> For the complete documentation index, see [llms.txt](https://laurence-wilse-samson.gitbook.io/textbooks/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://laurence-wilse-samson.gitbook.io/textbooks/financial-economics-claims-prices-holders/part-iv-the-investor-ecology/chapter_16_institutional_investors.md).

# Chapter 16: Institutional Investors

*Part IV: The Investor Ecology — Financial Economics: Claims, Prices, and Holders*

***

## Opening Episode: The Sellers Who Were Getting Richer

On Friday 23 September 2022, the UK Chancellor Kwasi Kwarteng delivered a "mini-budget" containing some 45 billion pounds of unfunded tax cuts, unaccompanied by a forecast from the Office for Budget Responsibility. The gilt market's verdict was quick. The thirty-year yield rose 22 basis points that day and 113 basis points over the three sessions to Tuesday 27 September, which on a bond of that duration is a price move on the order of a fifth.

The largest forced sellers into that fall were the least likely institutions in the market: British defined benefit pension schemes, whose obligations run decades out and whose members cannot ask for their money back. A scheme owes a fixed schedule of payments valued by discounting, so its liability behaves like a very long bond, and what a trustee fears is a *fall* in yields, which raises the cost of the promise while doing nothing for the assets. Liability-driven investment is the hedge against that, and it is bought with a small pot of collateral rather than a portfolio full of gilts: long gilts financed in repo, gilt total return swaps, interest-rate swaps. The hedge is levered by construction, and levered positions are margined daily.

So the rise in yields arrived as a demand for cash. Collateral calls went out; schemes met them by selling the most liquid asset they owned, which was gilts; the selling pushed long yields higher, which generated the next round of calls. Pooled LDI vehicles were calling capital on a timetable measured in hours from trustee boards that needed days.

Every basis point of that rise was making the sellers richer. A scheme's liabilities are longer than its assets, so a parallel rise in yields cuts the present value of what it owes by more than the value of what it holds, and the aggregate funded position of UK defined benefit schemes improved sharply over 2022. The institutions dumping gilts into a falling market were the ones the move had made solvent. Solvency was not the binding constraint. Producing cash by Thursday afternoon was.

It ended with a balance sheet that faces no collateral call. On the morning of Wednesday 28 September the Bank of England announced that it would buy long-dated gilts on whatever scale was required, for a strictly limited period, to arrest what it called a self-reinforcing spiral — a financial-stability intervention by a committee that was at that moment preparing to *sell* gilts for monetary-policy reasons. The whole 113 basis points came back off in a single session.

![Figure 16.9: September 2022](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-787f7b066f984bb694f71b55f07f452808305e79%2Ffig_16_09_september_2022.png?alt=media)

**Figure 16.9: September 2022.** The thirty-year gilt yield, daily, 1 September to 31 October 2022, with the ten-year drawn behind it for contrast: the shock landed on the long end, where the LDI hedges were. The mini-budget of 23 September added 22 basis points on the day and 113 over the three sessions to 27 September; the Bank of England's announcement on the morning of 28 September that it would buy long-dated gilts took the same 113 basis points back off in a single session, by a wide margin the largest one-day fall of the two months shown. Yields then climbed back to within four basis points of the pre-intervention peak while the facility was still open, and only fell for good after the fiscal policy itself was withdrawn. This is §16.2's paradox in one line: every basis point of the rise improved the funded status of the plans that were selling, because their liabilities fell faster than their assets. What failed was not solvency but the collateral call on the repo funding the hedge: this is the mechanism of Figure 16.2 with gilts as the collateral. Solvency improved while liquidity failed. *Source: Bank of England, government liability curve (nominal) daily spot rates, thirty-year and ten-year; author's calculations.*

Nothing about a gilt's promised cash flows changed in those five sessions. The sovereign's willingness to pay the coupons on its 2052 stock was not in question before the mini-budget or after it. What changed was who was able to hold the paper, and what the holders who could not had to pay someone else to take it. That is this book's thesis in miniature, and this chapter is where it is stated: **the constraints of the holders, not the cash flows of the claim, set the price.**

![Figure 16.10: The LDI spiral](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-3433908d5823179f29a6b61fbd828e2c914791e8%2Ffig_16_10_the_ldi_spiral.png?alt=media)

**Figure 16.10: The LDI spiral.** The loop of 23 to 28 September 2022, with each step's direction fixed by the one before it. Long gilt yields rise; the repo funding the hedge takes a collateral call; the call is due in hours and the scheme's other assets are not; the most liquid thing it holds is gilts, so gilts are sold; and the sale pushes long yields higher, which starts the loop again. Two features are worth naming. The loop is closed — the response to the shock is the shock — and it has no equilibrium inside itself, because nothing in it slows as the price moves; a scheme facing a call by Thursday is not more willing to sell at a worse price, it is equally obliged to. And the paradox on the right is not a detail. Every basis point of the rise made the sellers *richer*: a defined benefit scheme's liabilities are longer than its assets, so the aggregate funded position of UK schemes improved sharply over 2022. The institutions dumping gilts into a falling market were the ones the move had made solvent. What broke the loop was a balance sheet that faces no collateral call, announced on the morning of 28 September, and Figure 16.9 shows what it did to the price in a single session.

The schemes selling gilts that week belong to a class of holder most textbooks leave offstage. When retail investors bid up GameStop through Robinhood in January 2021 and asked who exactly they were trading against, the answer — "institutional investors" — named roughly $120 trillion of assets under management globally: pension funds, insurance companies, mutual funds and ETFs, sovereign wealth funds, endowments, which between them own the majority of publicly traded securities in developed markets. This chapter takes the *institutional view* of what that implies — the approach of Markus Brunnermeier, Hyun Shin, and Perry Mehrling, now central to how financial stability is understood. Rather than starting from a representative agent or a frictionless market, it asks who holds the assets, what rules govern them, and how their balance sheets and mandates shape prices. Leverage ratios, margin requirements, redemption terms, and regulatory constraints can force sales with fundamentals entirely intact.

This is the thesis chapter of Part IV, and of the book. Everything that follows in the ecology — the private funds of Chapter 18, the dealers of Chapter 19, the estimated demand curves of Chapter 20 — is an elaboration of one claim made here: **constrained capital moves prices**. Two things this chapter does not do. It does not cover the rise of index funds and ETFs; the passive revolution gets its own chapter, Chapter 17. And it does not rebuild the monetary layers of the money view, which belong to the companion volume; §16.4 explains the division.

***

## 16.1 The Institutional View of Financial Markets

### From Representative Agents to Institutional Realities

Standard asset pricing theory imagines a representative investor who holds the market portfolio and prices assets by their covariance with aggregate consumption. That framework yields the CAPM, the consumption-based model, and risk-neutral pricing, and it abstracts away from a fact the rest of this part cannot ignore: financial markets are populated by *institutions*, not individuals.

These institutions differ in fundamental ways:

| Dimension                  | Variation Across Institutions                                                                           |
| -------------------------- | ------------------------------------------------------------------------------------------------------- |
| **Liability structure**    | Pension funds have long-dated liabilities; MMFs have overnight liabilities                              |
| **Regulatory constraints** | Banks face capital requirements; insurance faces RBC; mutual funds face diversification rules           |
| **Investment mandates**    | Index funds must track benchmarks; endowments have spending rules                                       |
| **Redemption terms**       | Hedge funds have lockups; mutual funds offer daily liquidity                                            |
| **Leverage**               | Banks leverage 10-12x; mutual funds are held near 1x by an asset-coverage test; hedge funds lever 2-10x |
| **Tax status**             | Pension funds are tax-exempt; hedge funds pass through to taxable investors                             |

*Source: Author's construction; leverage ranges as in Table 16.7.*

These differences matter. When corporate bond spreads widen, an insurer at its risk-based capital constraint may be forced to sell, a pension fund with a thirty-year horizon may buy the dip, a leveraged hedge fund may face margin calls, and a mutual fund may face redemptions. The *aggregate* market response depends on who holds what, and what constraints they face.

Notice what this does to the pricing equation of Chapter 3. If the marginal holder of a corporate bond in March 2009 was an insurer at its capital floor, then the discount rate in that bond's price is that insurer's shadow cost of capital, not a representative household's marginal rate of substitution. The question Chapter 3 planted — *whose* $$m$$? — is answered institution by institution, and the answer changes with the state of the world.

### Balance Sheet Constraints and Fire Sales

The core mechanism is simple: **balance sheet constraints force sales, sales depress prices, price declines tighten constraints, triggering more sales**. This feedback loop, studied by Brunnermeier and Pedersen (2009), explains why asset prices can deviate dramatically from fundamentals during stress.

Consider a simplified balance sheet. An institution holds $100 of securities, funded by $90 of debt — repo or margin — and $10 of equity, a leverage ratio of 10x. Now let securities prices fall 5%: assets are worth $95, the debt is unchanged, equity has absorbed the whole loss and stands at $5, and leverage is 19x. Figure 16.3's top panel draws the two balance sheets as a before/after pair.

