> 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_19_intermediaries.md).

# Chapter 19: Banks, Dealers, and Intermediary Asset Pricing

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

***

## Opening Episode: The Week the Safe Asset Stopped Working

On March 9, 2020, the yield on the ten-year US Treasury note closed at roughly 0.54 percent, the lowest level then on record. Equity markets had fallen far enough that morning to trigger the exchange-wide circuit breaker, and the world was doing what it always does when it is frightened: buying Treasuries. The textbook had a name for it. Flight to quality. The safest claim in the world gets bid up, its yield falls, and the price of everything else falls against it.

Over the following eight trading days the equity market kept falling — by March 20 the S\&P 500 was down roughly a third from its February peak — and the ten-year Treasury yield *rose*, to around 1.18 percent by March 18. The safe asset was selling off in the middle of the worst risk-off shock since 2008. Inside the Treasury market the dysfunction was easier to see than in the headline yield. Bid-ask spreads on off-the-run Treasuries widened by roughly an order of magnitude. The spread between an off-the-run note and its on-the-run twin — two claims on the same sovereign, differing only in issue date — blew out to levels not seen since the crisis. The cash-futures basis, ordinarily a few basis points, went to tens of basis points and stayed there.

None of this is explicable in the language of Part II. The payoffs had not changed. What had changed was who could hold the claim.

The sellers arrived from every direction at once. Foreign official holders sold Treasuries to raise dollars. Bond mutual funds facing redemptions sold their most liquid holdings first, which is always the Treasuries. Corporations drew down credit lines and parked nothing. And the hedge funds running the cash-futures basis trade — long the cheap cash bond, short the rich future, financed in repo at leverage that could reach thirty or fifty to one — met rising repo haircuts and futures margin calls simultaneously and unwound, which meant selling cash Treasuries. Chapter 16 §16.5 names that mechanism and states it once for the whole book; this is it, running in the market that is supposed to be immune to it.

The buyer of last resort in a Treasury selloff is the dealer. Primary dealers make markets in Treasuries by taking the other side and holding inventory until a buyer appears. In March 2020 they did not. Their balance sheets were already full: net Treasury positions had climbed to record levels in the preceding months, in part as the mirror image of the same hedge-fund basis positions, and they were simultaneously absorbing corporate bond inventory from a credit market where nobody wanted to bid. A dealer that cannot expand its balance sheet cannot intermediate, and a market whose intermediary cannot intermediate stops clearing at prices that make sense.

What ended it was a balance sheet that faces no such constraint. On March 15 the Federal Reserve announced purchases of $500 billion of Treasury securities and $200 billion of agency mortgage-backed securities; on March 23 it removed the cap. In the last full week of March the Desk was buying Treasuries at an announced pace of roughly $75 billion a day, and in the space of about a month the Federal Reserve's Treasury holdings rose by something on the order of $1 trillion — an amount comparable to the entire first round of quantitative easing, executed in weeks rather than months. Total assets on its balance sheet went from roughly $4.2 trillion in early March to roughly $6.7 trillion two months later. On April 1 it went further and temporarily excluded Treasuries and reserves from the supplementary leverage ratio, which is a direct admission of what the problem was: not a shortage of willingness to hold Treasuries, but a shortage of balance sheet on which to hold them.

![Figure 19.2: The week the safe asset stopped working](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-547bf4aefc6cd0f2bc206e3f1c9a95024b251b82%2Ffig_19_02_the_week_the_safe_asset_stopped_working.png?alt=media)

