclassified by its politics, and should be analysed as what it does.

Practice set

Work each problem fully before reading its solution. A calculator is assumed. Numeric answers within 1% score as correct unless a reconciliation is demanded, in which case it must tie exactly.

P1 (guided). Funded ratio and the two ways to close a deficit. An Indian trust holds assets of ₹742.0 crore against a liability present value of ₹815.0 crore. Compute the funded ratio and the deficit, then state the two ways to reach 100% funding and quantify each.

Solution. Funded ratio 742.0 / 815.0 = 91.042945%; deficit 742.0 - 815.0 = -₹73.0000 crore. The first route is a sponsor contribution of ₹73.0000 crore. The second is an asset return, with the liability unchanged, of 815.0/742.0 - 1 = 9.838275%. Those two are not equivalent in risk: the contribution is certain and the return is a hope, which is why funding rules in most jurisdictions specify the first.

P2 (guided). Liability duration from a three-payment schedule. A US plan owes $120.0m at year 3, $260.0m at year 8 and $410.0m at year 15, discounted at 6.85%. Compute the present value, the Macaulay duration and the modified duration, showing the weights.

Solution. Present values: 120/1.0685^3 = $98.368866m, weight 24.399335%; 260/1.0685^8 = $153.030197m, weight 37.957487%; 410/1.0685^15 = $151.763020m, weight 37.643178%. Total $403.162083m. Macaulay = 3(0.24399335) + 8(0.37957487) + 15(0.37643178) = 9.415056 years; modified = 9.415056/1.0685 = 8.811470 years; convexity 105.633491. The weights must sum to 1.000000, which is the check that catches a mis-keyed exponent.

P3 (guided). The hedge ratio when assets and liabilities differ in size. A plan holds ₹880 crore at a modified duration of 6.20 against ₹1,000 crore of liabilities at 13.40. Compute the current hedge ratio, the asset duration required for a full hedge and for a 60% hedge, and state what simply matching durations would achieve.

Solution. Current hedge ratio = (880 x 6.20)/(1,000 x 13.40) = 40.716418%. Full hedge needs (1,000 x 13.40)/880 = 15.227273 years; a 60% hedge needs 0.60 x 15.227273 = 9.136364 years. Matching durations at 13.40 would give a hedge ratio of (880 x 13.40)/(1,000 x 13.40) = 88.000000%, still 12.0000 points short, because the plan is 88% funded and matched durations can never hedge more than the funded ratio.

P4. Simple against smoothed, over a crash. A $500.0m endowment spends 4.75% of prior market value under a simple rule, or 4.75% of a three-year average under a smoothed rule with a flat $500.0m history. Returns are +18.0%, -22.0%, +11.5%. Compute both distribution streams and both corpus paths, then state the year-three difference.

Solution. Simple: distributions $23.7500m, $26.6938m, $19.8322m; corpus $561.9750m, $417.5193m, $443.4212m. Smoothed: distributions $23.7500m, $24.7313m, $23.4496m; corpus $561.9750m, $419.0501m, $441.0946m. In year three the smoothed rule distributes $3.617396m more, which is 18.240044%, and leaves $2.326574m less corpus. That is the intergenerational transfer in a single number: the students of year three are $3.6m better off and every cohort after them is $2.3m worse off.

P5. A foundation's requirement. Payout 5.00%, investment expense 0.85%, excise tax 1.39%, inflation 2.75%. Compute the required nominal return exactly, and the error in the additive shortcut.

Solution. R(1 - 0.0139) = 0.0275 + 0.0500 + 0.0085 - 0.0139 x 0.0085, so R = 8.709243%. The additive shortcut gives 5.00 + 0.85 + 2.75 = 8.600000%, understating by 10.9243 basis points. The shortcut's error grows with the excise rate and with the required return itself, since the tax is charged on income the return produces.

P6. An available-for-sale mark and the capital ratio. A US bank holds $6,200.0m of CET1 against $62,000.0m of RWA and a $14,000.0m securities book that marks down 11.8%. Tax is 21% and the securities carry a zero risk weight. Compute the new ratio, then the markdown that would take the bank to a 7% buffered minimum.

Solution. Loss 14,000.0 x 0.118 = $1,652.0000m pre-tax, x 0.79 = $1,305.0800m after tax. CET1 falls to $4,894.9200m and the ratio from 10.000000% to 7.895032%, a fall of 2.1050 points. To hit 7%, CET1 may fall to 0.07 x 62,000.0 = $4,340.0m, so the tolerable after-tax loss is $1,860.0m, the pre-tax loss is 1,860.0/0.79 = $2,354.430380m, and the markdown is 2,354.430380/14,000.0 = 16.817360% of the book.