![Figure 16.3: Leverage amplification is convex](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-10153f9ce7241c96459fc0fa8e0f4908b8b21b6a%2Ffig_16_03_leverage_amplification.png?alt=media)

**Figure 16.3: Leverage amplification is convex.** Panels (a) and (b): the two illustrative balance sheets of §16.1 as a before/after pair — a 5% fall in securities prices halves equity and takes leverage from 10x to 19x. Panel (c): L′ = L(1−κ)/(1−Lκ) against κ for L = 5, 10 and 25, with the linear approximation L(1+(L−1)κ) drawn dashed to show where it fails, and a chevron on the top frame wherever a curve leaves the panel rather than ending there. The approximation holds only while Lκ ≪ 1, and the interesting cases are the ones where it does not. *Source: Author's construction; balance sheets as in §16.1.*

The institution's leverage has nearly doubled. Facing a leverage constraint — say a 15x maximum — it must either raise equity, which is difficult in a crisis, or sell. To restore 10x leverage with $5 of equity it must shrink assets to $50, selling $45 of securities. That forced selling depresses prices further, and may trigger constraints at other institutions.

> **Key Equation: Leverage Dynamics**
>
> Let $$L = A/E$$ be leverage, where $$A$$ is assets and $$E$$ is equity. If asset prices fall by fraction $$\kappa$$, and debt is fixed, new leverage is:
>
> $$
> L' = \frac{A(1-\kappa)}{E - A\kappa} = \frac{A(1-\kappa)}{A/L - A\kappa} = \frac{L(1-\kappa)}{1 - L\kappa}
> $$
>
> For small $$\kappa$$: $$L' \approx L(1 + (L-1)\kappa)$$
>
> **Interpretation:** Higher initial leverage means greater amplification from a price decline. The approximation holds only while $$L\kappa \ll 1$$, and the interesting cases are the ones where it does not: at $$L=10$$ and $$\kappa = 5$$ percent, $$L\kappa = 0.5$$ and the exact formula gives $$L' = 19$$ — the near-doubling computed on the balance sheets above, not the $$14.5$$ the linear approximation suggests. Amplification is itself convex in the size of the shock.

The algebra assumes that $$E$$ is a well-defined number, and on a real institution's accounts it is not; **Appendix C** owns the accounting — book equity against regulatory capital, and the statement conventions that make an insurer's equity a different object from a dealer's — and is self-contained.

This is why the 2008 crisis was so severe: investment banks ran at 25-35x, so a decline in mortgage-backed securities forced sales that depressed prices that tightened constraints across the system. Section 16.5 develops the dynamics; the rest of this section establishes who the institutions are and what binds them.

***

## 16.2 Pension Funds and Insurance Companies

### Pension Funds: The Patient Capital

Pension funds are among the largest institutional investors, with US retirement assets measured in the tens of trillions of dollars, and they come in two varieties whose investment implications differ completely. **Defined benefit (DB)** plans promise a specific benefit at retirement, usually a function of salary and years of service, and the sponsor must generate the returns to meet it. **Defined contribution (DC)** plans — 401(k)s, dominantly — fix the contribution instead and leave the investment risk with the employee.

| Feature                | Defined Benefit            | Defined Contribution         |
| ---------------------- | -------------------------- | ---------------------------- |
| Investment risk bearer | Employer/sponsor           | Employee                     |
| Liability duration     | 15-25 years (mature plans) | Varies by employee age       |
| Investment horizon     | Very long                  | Varies                       |
| Asset allocation       | 60/40 to LDI               | Target-date or self-directed |
| Regulatory framework   | ERISA, PBGC                | ERISA (lighter)              |
| Assets (US, 2023)      | \~$3.0 trillion            | \~$7.9 trillion              |

*Source: Investment Company Institute, US retirement market, 2023; cross-checked against Department of Labor EBSA, Private Pension Plan Bulletin (Historical Tables and Graphs), Table E10, which puts private-sector defined benefit assets at $2.99 trillion at year-end 2023. Both sources agree at this precision. The DB figure covers private-sector plans and the DC figure 401(k) plans specifically; neither includes IRAs, other DC plan types, or the state and local government plans that keep the public-sector DB system large. Chapter 2's Table 2.4 reports the wider aggregates, and Table 2.6 the DB share of all private pension assets.*

![Figure 16.5: Defined benefit to defined contribution](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-20569ab7b4b64b4a57b94cb6d5dc5794cac32f0a%2Ffig_16_05_defined_benefit_to_defined_contribution.png?alt=media)

**Figure 16.5: Defined benefit to defined contribution.** The US retirement market by vehicle, at the dates the Investment Company Institute publishes, with the three defined benefit systems separated from 401(k) plans, other defined contribution plans, IRAs and annuities. The dashed line is the top of the promise: everything below it is somebody else's obligation to pay a stated benefit, and everything above it is an account balance worth what the market says today. Read the two facts together. The promise falls from 53 percent of the retirement market in 1995 to 28 percent now — and the level of the promise did not fall at all. The three defined benefit systems are together larger in dollars than they have ever been, and the state and local system in particular has more than quadrupled. What changed is the share, and with it the identity of the holder: one balance sheet with a liability, a duration target and a professional making allocation decisions, against millions of balance sheets with a default option. This is the vehicle-level cut of the same rotation Chapter 2's Figure 2.5 draws from the Financial Accounts; the two differ because the Z.1 puts annuities inside insurance reserves and does not separate 401(k) plans from other defined contribution plans. *Source: Investment Company Institute Fact Book, US retirement market assets. Author's calculations.*

**Table 16.1: US Pension Fund Asset Allocation (2023)**

| Asset Class              | DB Plans | DC Plans (401k) |
| ------------------------ | -------- | --------------- |
| Equities (domestic)      | 28%      | 42%             |
| Equities (international) | 15%      | 18%             |
| Fixed income             | 32%      | 25%             |
| Real estate              | 8%       | 3%              |
| Alternatives (PE, HF)    | 12%      | 2%              |
| Cash/other               | 5%       | 10%             |

*Source: Investment Company Institute, Willis Towers Watson*

The shift from DB to DC is the single largest change in the ownership of American financial claims in the past half century, and it is not neutral for prices. A DB plan is one balance sheet with a liability, a duration target, and a professional making allocation decisions. A DC plan is millions of balance sheets with a default option. Chapter 14 works through what households do with that discretion; Chapter 17 works through where the money ends up.

### Liability-Driven Investment (LDI)

**Liability-driven investment (LDI)**, the most important development in pension fund management of the past two decades, is the opening episode's hedge stated generally: match the assets to the liability rather than simply maximize the return. The liability is a series of promised payments to retirees, valued as

$$
PV\_{liabilities} = \sum\_{t=1}^{T} \frac{B\_t}{(1+r\_t)^t}
$$

where $$B\_t$$ is the benefit payment at time $$t$$ and $$r\_t$$ is the discount rate. So **pension liabilities behave like long-duration bonds**, and a plan holding short-duration assets is mismatched: falling rates raise the present value of what it owes while leaving what it holds relatively unchanged.

A plan that hedges this mismatch becomes a structural buyer of duration, for reasons having nothing to do with the expected return on long bonds — the preferred-habitat demand of Chapter 9's holder section, arriving from the liability side.

**What September 2022 was a case of.** Two features of the opening episode generalize past it. The first is that solvency and liquidity are separate constraints and only one was binding: the sellers were the archetypal patient investor, liabilities decades away and no redemption risk, and the rise in yields *improved* their funded status — but a collateral call is a demand for cash on a date rather than a claim on net worth. Solvency improved while liquidity failed. The second is that the positions were correlated. Every scheme held the same hedge against the same instrument and got the same call on the same morning, so the trade each had to do was the trade that made the position worse for all of them. Leverage, daily margining, and correlated positions add up to systemic risk with nobody having been wrong about fundamentals — and the leverage that mattered appeared nowhere on the schemes' balance sheets, a problem §16.5 returns to when it tabulates leverage by institution.

**The endowment's version of the same problem:**

A university endowment has no promised benefit payments and so, apparently, no liability at all. In practice it has one, written by its own trustees: a **spending rule**, most commonly a fixed percentage of a trailing average of market value, which converts the portfolio into an obligation to fund a stable share of the operating budget every year. The form of the rule does the work. A payout tied to current market value transmits every market decline straight into next year's budget, and a board that knows this holds less risk; a payout smoothed over several years, or one blending a target rate with an inflation-adjusted floor, absorbs the shock inside the endowment and permits a more volatile and less liquid portfolio. The mechanism is LDI's exactly — a liability rule dictating the asset choice — except that the endowment writes its own liability and can rewrite it. Chapter 18 §18.6 asks what that permission is worth in claims that cannot be sold.

### Insurance Companies

Insurance companies are natural long-horizon investors with relatively predictable liabilities, stretching decades into the future in the life lines. Those liabilities are written against counterparties who know more about their own risk than the insurer does, which is what forces the deductibles, exclusions, and coverage limits every policy carries; the screening apparatus behind that — Rothschild and Stiglitz's separating equilibrium, and the result that it rations the *low*-risk buyer — is set out in Chapter 24, Box 24.2, which uses this section's setting and serves the material here.