**Figure 19.2: The week the safe asset stopped working.** The episode in the three series it turns on, 1 February to 30 April 2020, with 9, 15 and 23 March marked — the then-record low close, the announcement of 500 billion dollars of Treasury and 200 billion of agency MBS purchases, and the day the cap came off. Panel (a) is the fact that has no explanation in Part II's language: the ten-year yield closes at 0.54 on 9 March and is at 1.18 nine days later, rising through the worst equity drawdown since 2008. Panel (b) is that drawdown — the S\&P 500 against its February peak, down 32 percent by 20 March and 34 percent at the 23 March trough. The two panels move the same way for eight trading days, which is the opposite of flight to quality and the reason this chapter exists. Panel (c) is what ended it. The Federal Reserve's balance sheet goes from 4.2 trillion dollars in early March to 6.7 two months later, and the steepest part of that climb is the fortnight after 15 March. The 9 March close was the lowest *then* on record, as the episode says and as the mark on panel (a) is drawn: the same series closed at 0.52 on 4 August 2020, so the record did not stand out the year. *Source: Board of Governors of the Federal Reserve System (H.15 daily yields and H.4.1 weekly balance sheet) and S\&P Dow Jones Indices, via FRED. Author's calculations.*

Spreads normalized within days. Duffie's (2020) account of the episode draws the conclusion that organizes this chapter: the Treasury market's capacity to absorb a shock is not a property of Treasury securities. It is a property of the dealers' balance sheets, and those balance sheets grew far more slowly than the market they intermediate.

That is the thesis. When the balance sheets of financial intermediaries bind, prices move for balance-sheet reasons, and the identity of the constrained intermediary becomes an asset pricing fact rather than an institutional detail. Chapters 16 and 18 established that constrained capital moves prices. This chapter takes the last step: it puts the intermediary's constraint inside the discount factor, and asks what the resulting model predicts and whether it works.

Two prior questions have to be answered first, because they determine what the constraint is. Why do these institutions exist at all, and what do they hold?

***

## 19.1 Why Intermediaries Exist: Delegated Monitoring

A bank sits between savers and borrowers and takes a spread. The obvious question is why the savers do not lend directly and keep the spread.

Diamond's (1984) answer is that lending requires monitoring, and monitoring does not scale down. Suppose a borrower's project outcome is observable only at a cost, so a lender must either pay to verify it or accept whatever the borrower reports. If a thousand savers each lend a thousandth of the loan, the monitoring cost is paid a thousand times, or — since no individual saver will bear the whole cost for a thousandth of the benefit — not at all. Delegating monitoring to one agent pays it once.

That merely relocates the problem: who monitors the monitor? Diamond's contribution is to show that diversification solves the second problem given the first. The delegated monitor funds itself with debt — deposits — whose payoff is fixed and therefore requires no monitoring as long as it is paid. If the monitor holds one loan, its ability to pay depends on that loan and the depositors are back where they started. If it holds a large number of imperfectly correlated loans, the law of large numbers makes the total portfolio return nearly deterministic, so a fixed promise slightly below the expected return is kept with probability near one, and the expected cost of the monitor's own default falls toward zero as the portfolio grows.

So the bank is a device for economizing on monitoring costs, and its capital structure is not incidental to that function: it is *debt-funded and diversified* because those are the two conditions under which delegation is cheaper than direct lending. Both conditions have a corollary this chapter will keep returning to. Debt funding means the intermediary is levered. Diversification means it is large. A levered, large holder is exactly the kind of holder whose constraints show up in prices.

The argument is also testable, and its two obvious implications have both been found. If the intermediary's value comes from knowing a borrower it monitors, then the relationship itself should be worth something — and small firms with longer and more concentrated banking relationships do obtain credit more readily and on better terms than otherwise similar firms without them. And if a bank loan certifies a borrower in a way an arm's-length security cannot, then the announcement of a new bank credit agreement should move the borrower's share price where the announcement of a comparable public debt issue does not, which is what the event-study evidence reports.