P7. Spread compression on a guaranteed block. An insurer's book yields 7.25% against a 5.00% guarantee. Thirty percent of the book, currently yielding 8.40%, rolls into a 5.55% market. Compute the new book yield, the new spread and the share of the original spread lost.

Solution. The untouched 70% yields (7.25 - 0.30 x 8.40)/0.70 = 6.757143%. New book yield = 0.30 x 5.55 + 0.70 x 6.757143 = 6.395000%. New spread = 6.395 - 5.00 = 1.395000 points, from 2.2500. The loss is 85.5000 basis points, which is 38.000000% of the original spread, out of a roll of only 30% of the book.

P8. Proration and the taxable-equivalent yield. A US property and casualty insurer compares a 3.95% municipal with a 5.05% corporate at a 21% federal rate and a 25% proration percentage. Compute both after-tax yields, the municipal's taxable-equivalent yield, and the municipal yield at which the insurer is indifferent.

Solution. Effective tax on municipal interest = 0.25 x 0.21 = 5.2500%. After tax: municipal 3.95 x 0.9475 = 3.742625%; corporate 5.05 x 0.79 = 3.989500%. The corporate wins by 24.6875 basis points. Taxable-equivalent municipal yield = 3.742625/0.79 = 4.737500%. Indifference municipal yield = 3.989500/0.9475 = 4.210554%, so the municipal is 26.1 basis points too cheap in yield terms to be worth holding here.

P9. Stabilisation cover. A fund of $140.0bn backs a budget breaking even at $74 a barrel for a country exporting 2,400,000 barrels a day. Oil is at $52. Compute the annual shortfall, the years of cover, and the liquid share the fund needs to promise four years of cover.

Solution. Annual shortfall = 2,400,000 x 365 x 22 = $19.272000bn. Years of cover = 140.0/19.272 = 7.264425. Four years of cover is 4 x 19.272 = $77.088bn, which is 55.062857% of the fund and must sit in instruments sellable inside the promise period.

P10. Pricing a binding constraint. Trustees would hold 35% equity at 11.40%, 10% trust units at 9.20%, 35% government securities at 7.10%, 18% corporate debt at 7.75% and 2% short-term at 6.60%. The mandate caps equity at 15% and trust units at 5%, and the constrained portfolio becomes 15/5/52/25/3. Compute the annual cost and the twenty-year cost on ₹1,000 crore.

Solution. Unconstrained E[r] = 0.35(11.40) + 0.10(9.20) + 0.35(7.10) + 0.18(7.75) + 0.02(6.60) = 8.922000%. Constrained = 0.15(11.40) + 0.05(9.20) + 0.52(7.10) + 0.25(7.75) + 0.03(6.60) = 7.997500%. The constraint costs 92.4500 basis points a year, and over twenty years on ₹1,000 crore, 1,000 x (1.08922^20 - 1.079975^20) = ₹865.9440 crore. Confirm both weight vectors sum to 1.000000 before believing either figure.

P11. Endowment against foundation on the same corpus. A $400.0m endowment sets a 4.50% board policy rate and pays 0.70% in fees against 2.50% inflation. A $400.0m foundation faces a 5.00% statutory payout, the same fees, the 1.39% excise tax and the same inflation. Compute both required returns, the annual gap and the thirty-year terminal difference.

Solution. Endowment = 4.50 + 0.70 + 2.50 = 7.700000%. Foundation = (0.0250 + 0.0500 + 0.0070 - 0.0139 x 0.0070)/(1 - 0.0139) = 8.305720%. Gap 60.5720 basis points a year. Terminal difference = 400 x (1.0830572^30 - 1.077^30) = $678.4803m. The gap is entirely a legal fact, not an investment one.

P12. A casualty book's blended duration and what it takes to match it. Reserves are 55% at a payout duration of 0.90 years, 15% at 2.80 and 30% at 7.20, on a $3,000m book. Compute the blended duration, the value change on a 100 basis point rise, and the share of reserves that would have to sit in a 5.5-year asset sleeve to match.

Solution. Blended = 0.55(0.90) + 0.15(2.80) + 0.30(7.20) = 3.075000 years. A 100 basis point rise changes the economic value of the reserves by 3.0750%, which is $92.2500m. Matching with a 5.5-year sleeve alone needs 3.075/5.5 = 55.909091% of the reserves in that sleeve, with the rest in cash. The blended figure hides the real problem, which is that the short-tail book cannot hold a 5.5-year sleeve at all: matching must be done line by line.