**Table 16.2: Insurance Company Investment Allocations (US, 2023)**

| Asset Class                | Life Insurers | P\&C Insurers |
| -------------------------- | ------------- | ------------- |
| Corporate bonds            | 45%           | 25%           |
| Government bonds           | 15%           | 35%           |
| Mortgage-backed securities | 12%           | 8%            |
| Equities                   | 3%            | 18%           |
| Mortgages/real estate      | 12%           | 5%            |
| Policy loans               | 5%            | -             |
| Other                      | 8%            | 9%            |

*Source: NAIC, Federal Reserve*

Insurance companies also face **risk-based capital (RBC)** requirements, which attach a capital charge to each asset class and rating bucket and so make required capital a function of portfolio composition. Box 16.1 sets out the schedule and reads it as a price list; the tilt toward investment-grade credit in Table 16.2 is what that price list buys.

**The "Reach for Yield" Problem:**

When interest rates are low, insurers face a dilemma: their liabilities promise policyholders a crediting rate that safe assets no longer cover, which creates pressure to "reach for yield" by buying riskier assets. Through 2010-2020 that took four forms — extending duration, moving down the credit spectrum from AAA toward BBB, increasing allocations to private credit and alternatives, and writing more variable annuities, which shifts the risk to the policyholder.

Becker and Ivashina (2015) show that this is measurable within the rules rather than around them: insurers systematically bought the highest-yielding bond available inside each regulatory rating bucket, which is exactly the behavior a coarse capital charge invites. The reach for yield concentrated risks across the insurance sector, creating potential for correlated stress if rates rose sharply (as they did in 2022).

***

> **Box 16.1 — The capital charge as a price list**
>
> Required capital is set asset class by asset class and rating bucket by rating bucket. Holding equities requires 75 times the capital of holding AAA corporate bonds, and government bonds carry no charge at all, which is most of the explanation for the shape of a life insurer's portfolio.
>
> **Table 16.3: Illustrative RBC Factors, US Life Insurers**
>
> *Source: NAIC*
>
> Read the table as a price schedule rather than a rulebook. The jump from 1.3% at BBB to 4.6% at BB is the reason the investment-grade boundary is the sharpest discontinuity in the corporate bond market: an insurer facing a downgrade of a holding across that line sees its required capital more than triple on an asset whose cash flows did not change that morning. Forced selling around downgrades — "fallen angel" dynamics — is the direct consequence, and it is why insurers are the marginal holder whose constraints show up in credit spreads (Chapter 10).

| Asset Class         | RBC Factor (Life) |
| ------------------- | ----------------- |
| Government bonds    | 0.0%              |
| AAA corporate bonds | 0.4%              |
| BBB corporate bonds | 1.3%              |
| BB corporate bonds  | 4.6%              |
| Equities (common)   | 30.0%             |
| Real estate         | 10.0%             |

![Figure 16.7: The capital charge schedule](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-9721b40141c64acfe62bcb1fe31ff6c5906e4022%2Ffig_16_07_the_capital_charge_schedule.png?alt=media)

**Figure 16.7: The capital charge schedule.** Table 16.3 on a logarithmic axis, which is the scale the schedule is actually built on. Read left to right it is a price list: what an insurer must hold in capital against each dollar of each claim, and therefore what each claim costs it to own. Two features carry the section's argument. The step from BBB to BB more than triples the charge, from 1.3 to 4.6, at a boundary no cash flow crosses — which is why a downgrade produces selling rather than a shrug, and why the investment-grade line is the sharpest discontinuity in the corporate bond market. And common equity costs seventy-five times what AAA does, which is the whole explanation for a life insurer holding three percent equities in a portfolio a pension fund would run at sixty. The zero at the left is not a rounding: government bonds attract no charge at all, which is why a log axis cannot place the bar and why the schedule's top and bottom are separated by more than two orders of magnitude rather than by degree. *Source: NAIC risk-based capital factors, as printed in Table 16.3.*

***

### The Liability Side Drives the Asset Side

Table 16.2 is usually read as a statement about preferences. It is better read as a statement about liabilities. Two insurers holding opposite portfolios are not disagreeing about expected returns; they are writing different promises.

**Life insurers** sell claims whose *timing* is uncertain for any one policyholder and highly predictable in aggregate: mortality obeys a law of large numbers, and a book of a million policies has a payout schedule an actuary can project decades ahead. The resulting liability is long, nominal, and rate-sensitive, valued like a pension obligation by discounting a fixed schedule, and it has one natural asset-side answer — long-dated investment-grade credit held to maturity, plus private placements and commercial mortgages paying an illiquidity premium the insurer can capture because nobody can demand the money back on short notice. Hence 45% corporate bonds and 3% equities.

The qualification is that "nobody can demand the money back" is not quite true. Life liabilities carry embedded options — policy loans, surrender rights, guaranteed minimum benefits on variable annuities, and funding agreements that behave like wholesale debt — each exercised against the insurer precisely when rates move against the insurer's portfolio. Koijen and Yogo (2015) show what happens when the constraint binds: during the 2008-2009 stress, life insurers cut prices on policies that generated favorable statutory accounting treatment, selling long-dated claims well below actuarial value to relieve a capital constraint. An institution that sells its own liabilities cheap to raise regulatory capital is doing on the liability side exactly what a fire-selling hedge fund does on the asset side.

**Property and casualty insurers** write a different claim. Timing is short for property and auto, long for liability and workers' compensation, but in every line the *severity* is uncertain, not merely the date: a hurricane season is one draw from a fat-tailed distribution, and the claim arrives as a demand for cash within months. Two consequences follow. P\&C portfolios hold far more government paper (35% versus 15%), because the asset sold to pay claims after a catastrophe cannot be an asset whose price falls when catastrophes happen. And P\&C surplus — capital in excess of reserves — is genuinely long-horizon money with no promised crediting rate, so it can go into equities (18% versus 3%). Berkshire Hathaway's balance sheet is an extreme version of that arithmetic.

The general point is the one this book keeps making from different directions: an institution's demand curve for an asset is a function of the claims it has written. Insurers are the largest private holders of long-dated corporate credit not because they have a view on credit but because they owe money in 2050.

### Catastrophe Bonds and Insurance-Linked Securities

Insurance is also an issuer. A catastrophe bond is a security sold by an insurer or reinsurer, usually through a special purpose vehicle, whose principal is forgiven if a defined event occurs — a trigger tied to the sponsor's own losses, to an industry-loss index, or to a parameter such as a wind speed or an earthquake magnitude at a stated location. The proceeds sit in a collateral trust in short-dated government paper; investors earn a spread over the collateral yield for bearing the event risk, and lose principal if the event happens. Insurance-linked securities (ILS) generalize the structure to collateralized reinsurance, industry loss warranties, and sidecars.

For a portfolio theorist this is close to an ideal asset. Hurricane risk has almost no beta: whether a storm makes landfall in Florida is uncorrelated with the marginal utility of consumption in any model in Part II, and a claim with a positive expected return and no systematic risk should be bid until its spread collapses. Every large diversified investor should hold some.

They do not. Outstanding catastrophe bonds are measured in the tens of billions of dollars — an order of magnitude smaller than the capital supporting traditional catastrophe reinsurance, and a rounding error against the $120 trillion of Table 16.4. The reasons are the chapter's reasons, not the theory's. Underwriting the risk requires a vendor hazard model, a claim about a non-stationary climate, and a specialist team, so the fixed cost of participating is high relative to any position an allocator could take; most institutional mandates have no bucket for it, since it is not credit, not equity, and not rated in a way an RBC or Solvency framework recognizes cheaply; and the sponsor side often prefers traditional reinsurance, which offers reinstatement, relationship pricing, and no basis risk between the trigger and the actual loss. Froot's (2001) study of the catastrophe reinsurance market reached the same conclusion by a different route: prices for cat risk stand far above actuarially fair levels, and the best explanation is not investor risk aversion but the limited and specialized capital willing to supply the cover.

So the market is small and expensive because of who can hold it, which is this chapter's thesis in an unusually clean setting. Chapter 8 §8.6's demand-based option pricing is the same story told about a different claim.

***

## 16.3 Delegation and the Asset Management Industry

### The Rise of Delegated Asset Management

The modern financial system is characterized by *delegation*: individuals delegate investment decisions to professional managers, and the delegation creates its own agency problems and constraints.

**Table 16.4: Global Assets Under Management by Institution Type (2023)**

| Institution Type       | AUM ($ trillions) | Share |
| ---------------------- | ----------------- | ----- |
| Mutual funds           | $63               | 52%   |
| Pension funds (DC)     | $27               | 22%   |
| Insurance              | $18               | 15%   |
| Sovereign wealth funds | $11               | 9%    |
| Hedge funds            | $5                | 4%    |
| Private equity         | $8                | 7%    |
| **Total**              | \~$120            | -     |

*Source: ICI, Preqin, SWFI. Categories overlap.*

### Mutual Fund Constraints and Behavior

Mutual funds are the most common vehicle for retail investment. In the US, mutual funds hold approximately $27 trillion in assets (2023), roughly equal to US GDP.