> **Box 19.1 — 12 March 2020**
>
> The opening episode covers a fortnight. One day inside it is worth isolating, because everything the chapter argues was visible in a single session.
>
> On Thursday 12 March 2020 the S\&P 500 fell about nine and a half percent, its worst day since 1987. The ten-year Treasury yield *rose*. Both facts are in Figure 19.2, and the second is the one with no explanation in Part II's language: the safest claim in the world was being sold into the worst equity day in three decades.
>
> Inside the Treasury market the dysfunction was in the plumbing rather than in the headline. Bid-ask spreads on off-the-run issues widened by an order of magnitude, the spread between an off-the-run note and its on-the-run twin blew out, and the cash-futures basis went from a few basis points to tens. Dealers, whose net Treasury positions had climbed to records in the preceding months as the mirror image of hedge-fund basis positions, were absorbing corporate bond inventory at the same time and stopped taking the other side.
>
> The Federal Reserve Bank of New York's Desk announced very large repo operations that afternoon and a change in the maturity composition of its Treasury purchases. It was not enough; the market did not settle until the announcement of outright purchases on 15 March and the removal of the cap on 23 March.
>
> Three sentences of this chapter are on the record in that one session. Section 19.2's run is a coordination failure in a liability structure, and every cash-raiser that day was running from something. Section 19.3's dealer is a balance sheet before it is a preference, and this dealer's was full. And §19.5's intermediary discount factor says risk premia rise when the sector's capital is scarce, without any news about payoffs — which is what a nine percent equity fall and a rising Treasury yield look like on the same afternoon.

***

## 19.2 Liquidity Transformation and the Run

Delegated monitoring explains the asset side. It does not explain why the liability is a *demandable* claim — money the depositor can take back at par, today, without notice. That is the second function, and the more consequential one.

### The Diamond-Dybvig economy

Diamond and Dybvig's (1983) model is the cleanest statement in economics of what a bank does and why it is fragile. There are three dates, $$t = 0, 1, 2$$, and a continuum of identical depositors, each endowed with one unit of goods at date 0.

There is one technology. A unit invested at date 0 returns $$R > 1$$ if left until date 2, and exactly 1 if interrupted at date 1. Long investment is productive; interruption destroys the productivity, not the principal.

At date 1 each depositor privately learns her type. With probability $$\pi$$ she is **impatient** and values only date-1 consumption; with probability $$1-\pi$$ she is **patient** and values only date-2 consumption. By the law of large numbers, $$\pi$$ is also the fraction of the population that turns out to be impatient. The type is private information, so no contract can condition on it directly.

Without a bank, each depositor invests alone and must decide at date 0 how much to place in the long technology. Whatever she does, the impatient outcome is 1 and the patient outcome is $$R$$: interruption is a pure loss, and there is no insurance against being the one who is interrupted.

A bank pools the endowments and offers a **demand deposit contract**: withdraw at date 1 and receive $$c\_1$$, wait until date 2 and receive $$c\_2$$. If only the impatient withdraw early, the bank liquidates $$\pi c\_1$$ at date 1 and invests the rest, so

$$
c\_2 = \frac{R(1 - \pi c\_1)}{1 - \pi}.
$$

The contract that maximizes a depositor's expected utility before she knows her type satisfies $$u'(c\_1) = Ru'(c\_2)$$.

**A worked example.** Take $$\pi = 0.25$$, $$R = 2$$, and power utility with relative risk aversion $$\gamma = 2$$, so $$u'(c) = c^{-2}$$ and the first-order condition reads $$c\_2 = \sqrt{R}c\_1$$. Combining it with the budget constraint gives $$c\_1 = \sqrt{R}/\[(1-\pi) + \sqrt{R}\pi]$$.

**Table 19.1: The demand deposit contract,** $$\pi = 0.25$$**,** $$R = 2$$**,** $$\gamma = 2$$

|                         | Impatient depositor (date 1) | Patient depositor (date 2) |
| ----------------------- | ---------------------------- | -------------------------- |
| No bank (autarky)       | 1.0000                       | 2.0000                     |
| Demand deposit contract | 1.2815                       | 1.8123                     |

*Source: Author's calculation from the first-order condition and the budget constraint above; verified numerically.*

The bank pays the impatient depositor 28 percent more than she could get alone and the patient depositor 9 percent less than she could get alone. That is not a transfer; it is **insurance**. At date 0 nobody knows which she will be, and expected utility under the contract exceeds expected utility under autarky. The bank has made an illiquid portfolio — one that pays 2 only if undisturbed — support a liquid claim.