Full-precision reference for every computed figure

Worked Example 1: liability PV ₹706.563187 crore, Macaulay 11.974452, modified 11.180627, convexity 180.228826, revalued at 6.10% to ₹792.357030 crore. Asset duration 6.176000, expected return 7.859000%, funded ratio 90.579302%. Currency durations ₹3,952.640000 and ₹7,899.819746 crore, hedge ratio 50.034559%. Required asset duration 8.640428 at 70% and 12.343468 at 100%. Forty-year par bond Macaulay 14.114104, modified 13.178435; mandate maximum 10.965983 and 88.840367%. Hedged portfolio 59.293192% government and 17.706808% corporate, expected return 7.950094%. Post-shock funded ratios 85.760128% and 87.750687%. Constraint cost 68.0500 bp, hedge cost 4.7406 bp.

Worked Example 2: geometric mean 6.051379%, deflator 1.335354, distribution standard deviations 4.2987, 1.6429, 1.5578 and 2.7463, year-on-year 11.6737%, 3.7432%, 2.4616% and 2.8368%. Terminal real corpus 968.2424, 968.0509, 939.5980 and 943.5487. Mean effective rates 5.0000%, 5.0013%, 5.2841% and 5.2444%.

Worked Example 3: required return 8.124310% against an additive 8.020000%, excise 10.4310 bp; the one-year simulation closes at $256.000000m. Endowment comparison 7.700000% against 8.305720%, gap 60.5720 bp.

Worked Example 4: modified duration 8.443794, convexity 85.756363, price 84.705432. Loss $3,058.913505m pre-tax and $2,416.541669m after tax; ratios 7.456272% and 10.000000%. Forced sale $7,319.483319m par, after-tax loss $884.391822m, ratio 9.069061%.

Worked Example 5: PV ₹7,879.397344 crore, Macaulay 9.896685, modified 9.301396, hedge ratio 92.291663%, full-hedge duration 8.234763. Book yields 6.482000% and 6.157000%, break-even 5.050000%, margin 85.0000 bp or ₹75.650000 crore.

Worked Example 6: blended duration 3.145000, break-even combined ratio 107.525000%, after-tax yields 4.074250% and 4.187000%, taxable-equivalent 5.157278%, indifference 4.418997%.

Worked Example 7: annual shortfall $14.855500bn, three-year draw $44.566500bn or 48.441848% of the fund, cover 6.192992 years, exhaustion price $22.584722. Pension reserve PV 7.129955, Macaulay 32.377471, deferral exactly 18.000000. Governance: 36.0000 bp a year, $129.972456m over 25 years on $250m.

Applied mini-project

Write one institutional policy statement, derive its policy portfolio, and price its binding constraint. Budget about three hours. Pick one of the six investor types. The deliverable is three artefacts, each with a test it must pass.

Step 1, choose and source (about 25 minutes). Pick a real institution of your chosen type and find its actual constraint set from a primary document: a pension's annual report or its notified pattern of investment, an endowment's published spending policy, a foundation's Form 990-PF, a bank's regulatory capital disclosure, an insurer's statutory filing, or a sovereign fund's published mandate. Record the document, the page and the date you pulled it. Where a figure is perishable, say so on the page.

Step 2, the policy statement (about 50 minutes). Write the seven lines: return objective, risk tolerance, liquidity, horizon, tax, legal and regulatory, unique circumstances. Every line must contain at least one number and must name where the number comes from. The return objective must be derived, not asserted: a liability schedule discounted, a payout floor plus costs plus inflation, or a stated real-return target with the arithmetic shown.

Step 3, the policy portfolio (about 45 minutes). Using a capital-market-expectations table, state the portfolio your institution should hold and confirm it satisfies every constraint you recorded in step 1, row by row, with the slack in percentage points. Report its expected return and, where you have the covariance inputs, its expected volatility.

Step 4, price the binding constraint (about 40 minutes). State the portfolio you would hold if the single most restrictive constraint did not exist. Compute the difference in expected return in basis points, and compound it over the institution's stated horizon on its actual corpus. Then do the same for the second most restrictive constraint, so the ranking is visible rather than asserted.

Step 5, the one-page finding (about 20 minutes). Under 500 words: what the institution is for, what its portfolio should hold, which constraint binds, what that constraint costs in basis points and in currency over the horizon, and what would have to change for the constraint to lift. Close with one paragraph naming every place your numbers rest on an assumption rather than a source.

Four tests decide whether the artefacts count. Test 1: both weight vectors sum to 1.000000 and every constraint row shows its slack. Test 2: the return objective is reproduced from its own inputs, so a reader can rebuild it from the numbers on the page. Test 3: the constraint cost is computed against a named alternative portfolio rather than a vague unconstrained idea. Test 4: every perishable figure carries its source and the date it was checked.