**Key Regulatory Constraints (1940 Investment Company Act and the SEC rules under it).** The first four are routinely quoted as blanket statutory prohibitions. None is quite that, and the differences matter for what actually binds:

1. **Diversification (statutory, and elective):** a fund that *elects* "diversified" status cannot, within 75% of its assets, hold more than 5% in any single issuer or more than 10% of an issuer's voting securities. A fund may instead register as non-diversified, and must then say so.
2. **Concentration (a disclosed policy, not a ceiling):** investing more than 25% in a single industry is not prohibited. A fund must adopt and disclose a concentration policy and may change it only with shareholder approval, so the familiar 25% figure is a commitment to its own investors rather than a cap the Act imposes.
3. **Illiquidity (open-end funds):** under the SEC's liquidity risk management rule, an open-end fund cannot hold more than 15% of net assets in illiquid investments. Closed-end funds and the private funds of Chapter 18 are outside the rule.
4. **Leverage (constrained, not prohibited):** Section 18's asset-coverage test requires 300% coverage for bank borrowing — at most one dollar of debt for every two dollars of net assets — which in practice keeps open-end funds close to unlevered rather than barring borrowing outright.
5. **Daily pricing:** Must calculate and publish NAV daily
6. **Redemptions:** Must honor redemption requests within 7 days

These constraints shape behavior in three well-documented ways. **Benchmark hugging:** a fund evaluated against an index faces career risk from significant underperformance, so it holds a portfolio close to the index and takes active positions only where conviction is highest. **Window dressing:** holdings are reported quarterly, and a manager has an incentive to sell losers and buy winners before the reporting date, making the portfolio look more prescient than it was. **Flow-performance:** investors chase returns, and asymmetrically, since outflows from poor performers exceed inflows to strong ones.

**Table 16.5: Flow-Performance Sensitivity (Equity Mutual Funds)**

| Performance Quintile | Net Flows (% of assets) |
| -------------------- | ----------------------- |
| Bottom 20%           | -8%                     |
| 20-40%               | -2%                     |
| 40-60%               | +1%                     |
| 60-80%               | +4%                     |
| Top 20%              | +12%                    |

*Source: ICI, academic studies*

The asymmetry creates fragility: a fund facing outflows must sell to meet redemptions, which can depress prices and trigger more outflows. Viewed from the manager's side rather than the market's, the same relationship is the engine of the Berk-Green equilibrium in Chapter 17. Note what it does in combination with constraint 4. A mutual fund can lever only slightly, so it is rarely forced to sell by a margin call — but it can be forced to sell by a redemption, and the redemption is triggered by exactly the price declines that a margin call would be. The constraint differs; the fire-sale mechanics of §16.1 do not.

### The Agency Problems of Delegation

When investors delegate to managers, they face the classic principal-agent problem — the manager's interests may diverge from the investor's — in three ways worth naming. A manager evaluated against a benchmark cares about *relative* performance: losing 15% against a benchmark that lost 20% counts as outperformance, which rewards systematic risk that moves with the benchmark over the search for uncorrelated alpha. A manager paid a percentage of assets under management has an incentive to gather assets rather than merely to invest them, to avoid the appearance of closet indexing while still hugging the benchmark, and never to close a successful fund to new money. And a manager with a career has an incentive to lose money the way everyone else is losing it, because losing it differently is what gets people fired.

> **Keynes on Institutional Herding:**
>
> "Worldly wisdom teaches that it is better for reputation to fail conventionally than to succeed unconventionally."
>
> — J.M. Keynes, *General Theory* (1936), Chapter 12

These agency problems help explain several market phenomena: institutional herding amplifies price trends, which is momentum; career risk deters contrarian positions, which is a limit to arbitrage; and correlated trading amplifies price swings, which is excess volatility. The second of these is the hinge between this chapter and Chapter 15. Behavioral finance explains why mispricings appear; delegation explains why they persist. A manager who can identify a mispriced security but expects it to widen before it converges faces the possibility of being redeemed out of the position before being proved right — the Shleifer-Vishny problem, arriving here as an institutional fact rather than a modeling assumption.

***

## 16.4 The Hierarchy of Money and Credit

Perry Mehrling's "money view" starts from a simple insight: *not all dollars are created equal*. There is a hierarchy of money and credit, and an instrument's price depends on its position in it.

The monetary layers of that hierarchy — reserves, deposits, and the dealer system that ties them together — are developed fully in *International Finance*, Chapter 2; here we need the portfolio layers, which Figure 16.1 sets out.

![Figure 16.1: The hierarchy of money and credit](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-15868a165d8e4d71c9c2e4c82ec3eaa564bbe12d%2Ffig_16_01_money_hierarchy.png?alt=media)

**Figure 16.1: The hierarchy of money and credit.** Instruments ordered by the reliability of the promise behind them, from central bank reserves at the top to residual claims at the base. The ordering is not a ranking by risk in the variance sense: credit instruments are promises to pay money, and the hierarchy orders them by how reliable the promise is. The tiers widen downward to draw that ordering and nothing else: a layer's width says how far down the hierarchy the instrument sits, not how much of it exists. Spreads between adjacent layers are small in normal times and explode in a crisis, and the arrow up the outside of the left slope is that crisis — a flight to quality is everyone climbing the hierarchy at once. *Source: Author's construction, after Mehrling (2011).*

Walk down it. Central bank reserves need no promise — they *are* money. Government bonds are a promise by the sovereign that issues the currency; bank deposits a promise by regulated institutions with access to that sovereign's central bank; money market instruments short-term promises by creditworthy issuers; corporate bonds longer-term promises by firms that may default. Equities make no promise at all, since dividends are discretionary. In normal times the layers trade at small spreads to each other and the hierarchy is flat; in a crisis everyone climbs it at once and the spreads between layers explode. The flight to quality is not irrational: it reflects the institutional reality that promises further down may not be kept.

![Figure 16.4: The hierarchy steepens](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-f9932645e229e08f46e7c3e0dbb7f31ed78e4087%2Ffig_16_04_the_hierarchy_steepens.png?alt=media)

**Figure 16.4: The hierarchy steepens.** Panel (a) is Table 16.6 drawn: the spread each layer pays over Treasuries, in calm markets and at the 2008 peak. The hierarchy is nearly flat in normal times — a quarter point separates agency MBS from Treasuries, and four points separate high yield from them — and in crisis it fans out to twenty-one. What the flight to quality does is not shift every promise down by a constant; it prices the *distance* between promises, and the distance is not a fixed property of any of them. Panel (b) puts the same idea on series a reader can still fetch, and the reason for the second panel is itself worth stating. The ICE BofA option-adjusted spreads behind panel (a) are no longer free at this history: the Federal Reserve's mirror now serves a rolling three-year window, and the vintage archive was reset with it, so nothing recovers the past. The substitutes drawn here — Moody's seasoned Aaa and Baa yields and the thirty-year mortgage rate, each less the ten-year Treasury — reach back to 1971 and cover both episodes, but they are monthly averages of seasoned bond yields rather than daily option-adjusted spreads, so they run well below panel (a) at the peaks and the high-yield layer has no free counterpart at all. The ordering and the steepening carry across; the levels do not. *Source: Table 16.6 as printed; Moody's seasoned Aaa and Baa corporate bond yields, the 30-year mortgage rate and the 10-year Treasury constant maturity via the FRED mirror. Author's calculations.*

**Table 16.6: Credit Hierarchy Spreads (Normal vs. Crisis)**

| Instrument    | Spread to Treasuries (Normal) | Spread to Treasuries (Crisis 2008) |
| ------------- | ----------------------------- | ---------------------------------- |
| Agency MBS    | 0.25%                         | 1.80%                              |
| AAA corporate | 0.60%                         | 6.00%                              |
| A corporate   | 1.20%                         | 8.50%                              |
| BBB corporate | 2.00%                         | 11.00%                             |
| High yield    | 4.00%                         | 21.00%                             |

*Source: FRED, Bloomberg*

The key insight: **liquidity is not a property of an asset; it is a property of a balance sheet position**. A Treasury bond is liquid for a mutual fund that can sell it without constraint. The same bond is illiquid for a leveraged hedge fund facing a margin call, because selling triggers losses that worsen the margin position. Which is why the useful thing to do with the pyramid is to locate each institution on it, and Figure 16.14 sets two balance sheets side by side to make the point.

![Figure 16.14: Two balance sheets on the pyramid](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-ccfc8743dd178bf83980edd94b83eea23e09ffd5%2Ffig_16_14_two_balance_sheets.png?alt=media)

**Figure 16.14: Two balance sheets on the pyramid.** Money market fund and pension fund T-accounts side by side, each with its asset-side and liability-side layer positions marked against Figure 16.1: L2 is bills and deposits, L3 repo, commercial paper and MMF shares, L4 credit, L5 residual claims. The MMF holds assets one layer below deposits and issues a claim its holders treat as sitting at the deposit layer; that gap is the whole business, and with no capital buffer and no insurance behind it, it is why MMFs are fragile. The pension fund is the mirror image — assets at the base of the pyramid, a promise its beneficiaries regard as near the top, made possible only because the promise is not redeemable on demand. *Source: Author's construction; allocations illustrative, as in §16.4.*

MMF shares function as "shadow money": institutional cash management that pays a little more than a bank deposit, with no capital buffer and no deposit insurance standing behind the par promise. That gap is the whole business and it is the whole fragility — in 2008, when the Reserve Primary Fund "broke the buck," its holders ran. What protects the pension fund from the same run is that its promise is not redeemable on demand, and leveraged LDI removed exactly that protection: a repo liability with daily margining, attached to a portfolio held at the base of the pyramid, is how an institution with a pension fund's assets acquired a money market fund's fragility.