### The run as a coordination equilibrium

Now count what the bank can actually pay. It holds one unit of the long technology per depositor, worth 1 per unit if liquidated at date 1. If every depositor demands $$c\_1 = 1.2815$$ at date 1, the bank can serve only

$$
\frac{1}{c\_1} = \frac{1}{1.2815} = 0.780
$$

of them. Depositors are served in the order they arrive — the **sequential service constraint** — so 78 percent receive 1.2815 and 22 percent receive nothing. There is no date 2, because there are no assets left.

This makes the patient depositor's decision strategic. If she expects only the impatient to withdraw, waiting delivers 1.8123 and withdrawing delivers 1.2815, so she waits. If she expects everyone to withdraw, waiting delivers zero for certain and joining the queue delivers 1.2815 with probability 0.78, so she runs. **Both are equilibria.** Neither requires anyone to be irrational, mistaken, or panicked in any psychological sense, and neither involves any news about $$R$$. The bank's assets are exactly as good in the run equilibrium as in the good one.

Figure 19.3 puts both equilibria, and the threshold between them, on one pair of axes.

![Figure 19.3: Two equilibria](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-7b0429d71d51107296c7c080a9e84d08c0666978%2Ffig_19_03_two_equilibria.png?alt=media)

**Figure 19.3: Two equilibria.** What a patient depositor gets by waiting, against what she gets by joining the queue, as a function of how many others withdraw. The flat line is the contract, 1.2815, and it does not depend on anyone else's behaviour — that is what "demandable at par" means. The falling curve is what waiting is worth once the bank has liquidated enough of the long asset to serve those who came early, and it falls because liquidation destroys value: at a withdrawal fraction of 0.780 the bank has nothing left and waiting is worth zero. The two curves cross at 0.561. To the left of that point waiting dominates and only the impatient withdraw; to the right, joining dominates and everybody does. Both marked points are equilibria in the strict sense — each is a best response to itself — and the figure shows how little separates them: the good one survives only as long as fewer than 56 percent of depositors expect otherwise. Nothing in the picture is a statement about psychology, and nothing in it depends on any news about the long asset's return, which is the same in both.

The threshold is worth computing, because it shows how little coordination failure is needed. Let $$\nu$$ be the fraction withdrawing at date 1. Remaining assets are $$1 - \nu c\_1$$, shared among $$1 - \nu$$ depositors, so a patient depositor prefers to wait as long as

$$
\frac{R(1 - \nu c\_1)}{1 - \nu} \ge c\_1 \qquad\Longleftrightarrow\qquad \nu \le \nu^{\ast} = \frac{R - c\_1}{c\_1(R-1)}.
$$

At the numbers above, $$\nu^{\ast} = 0.561$$. Once more than about 56 percent of depositors are heading for the door, joining them is the individually correct decision. The good equilibrium is not robust; it is a fixed point that holds as long as everybody believes it holds.

Two features of the model do all the work, and both survive far beyond banking. The claim is **demandable at par**, so its value does not fall when many people exercise it at once. And the asset **loses value when liquidated early**, so many people exercising at once destroys the thing that backs the claim. Any institution with those two properties is runnable regardless of what its charter says. A money market fund promising a stable net asset value against commercial paper has them; the Reserve Primary Fund's break in September 2008 was a Diamond-Dybvig run in a vehicle with no deposits. A leveraged fund financed by overnight repo has them, where the "depositors" are the repo lenders and the run takes the form of refusing to roll. That is the repo run of 2007-2008 and, in a different market, the basis-trade unwind of the opening episode.

### Deposit insurance, held to one paragraph

The model contains its own remedy. If the deposit is guaranteed, the patient depositor's payoff from waiting no longer depends on what anyone else does, the run equilibrium is eliminated, and — this is the elegant part — the guarantee is never called upon, so in equilibrium it costs nothing. That is the Diamond-Dybvig case for deposit insurance, and it is the reason the United States has had no systemic retail bank run since 1933. The price is the standard one: a bank whose funding cost no longer responds to its asset risk has an incentive to take more of it, and the insurer must therefore supervise and constrain what it insures. The 2023 failures of Silicon Valley Bank and others were runs by *uninsured* depositors, which is the same model with the guarantee removed above a threshold. The rest of the safety net — the lender of last resort, the design of emergency facilities, resolution regimes, and the international architecture that governs all of it — is developed in *International Finance*, Chapters 15 and 16. This book needs only the mechanism and its pricing consequence.