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

Any artefact whose test fails scores zero on that row, however well the page is written. A priced constraint that rests on an unstated alternative portfolio is not a priced constraint, and a policy portfolio that has not been checked against every row of the mandate is a suggestion.

Reading & resources

Core (do these).

• CFA Institute, the Institutional Investors readings in the Portfolio Management curriculum: the standard treatment of the six types and the objectives-and-constraints structure used above. The comparison across types is the part worth committing to memory. [Paid] [Intermediate]
• Ministry of Labour and Employment, the notified pattern of investment for non-government provident, superannuation and gratuity funds: the primary source for what an Indian retirement trust may hold, and the document behind the synthetic mandate in Worked Example 1. Read the current notification rather than any summary of it. [Free] [Intermediate]
• IRDAI, the Investment Regulations and the master circulars issued under them: the primary source for an Indian insurer's investment pattern, including the government-securities floors and the approved-investment test. Perishable and amended regularly. [Free] [Intermediate]
• US Internal Revenue Code sections 4940, 4942 and 4945, with the Form 990-PF instructions: the excise tax, the minimum distribution and the taxable-expenditure rules that set a US private foundation's constraint set. The Form 990-PF instructions are the readable route in. [Free] [Intermediate]
• The US regulatory capital rule (12 CFR parts 3, 217 and 324) on the AOCI opt-out election and risk weights: the primary source for Worked Example 4's three treatments. Read the opt-out provision itself, which is short. [Free] [Advanced]

Going deeper.

• Swensen, Pioneering Portfolio Management: the case for the endowment model, made by the person who built it, including the spending-rule design and the governance argument that most readers skip and should not. [Paid] [Intermediate to Advanced]
• Tobin (1974), "What Is Permanent Endowment Income?", American Economic Review: the paper that put intergenerational equity on a formal footing, and short enough to read in a sitting. [Paid] [Advanced]
• NACUBO-Commonfund Study of Endowments, published annually: effective spending rates, allocation shares and returns across the US endowment universe, and the right place to check whether a stated policy rate matches a realised one. [Free summary, paid full] [Beginner]
• Ang, Asset Management: A Systematic Approach to Factor Investing, on liability-driven investing and on sovereign wealth funds: the clearest available treatment of why an institution's liability, rather than its risk appetite, sets its allocation. [Paid] [Advanced]
• The Santiago Principles (International Forum of Sovereign Wealth Funds), and Yale University's annual endowment report: the governance framework sovereign funds subscribe to, and a published spending policy with its weights stated, which together are the best pair of primary documents on how these institutions write their own rules. [Free] [Beginner to Intermediate]

Data and primary documents (free).

• SEC EDGAR for US bank holding company filings and insurer statutory-basis disclosures, and the FFIEC's Call Report and FR Y-9C data for securities-book and capital figures. [Free]
• EPFO and the Ministry of Labour and Employment for the Indian retirement mandate, IRDAI's annual report and handbook for insurer investment aggregates, and the IFSWF's member profiles for sovereign mandates as the funds themselves state them. [Free]

One exercise beats any of the reading above. Take an institution's published policy statement and try to reconstruct its return objective from the numbers in the document alone. Most of the time you will find you cannot, because one input is missing. That missing input is almost always the one doing the most work, and finding it is the whole skill.

Teach it back & journal

Feynman prompt. Explain to a trustee who has just been told the fund is "90% funded and duration-matched" why those two phrases together do not mean what they sound like. Use the actual arithmetic: ninety paise of assets moving for every rupee of liability, a currency-duration hedge ratio of 50.03% where the ratio of durations said 55%, and 4.82 points of funded ratio lost on a single 100 basis point fall in which the assets rose 6.18%. Then, without changing your tone, tell the same trustee that the hedge everyone has been arguing about is worth 4.74 basis points a year and the mandate's equity cap is worth 68.05, so the meeting has been spending its time on the smaller number. If your listener asks, unprompted, "what would it take to change the pattern of investment", you have taught the substance rather than the formula.

Journal prompt. Find one institution whose investment policy you can read in a primary document, of any of the six types, and work out its return objective from the numbers in the document alone. Write down what you found. Could you rebuild the objective, or was one input missing? Which single constraint in that document is binding, and can you price it against a named alternative portfolio rather than against a vague unconstrained idea? Then write a paragraph on the thing this whole area keeps teaching, which is that institutional portfolios are rarely wrong because someone had a bad view about markets. They are wrong because a constraint nobody priced was doing more damage than the risk everybody discussed, or because a rule adopted under one label turned out to run at a different number, or because a protection held right up until the moment it was needed. Which of those three failures is most likely in the institution you just read? And what one question, asked at the next meeting, would surface it a year earlier than it would otherwise appear?

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