A dollar stablecoin belongs on the same picture, and locating it is more useful than arguing about whether it is money. It is a claim with an issuer, a holder base, a promise of redemption at par, and a reserve portfolio that has to be sold to honor the promise: an MMF-shaped position on the hierarchy, one layer below deposits on the asset side, issuing a claim its holders treat as sitting at the deposit layer — without the capital, disclosure, and liquidity apparatus that the 1940 Act and the money market fund rules wrap around the fund version. The runs of 2022 and 2023 were holders discovering what they actually owned: that an algorithmic coin's par promise had no reserve behind it at all, and that a fully reserved coin's reserve included an uninsured deposit at a bank that had just failed. Both are §16.5's mechanism with different nouns, and Chapter 2's Box 2.3 places the same claims on the master map of holders.

Between all of these sit dealers, who fund securities inventory with short-term repo and are therefore vulnerable to repo runs: when lenders refuse to roll, dealers must sell inventory, transmitting the shock across every market they make. Chapter 19 puts that balance sheet at the center.

***

## 16.5 Leverage, Fire Sales, and Margin Spirals

### Leverage and Procyclicality

A key feature of institutional finance is **procyclicality**: balance sheets expand when times are good and contract when times are bad, amplifying the cycle. The mechanism runs off a leverage target. When prices rise, equity increases, leverage falls below target, and the institution borrows to buy more, which pushes prices higher again; when prices fall, equity shrinks, leverage rises above target, the institution sells, and the sales push prices lower. This leverage cycle, formalized by Geanakoplos (2010) and Adrian and Shin (2014), helps explain why credit booms and busts are so severe.

**Table 16.7: Leverage Across Institution Types**

| Institution                 | Typical Leverage (Assets/Equity) | Notes                           |
| --------------------------- | -------------------------------- | ------------------------------- |
| Commercial banks            | 10-12x                           | Regulatory capital requirements |
| Investment banks (pre-2008) | 25-35x                           | Repo funding, mark-to-market    |
| Hedge funds                 | 2-10x                            | Prime broker margining          |
| Money market funds          | 1x (no leverage)                 | Cannot borrow                   |
| Pension funds               | \~1x (no leverage)               | Regulation prohibits            |
| Insurance companies         | 8-12x                            | Risk-based capital              |

*Source: Author's construction; indicative ranges from supervisory and industry reporting*

Higher leverage means greater sensitivity to asset price changes — and greater potential for destabilizing feedback loops. Funding *maturity* does the same work and appears in no column of the table: a lender who shortens the term of its funding buys itself the option to leave before the others do, which is privately sensible and collectively corrosive, since every shortening raises the chance that the borrower's remaining lenders are the ones left holding a run. The result is a rat race in which the equilibrium maturity is shorter than any lender would choose if all of them could commit, and the borrower's constraint tightens without any change in its leverage. The table also needs a warning: pension funds appear at 1x, and it was pension funds that had to be rescued in 2022. The leverage that matters is the leverage in the strategy, not the leverage on the audited balance sheet, and derivative overlays put it in places a levels table does not show.

### Margin Spirals and Liquidity Crises

Brunnermeier and Pedersen (2009) formalize the interaction between market liquidity (ease of trading) and funding liquidity (ease of obtaining financing). The key insight: **market liquidity and funding liquidity are mutually reinforcing**. Figure 16.2 draws the loop, with the haircut channel as its second arc.

![Figure 16.2: The margin spiral](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-0e5350e4613c3ce684a755c881f401ce2657ea50%2Ffig_16_02_margin_spiral.png?alt=media)

**Figure 16.2: The margin spiral.** The book's canonical constrained-capital loop: a price fall cuts mark-to-market equity, leverage rises, the constraint binds, the forced sale lands in a thin market, and the price impact deepens the fall — the five numbered steps round the ring, joined by solid arrows. The haircut channel is the second arc, drawn dashed and routed outside the ring: volatility rises, lenders raise haircuts, and the constraint tightens again with no change in fundamentals at all — a channel large enough that AAA ABS haircuts went from 3 percent to 50 percent between 2007 and 2008. Chapters 11, 15, 18, 19 and 26 cross-reference this figure rather than redrawing it. *Source: Author's construction, after Brunnermeier and Pedersen (2009); haircut magnitudes from Gorton and Metrick (2012), Table 16.8.*

This spiral can occur even if fundamentals are unchanged. It is a pure coordination failure: each lender rationally increases haircuts, but collectively they create the instability they fear.

Repo haircuts exploded during the crisis.

**Table 16.8: Repo Haircuts on Structured Collateral, 2007-2008**

| Collateral Type  | Haircut (Aug 2007) | Haircut (Dec 2008) |
| ---------------- | ------------------ | ------------------ |
| Treasury         | 0.25%              | 3%                 |
| Agency MBS       | 3%                 | 10%                |
| AAA ABS          | 3%                 | 50%                |
| AA/A ABS         | 8%                 | 70%                |
| High-yield bonds | 10%                | 40%                |

*Source: Gorton and Metrick (2012)*

A 50% haircut on AAA ABS means an institution needs $50 of equity to hold $100 of securities — leverage limited to 2x, where before the crisis $3 of equity carried the same $100. The haircut is worth treating as a price in its own right. It is set by lenders, it is not the interest rate, and it does not appear in any asset pricing model in Part II. Yet a move from 3% to 50% is a 94% reduction in the quantity of a security that the levered sector can hold, imposed within eighteen months, with no change in the security's promised cash flows. Whoever was holding that paper had to find an unlevered buyer, at whatever price an unlevered buyer would pay.

One further step makes the fire sale an equilibrium outcome rather than an assumed friction. Forced selling is *predictable*: the constraint is observable, the holdings are disclosed, and the timing follows from a redemption queue or a margin schedule, so other institutions position ahead of it. Chen, Hanson, Hong and Stein (2008) document precisely this for mutual funds in distress — hedge funds short the stocks that funds facing large outflows will have to sell, then cover into the forced selling — so the distressed seller's price impact is not merely the concession an unlevered buyer demands, but that concession after everyone who could see the sale coming has traded against it. The mechanism has a named counterparty on the other side, and Chapter 18 §18.4 files the result under where hedge fund returns come from.

Regulators responded to procyclicality with countercyclical capital tools — the Basel III conservation and countercyclical buffers, and a non-risk-weighted leverage ratio — whose common design principle is to force capital accumulation in booms so that it can be released in busts. The macroprudential architecture and its politics belong to *International Finance*, Chapter 25; the point that belongs here is narrower and unresolved. Any capital or margin requirement calibrated to current risk measures is mechanically procyclical, because risk measures fall in booms, and making the constraint countercyclical means making it discretionary — which is exactly what a rule was supposed to remove. Chapter 26 §26.6 returns to this as a problem in risk measurement and is the regulatory face of this section: a haircut set by a lender and a capital charge set by a supervisor are the same object seen from two sides of the desk, both calibrated to a measure that is low precisely when risk is building.

### The Canonical Statement

This section is the book's canonical statement that **constrained capital moves prices**. Asset prices are not set by a representative agent weighing consumption risk. They are set at the margin by institutions whose capacity to hold a claim is limited by a leverage ratio, a capital charge, a haircut, a redemption queue, or a mandate — and when that capacity contracts, prices fall by whatever it takes to move the claim to someone whose capacity has not contracted. Fundamentals need not move at all.

The rest of the book cites this section rather than restating it. Chapter 15 §15.5 supplies the complementary half — Shleifer and Vishny's performance-based arbitrage explains why an arbitrageur with capital may still decline the trade, where this chapter explains why the capital is not there. Chapter 18 asks who supplies arbitrage capital in practice and what fee and lockup structures do to its patience; Chapter 19 turns the intermediary's balance sheet from a propagation mechanism into a pricing factor, putting a constrained dealer's capital ratio inside the stochastic discount factor; Chapter 20 estimates the whole system.

***

## 16.6 Mandates and Nonpecuniary Demand: ESG and Divestment

Every constraint so far has been imposed from outside — by a regulator, a lender, or a redeeming client. Mandates are different. A pension board that excludes tobacco, a sovereign fund that divests coal, a university that sells its oil and gas holdings: these are constraints the holder chooses, and they bind just as hard. They are also the cleanest available test of the chapter's thesis, because the fundamentals of the excluded firms do not change on the day of the announcement. Only the identity of the holders does.

### ★ The Arithmetic of Divestment

Start with the simplest possible accounting. Suppose investors holding a fraction $$\phi$$ of aggregate wealth refuse to hold asset $$i$$, which has weight $$w\_i$$ in the market portfolio. The shares do not disappear. The remaining investors must hold the entire supply, so their weight in the asset rises from $$w\_i$$ to $$w\_i/(1-\phi)$$. With mean-variance preferences and risk aversion $$\gamma$$, bearing that extra concentrated exposure requires compensation of roughly

$$
\Delta E\[r\_i] \approx \gamma \frac{\phi}{1-\phi} w\_i \sigma\_i^2
$$

where $$\sigma\_i^2$$ is the part of the excluded asset's variance the remaining holders cannot diversify away.

Three things make this number small in practice. The excluded asset is typically a small share of the market, so $$w\_i$$ is small. Exclusions usually cover firms whose idiosyncratic risks are imperfectly correlated, so most of $$\sigma\_i^2$$ diversifies within the remaining portfolio. And $$\phi$$, measured honestly, is far below the headline, because the divesting fund's shares are bought by investors under no such restriction and the announced constraint covers a fraction of world capital. Berk and van Binsbergen (2025) push the calculation through with generous assumptions and conclude that divestment on any realistic scale moves the excluded firm's cost of capital by a few basis points — orders of magnitude too little to change an investment decision. Their inference is that impact-minded investors should engage rather than exit, because exit hands the claim to someone who does not care.

The expression also says exactly when divestment *would* move prices: when $$\phi$$ approaches one, when $$\sigma\_i^2$$ is large and undiversifiable, or when $$\gamma$$ is effectively high because the residual holders are few, specialized, and capital-constrained. That is the same condition as everywhere else in the chapter. Divestment matters when arbitrage capital is scarce.

### Equilibrium with Nonpecuniary Preferences

Pástor, Stambaugh and Taylor (2021) build the general case. Investors derive utility from holdings themselves, not only from their payoffs: a green asset delivers a nonpecuniary benefit, a brown asset a nonpecuniary cost. In equilibrium green assets are held at higher prices and therefore lower expected returns — a "greenium" — while brown assets carry a premium compensating their holders for taking the other side. Firms respond, because the cost of capital enters investment decisions, so the aggregate ESG tilt of investor tastes determines how much green investment gets financed.

The model has a sharp implication that saved the empirical literature from itself. Green assets have *lower expected* returns but can have *higher realized* returns whenever concerns about the environment strengthen unexpectedly, because the strengthening raises green prices; Pástor, Stambaugh and Taylor's follow-up work attributes much of the strong realized performance of green stocks in the late 2010s to precisely that channel rather than to a persistent green alpha. The distinction matters for anyone tempted to sell ESG investing as a free lunch: in equilibrium it is a preference, and preferences are paid for.

On the other side of the ledger, Hong and Kacperczyk (2009) document that "sin" stocks — alcohol, tobacco, gaming — are held less by norm-constrained institutions and have earned higher risk-adjusted returns, which is the segmentation prediction of the arithmetic above with $$\phi$$ measured across a genuinely large share of institutional capital. Matched-pair studies of green bonds find yield differentials against otherwise identical conventional bonds of at most a few basis points: small, but detectable, and in the direction the theory predicts.

### Mandates as Holder Constraints

The right way to file all of this is not as a separate topic called ESG. It is another instance of the chapter's mechanism. A mandate changes who is allowed to hold a claim; whoever remains must be paid to hold more of it; how much they must be paid depends on how constrained they are. The RBC schedule of Table 16.3 does the same thing by regulation, the 1940 Act's diversification limits do it by statute, a benchmark does it by contract, and an exclusion list does it by choice. In each case the constraint is on the holder and the effect is in the price.

What separates mandates from the rest is scale and direction. Regulatory constraints on insurers bind a few trillion dollars and tighten in crises; mandate-driven exclusions now cover a large and growing share of professionally managed money, and they tighten with public opinion. That makes them a slow-moving demand shock rather than a fast one, which is harder to identify empirically — and is why the cross-sectional climate-premium evidence discussed in Chapter 6 remains contested while the mechanism itself is not.

***

## Elsewhere in the Series

* **The hierarchy of money, the T-account mechanics of money creation, and the dealer system** — *International Finance*, Chapter 2. This chapter keeps the portfolio layers of the pyramid and the placement of funds within it; the monetary layers are developed there.
* **The shadow banking taxonomy** — *International Finance*, Chapter 8. MMFs, repo, securitization vehicles, and the nonbank inventory are catalogued there; this chapter uses only the balance sheets it needs.
* **Basel III, macroprudential policy, and the regulatory architecture** — *International Finance*, Chapter 25. Section 16.5 keeps the procyclicality point and defers the architecture.
* **The 2008 fire-sale episodes in full** — the 2008 crisis volume. Bear Stearns, Lehman, the money-market run, and the emergency facilities are narrated there; the tables in §16.5 are the evidence this book needs.
* **The passive revolution, ETF mechanics, and performance measurement** — this book, Chapter 17.
* **Noise-trader risk and the behavioral half of limits to arbitrage** — this book, Chapter 15. **Arbitrage capital and fund structures** — Chapter 18. **Intermediary asset pricing, and the March 2020 Treasury episode as this book's opener for it** — Chapter 19. **Demand-system estimation** — Chapter 20.
* **Why smart money does not correct mispricing, stated compactly for course use** — this book, Chapter 7 §7.5, which cites §16.5 for the balance-sheet mechanics and §16.3 for career risk rather than restating either; the Grossman-Stiglitz model those constraints sit alongside is Chapter 7 §7.2.
* **Preferred habitat and LDI duration demand in the term structure** — this book, Chapter 9. **Insurers as the marginal corporate bond holder** — Chapter 10. **Climate risk premia in the cross-section** — Chapter 6.

***

## Summary

Institutional investors — pension funds, insurance companies, mutual funds, hedge funds, dealers, and banks — operate under heterogeneous constraints: regulatory requirements, liability structures, redemption terms, leverage limits, and mandates. Those constraints shape behavior in ways that matter for market outcomes.

1. **Balance sheets matter.** Asset prices are not determined by a representative agent but by the interaction of institutions with different constraints. Fire sales, margin spirals, and leverage cycles arise from balance sheet mechanics, and §16.5 is this book's canonical statement of the mechanism.
2. **The liability side drives the asset side.** Pension funds hedge duration because they owe long-dated nominal payments; life insurers hold long corporate credit because they owe money in 2050; P\&C insurers hold governments and equities because they owe cash after hurricanes. Portfolio composition is a statement about promises written, not about return forecasts.
3. **There is a hierarchy of money and credit.** Not all dollars are equal. The distance from central bank reserves determines how an instrument behaves in a crisis, and each institution can be located on the pyramid by comparing the claims it holds with the claim it issues.
4. **Liquidity is a balance sheet property.** The same asset is liquid for an unleveraged investor and illiquid for a leveraged one facing margin calls. Market liquidity and funding liquidity are intertwined, and the haircut is a price that no Part II model contains.
5. **Delegation creates agency problems.** Institutional investors face career concerns, benchmark hugging, and herding incentives that can distort price discovery — and that keep mispricings alive after Chapter 15 has explained how they appeared.
6. **Mandates are constraints too.** Exclusion by itself moves the cost of capital very little, because the shares are absorbed by unconstrained holders. It moves prices when the residual holders are few and constrained — which is the same condition that governs every other mechanism in the chapter.

Understanding institutional investors is essential for understanding financial crises. The 2008 crisis, the 2020 Treasury market stress, and the 2022 UK LDI crisis all arose from institutional balance sheet dynamics, not from changes in fundamentals. The plumbing of finance is not peripheral; it is central to how markets function — and malfunction.

***

## Key Terms

* **Institutional investor**: An entity that holds and manages financial claims on behalf of others, subject to regulatory, contractual, and liability-driven constraints
* **Liability-driven investment (LDI)**: Investment strategy focused on matching assets to liabilities
* **Leverage cycle**: Procyclical expansion and contraction of institutional balance sheets
* **Hierarchy of money and credit**: The ordering of financial instruments by their proximity to central bank money, and by the reliability of the promise each embodies
* **Fire sale**: Forced selling at depressed prices due to balance sheet constraints
* **Margin spiral**: Feedback loop between margin requirements, forced selling, and price declines
* **Flow-performance relationship**: Tendency of investors to move money toward recent winners
* **Risk-based capital (RBC)**: The US insurance capital regime that assigns a capital charge to each asset class and rating bucket, making required capital a function of portfolio composition
* **Reach for yield**: The tendency of return-targeting institutions to buy the highest-yielding asset permitted within a regulatory or mandate category
* **Catastrophe bond**: A security whose principal is forgiven on the occurrence of a defined catastrophe, transferring insurance risk to capital-market investors
* **Nonpecuniary demand**: Demand for a claim arising from the utility of holding it rather than from its payoff; the source of the greenium and of divestment effects

***

## Readings

### Required

* Brunnermeier, M. and L. Pedersen (2009). "Market Liquidity and Funding Liquidity." *Review of Financial Studies* 22(6): 2201-2238. *The formal statement of the margin spiral in §16.5.*
* Mehrling, P. (2011). *The New Lombard Street: How the Fed Became the Dealer of Last Resort*. Princeton University Press. Chapters 1-3. *The money view; the monetary layers are developed in International Finance, Chapter 2.*

### Recommended

* Adrian, T. and H. Shin (2010). "Liquidity and Leverage." *Journal of Financial Intermediation* 19(3): 418-437.
* Brunnermeier, M. K. and M. Yogo (2009). "A Note on Liquidity Risk Management." *American Economic Review Papers and Proceedings* 99(2): 578-583. *Four pages on how a firm should manage the risk of being unable to roll its funding. The formal version of §16.2's claim that the liability side drives the asset side.*
* Brunnermeier, M. K. and M. Oehmke (2013). "The Maturity Rat Race." *Journal of Finance* 68(2): 483-521. *Why each lender's rational shortening of funding maturity worsens every other lender's position, and why the equilibrium maturity is inefficiently short. The liability-side complement to the asset-side margin spiral, and the source for the maturity paragraph in §16.5.*
* Gorton, G. and A. Metrick (2012). "Securitized Banking and the Run on Repo." *Journal of Financial Economics* 104(3): 425-451. *The 2007-2008 crisis told as a run on repo, with rising haircuts on collateral rather than queues of depositors as the observable.*
* Bolton, P., T. Santos and J. Scheinkman (2012). "Shadow Finance." *Why credit intermediation migrates to whichever balance sheet carries the lightest capital requirement, and why that migration is a predictable consequence of the requirement rather than an evasion of it.*
* Coval, J., J. Jurek and E. Stafford (2009). "The Economics of Structured Finance." *Journal of Economic Perspectives* 23(1): 3-25. *How pooling and tranching manufacture apparently safe claims, and why a senior tranche's rating is far more sensitive to the assumed correlation across the pool than the rating scale ever admits.*
* Becker, B. and V. Ivashina (2015). "Reaching for Yield in the Bond Market." *Journal of Finance* 70(5): 1863-1902. *Reaching for yield measured within rating buckets, which is where a coarse capital charge invites it.*
* Koijen, R. and M. Yogo (2015). "The Cost of Financial Frictions for Life Insurers." *American Economic Review* 105(1): 445-475. *An insurer selling its own liabilities below actuarial value to relieve a capital constraint.*
* Froot, K. (2001). "The Market for Catastrophe Risk: A Clinical Examination." *Journal of Financial Economics* 60(2-3): 529-571. *Catastrophe risk transfer examined at close range, with the puzzle that insurers ceded so little of it at spreads standing well above expected loss.*
* Pástor, Ľ., R. Stambaugh and L. Taylor (2021). "Sustainable Investing in Equilibrium." *Journal of Financial Economics* 142(2): 550-571. *The equilibrium greenium, and why realized and expected green returns can have opposite signs.*
* Hong, H. and M. Kacperczyk (2009). "The Price of Sin: The Effects of Social Norms on Markets." *Journal of Financial Economics* 93(1): 15-36. *The return premium on stocks that norm-constrained institutions will not hold, which is §16.6's nonpecuniary demand measured in the cross-section.*
* Berk, J. and J. van Binsbergen (2025). "The Impact of Impact Investing." *Journal of Financial Economics* 164: 103972. *The divestment arithmetic of §16.6, worked through with deliberately generous assumptions.*
* Shleifer, A. and R. Vishny (1997). "The Limits of Arbitrage." *Journal of Finance* 52(1): 35-55. *Read alongside Chapter 15.*
* Chen, J., S. Hanson, H. Hong and J. Stein (2008). "Do Hedge Funds Profit from Mutual-Fund Distress?" NBER Working Paper 13786. *The other side of §16.5's fire sale. Forced selling is predictable, so it is traded against, and the paper measures what the anticipation costs the distressed fund. The clearest available demonstration that a holder's constraint is a tradeable object.*
* Brunnermeier, M. K., S. Nagel and L. H. Pedersen (2008). "Carry Trades and Currency Crashes." *NBER Macroeconomics Annual* 23: 313-347. *One trade in which the unwinding of a funding constraint is visible in the return distribution: gradual gains, sudden crashes, with the skew appearing exactly where speculator positions were largest. The currency material belongs to International Finance, Chapter 16; the constraint argument belongs here.*

***

## Discussion Questions

1. **Balance sheet mechanics**: A hedge fund has $100 million in assets, $80 million in debt, and $20 million in equity. If asset values fall 10%, what happens to its leverage ratio? If the fund has a maximum leverage constraint of 6x, how much must it sell?
2. **The hierarchy in practice**: During the March 2020 COVID crisis, even US Treasury securities became difficult to trade. How does this challenge the standard view of Treasuries as the ultimate safe asset? What does it tell us about the hierarchy of money? (Chapter 19's opening episode narrates the episode and its dealer-balance-sheet mechanism; answer from the hierarchy, not from the narrative.)
3. **Divestment and the cost of capital**: A pension fund holding 2% of world equity announces that it will exclude fossil fuel producers. Using the expression in §16.6, estimate the effect on the excluded firms' cost of capital, stating your assumptions about $$\phi$$, $$w\_i$$, $$\gamma$$, and the undiversifiable share of $$\sigma\_i^2$$. Now change the exercise: what would have to be true of the *remaining* holders for the effect to be large enough to change a drilling decision? Given your answer, is exclusion or engagement the better instrument for an investor who wants to change firm behavior — and does that answer depend on whether other investors are also constrained?
4. **LDI and systemic risk**: The UK LDI crisis occurred in pension funds — supposedly long-term, stable investors. Why did long-term investors face short-term liquidity crises? What does this tell us about the risks of leverage in "safe" institutions?
5. **Career concerns and price discovery**: Keynes argued that institutional investors would "fail conventionally rather than succeed unconventionally." How do career concerns affect willingness to take contrarian positions? What are the implications for market efficiency and the correction of mispricing?

***

## Problems

**Problem 1 — Leverage dynamics at a dealer.** A securities dealer holds 500 of bonds, financed with 460 of repo and 40 of equity. The repo balance is fixed within the exercise, and the dealer's lenders impose a maximum leverage of 15 times equity.

(a) Compute the dealer's leverage $$L$$. (b) Bond prices fall by $$\kappa = 4$$ percent. Compute the new assets, the new equity, and the new leverage from the balance sheet directly. Verify that the Key Equation reproduces your answer, then compute the value the linear approximation $$L(1+(L-1)\kappa)$$ gives and report the error as a fraction of the exact figure. (c) Starting from the post-shock balance sheet, how much must the dealer sell to restore 15 times leverage? How much to restore its original leverage? Say in one sentence why the second number is the one that matters for the price of the bond. (d) At what $$\kappa$$ does the 15 times constraint first bind, and at what $$\kappa$$ is equity exhausted? Comment on the ratio of the two numbers, and on what it implies about how far a levered institution's *behavior* is from its point of insolvency.

**Problem 2 — Placing a claim on the hierarchy.** A prime money market fund holds 100 of assets — 30 in Treasury bills, 45 in repo secured by Treasuries, and 25 in unsecured commercial paper — against 100 of shares redeemable at par on demand. It has no equity capital and no insurance.

(a) Draw the fund's T-account and mark every asset and the liability with its layer on Figure 16.1, following Figure 16.14's convention. State in one sentence where the fund's business sits in the gap between the two sides. (b) Holders redeem 20 in a single day. Which asset does the fund sell first, and what does the sale do to the layer composition of what remains? Whose problem is that? (c) The commercial paper is instead marked down by 8 percent, with no redemptions. Compute the fund's net asset value per share and say what the fund is obliged to do next. (d) A stablecoin issuer has 100 coins outstanding against a reserve of 60 in Treasury bills and 40 in uninsured deposits at a single bank. The bank fails and the deposit is expected to recover 90 cents on the dollar. Compute the value per coin, identify which layer of the hierarchy the loss came from, and state which of the fund's protections in (c) the issuer does not have.

**Problem 3 ★ — One round of fire sale, and then the next.** Two identical funds each hold 200 of the same asset, financed with 160 of debt and 40 of equity, and each targets leverage of 5. Selling moves the price: every 10 of notional sold by the sector as a whole lowers the asset's price by 0.5 percent.

(a) An exogenous shock lowers the price by 3 percent. Compute each fund's assets, equity, and leverage immediately after the shock. (b) Each fund sells enough to restore leverage of 5. Compute the sale per fund and for the sector, and the price impact those sales generate. (c) Carry out the second round: recompute each fund's assets, equity, leverage, and required sale after the induced price fall. Report the ratio of the second-round sale to the first. (d) Show that with $$n$$ identical funds at target leverage $$L$$ and equity $$E$$, a price fall of $$\kappa$$ forces sales of $$nLE\kappa(L-1)$$, and hence that the spiral converges only if $$\theta n L(L-1)E < 1$$, where $$\theta$$ is the price impact per unit sold. Compute the critical $$\theta$$ for this sector and compare it to the assumed one. Which of the four terms would a regulator find easiest to change?

**Problem 4 — A collateral call.** A UK defined benefit scheme reports liabilities with a present value of 1,000 and a modified duration of 20, against assets of 900: 760 in equities and 140 committed as collateral to a levered gilt portfolio with a gross market value of 700, a modified duration of 20, and 560 of repo funding behind it. The repo lender requires collateral equal to 20 percent of the gilt portfolio's market value, marked daily and met in cash. Treat all yield moves as parallel and use the duration approximation throughout.

(a) Compute the scheme's funding ratio and its hedge ratio — the fraction of the liability's interest-rate sensitivity the gilt portfolio covers. (b) Long yields rise 30 basis points overnight. Compute the new liability value, the new gilt value, the new funding ratio, and the cash the scheme must post to restore the required collateral. (c) Now take the full move of the opening episode, 113 basis points. Recompute all four figures. State the funding ratio and the size of the cash call in the same sentence, and say which of the two a trustee could have been looking at on 27 September 2022 without seeing the other. (d) The scheme's own selling, and that of schemes like it, pushes long yields up a further 25 basis points. Recompute the cumulative cash requirement, and state in one sentence why an improving funded status was no help at all.

**Problem 5 — The same downgrade, five holders.** A widely held BBB corporate bond issue is downgraded to BB overnight. Its promised cash flows are unchanged and its issuer has made no announcement. The bond is held by a US life insurer, an open-end investment-grade bond mutual fund, a defined benefit pension scheme running a levered LDI overlay, a hedge fund financed on prime-broker margin, and a university endowment with a spending rule smoothed over three years.

(a) For each holder, name the constraint from the dimensions in §16.1's table that binds, if any, and classify it as a forced seller, a discretionary seller, or a potential buyer. Cite the table or box in this chapter that supplies the constraint. (b) Rank the five by the speed at which the constraint transmits into an actual trade — same day, days, quarters, never — and state what determines the ranking. (c) Two of the five appear at roughly 1 times leverage in Table 16.7. Explain why one of them can nonetheless be forced to sell within a day and the other cannot, and say what a table of leverage levels fails to show. (d) Replace the shock with a 20 percent fall in equity prices, credit spreads unchanged, and redo (a). Whose answer changes most? Using both shocks together, state what the exercise adds to the claim that constrained capital moves prices that either shock alone would not.

***

## Selected Solutions

*Solutions to Problems 1 and 2 follow. Solutions to the remainder are in the instructor materials.*

**Problem 1.**

(a) $$L = A/E = 500/40 = \mathbf{12.5}$$.

(b) Assets fall to $$500 \times 0.96 = \mathbf{480}$$. Debt is fixed at 460, so equity is $$480 - 460 = \mathbf{20}$$ — a four percent fall in prices has halved it. New leverage is $$480/20 = \mathbf{24.0}$$. The Key Equation gives the same number:

$$
L' = \frac{L(1-\kappa)}{1 - L\kappa} = \frac{12.5 \times 0.96}{1 - 0.5} = 24.0
$$

The linear approximation gives $$L(1 + (L-1)\kappa) = 12.5(1 + 11.5 \times 0.04) = 18.25$$, an error of $$\mathbf{-24.0}$$ **percent** of the exact figure. *The approximation is stated for small price declines, and four percent is already not small when leverage is twelve and a half — which is worth noticing, because the approximation understates leverage in exactly the states where the level matters.*

(c) To restore fifteen times on 20 of equity the dealer needs assets of 300, so it must sell $$480 - 300 = \mathbf{180}$$. To restore its original 12.5 times it needs assets of 250, so it must sell $$480 - 250 = \mathbf{230}$$. The second is the number that matters for the price of the bond, because a dealer that has just watched its equity halve does not aim to sit exactly on its constraint — it aims for the buffer it had before, and the difference between the two targets is fifty of additional selling into a market that has already fallen.

(d) The fifteen-times constraint binds when $$L(1-\kappa)/(1-L\kappa) = 15$$, that is at $$\kappa = \mathbf{1.43}$$ **percent**. Equity is exhausted when $$E - A\kappa = 0$$, at $$\kappa = 1/L = \mathbf{8.00}$$ **percent**. The ratio is **5.6**: the dealer is forced to act at a price decline less than a fifth of the one that would render it insolvent.

*That ratio is the chapter's central mechanism in one number, and it is the reason §16.5's spiral does not require anybody to be near failure. A four percent move — an ordinary week in a credit market — takes this dealer from comfortable to constrained, and the selling it must then do is a multiple of the loss that caused it. Solvency is not the binding constraint; the constraint is the constraint.*

**Problem 2.**

(a) The T-account, with each item's layer on Figure 16.1's hierarchy:

| Assets             |    | Layer                            | Liabilities           |     | Layer                                |
| ------------------ | -- | -------------------------------- | --------------------- | --- | ------------------------------------ |
| Treasury bills     | 30 | government debt (layer 2)        | Shares, par on demand | 100 | promises to pay *deposits* (layer 3) |
| Repo on Treasuries | 45 | secured money market (layer 3-4) |                       |     |                                      |
| Commercial paper   | 25 | unsecured money market (layer 4) |                       |     |                                      |

The fund's business sits exactly in the gap: it issues a claim at layer 3, redeemable at par on demand, against assets that average roughly layer 3.5, and the spread it earns is the price of that one-layer descent. **It has no capital and no insurance, so the entire buffer between the two sides is the assumption that the spread never has to be paid back.**

(b) It sells the Treasury bills first, because they are the asset that can be sold at a known price in size on the day. What remains is 10 of bills, 45 of repo and 25 of paper against 80 of shares: the redeeming holders have taken the *top* of the hierarchy with them, and the shareholders who stayed now own a portfolio that has moved down a layer without their doing anything. That is the classic first-mover advantage, and it is the remaining holders' problem — which is precisely why they run too.

(c) The paper is worth $$25 \times 0.92 = 23$$, so assets are $$30 + 45 + 23 = 98$$ and the net asset value per share is $$\mathbf{0.98}$$. The fund cannot pay par on demand out of 98, so the par promise has failed: it must either mark its shares to 0.98 and allocate the two percent to holders, or be made whole by its sponsor, which is a voluntary act by a party with no obligation to perform it. *This is the Reserve Primary Fund of §16.4 with the numbers changed. Note how small the shock is — an eight percent markdown on a quarter of the portfolio — and how complete the consequence: a claim either is redeemable at par or it is not.*

(d) The reserve is worth $$60 + 40 \times 0.90 = 96$$, so each coin is worth $$\mathbf{0.96}$$. The loss came from the **bank-deposit layer** — layer 3, one step below the Treasury bills — and it is the layer the issuer chose to hold precisely because it pays more than bills do. Two of the fund's protections in (c) are absent. There is no rulebook: no diversification limit that would have stopped forty percent of the reserve sitting at one bank, and no maturity or credit constraint of the kind a money fund operates under. And there is no orderly way to allocate the loss, because the coin has no net asset value to float and no shareholder register to allocate it across — a coin either redeems at one dollar or it does not, so the loss is allocated by who redeems first. *The instrument is a money market fund with the rulebook removed and the backstop removed, and the 2022 and 2023 de-pegs are what that combination produces.*

***

## Data Exercise: Who Holds What, and Why

**Part A — Institutional holdings from the Financial Accounts (free data).** The Federal Reserve's Z.1 release, downloadable in bulk from the Board's Data Download Program, reports the balance sheet of every domestic sector. Retrieve the levels tables for pension funds and for life and property-casualty insurers (L.116-L.117 and L.114-L.115 in recent vintages; the Z.1 renumbers between releases, so confirm against the current table of contents).

1. For each sector, construct the share of financial assets held in corporate equities, in corporate and foreign bonds, and in Treasury securities, annually from 1980 to the present. Plot the three series per sector on one panel.
2. The DB-to-DC shift and the LDI logic of §16.2 both predict a rising fixed-income share for defined benefit plans; the RBC schedule of Table 16.3 predicts that insurers' equity share stays low and stable regardless of equity valuations. Do the series show either pattern? Date any break you find and say what else was happening.
3. Overlay the ten-year Treasury yield. The reach-for-yield hypothesis predicts that the *composition* of insurers' bond holdings shifts toward credit when yields are low. Z.1 will not give you ratings; state precisely what data would be needed to test this properly, and what the sector aggregates can and cannot show.

**Part B — Holdings from 13F filings (free data).** Institutional managers above the reporting threshold file quarterly Form 13F holdings with the SEC, available in structured form through EDGAR.

1. Pick one large insurer and one large public pension manager. Retrieve their most recent 13F-HR filings and tabulate the ten largest reported positions.
2. Compare their equity holdings with the sector shares from Part A and explain the gap. 13F covers reportable US equity positions only, at the manager level, long positions only — so the discrepancy is mostly definitional. Quantifying that gap is the exercise.
3. Repeat for the quarter containing the largest drawdown in your sample and identify positions that were reduced. What can you infer about forced versus discretionary selling from holdings data alone, and what would you need to distinguish them?

**Part C ★ (if you have WRDS).** Using the NAIC Schedule D holdings via WRDS and TRACE transaction data, test the Becker-Ivashina prediction directly: within each NAIC rating bucket, do insurers' purchases concentrate in the highest-yielding available issues, and is the tilt stronger for insurers closer to their RBC constraint? State the identification problem in one paragraph before running anything.