### Capital requirements, compactly

Deposit insurance transfers the tail to the insurer; capital requirements are the instrument that makes the transfer tolerable. A capital requirement says that a bank's equity must be at least some fraction of its assets, with assets counted either at face value (a **leverage ratio**) or weighted by a supervisory risk schedule (a **risk-weighted capital ratio**). It does three things at once. It gives the bank's owners something to lose, so the moral hazard created by the guarantee is partly priced back in. It absorbs losses before the insurer does. And, because equity cannot run, it substitutes a claim that cannot demand repayment for one that can.

The design tension is that a requirement calibrated to *measured* current risk tightens exactly when risk measures spike, which is to say in the state where forced deleveraging is most damaging — the procyclicality that Chapter 16 §16.5 develops and that Chapter 26 §26.6 returns to as a problem in risk measurement. This chapter cites that result rather than re-deriving it. What matters here is narrower and will matter a great deal in §19.3: a capital requirement is a constraint on the *size* of the balance sheet, and therefore a constraint on how much of any claim the intermediary sector can hold.

***

## 19.3 What Banks and Dealers Hold

Open from Chapter 2's Table 2.5. Read down the "banks and depositories" column and the sector's function is legible without any theory: roughly $2 trillion of Treasury securities, about $3 trillion of agency and GSE-backed securities including agency MBS, a trillion of corporate and foreign bonds, a little under half a trillion of municipals, and — not shown in that table, because it is a claim on nonfinancial borrowers rather than a security — a loan book that is the largest item on the balance sheet. The sector totals are one table earlier: Chapter 2's Table 2.3 puts roughly $30 trillion of assets against something on the order of $3 trillion of equity, which is Chapter 2's observation that the depository sector runs at about ten to one, an order of magnitude more levered than the nonfinancial firms it lends to.

Three things about that column matter for what follows. The bank sector is a **large holder of long-duration fixed income**, which is why an increase in interest rates is a solvency event for it and not merely a mark; 2023 demonstrated the point. It is a **funding-sensitive** holder, because the liability side is deposits and short wholesale borrowing. And its holdings are governed by a capital schedule that assigns different weights to different claims, so its demand curve for a claim depends on that claim's regulatory treatment and not only on its expected return. That is the same structure as the insurers' RBC schedule in Chapter 16 §16.2, arriving in a larger balance sheet. Whether a mark reaches reported capital at all is an accounting question — banking book against trading book, amortized cost against fair value, held-to-maturity against available-for-sale — and **Appendix C** §C.4.2 owns those mechanics, which are the accounting behind the 2023 episode.

### The dealer function

The other half of this chapter's subject is not a lender at all. A **dealer** stands ready to buy from any seller and sell to any buyer, quoting a two-sided price and absorbing the difference in timing between them onto its own balance sheet. The inventory it accumulates is financed with short-term secured borrowing — **repurchase agreements**, or repo — in which the dealer sells a security and agrees to buy it back, posting the security as collateral and taking a haircut. The whole apparatus is a machine for converting a security into cash and back, and the constraint on it is the size of the balance sheet the dealer can fund.

![Figure 19.4: What banks and dealers hold](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-6cf48c78a9ac76f8b442eb8d811b2c2eac67cf94%2Ffig_19_04_what_banks_and_dealers_hold.png?alt=media)

**Figure 19.4: What banks and dealers hold.** The asset sides of the Financial Accounts' L.111 and L.130, each as a share of its own sector's total financial assets, with the level on the axis label because the two differ by a factor of four and a common scale would make the dealer bar a line. The bank rows are the same series Chapter 2's master map uses for its "banks and depositories" column, so the two exhibits cannot disagree. Read the two bars against each other. More than half of the bank's balance sheet is a loan book — a claim on a nonfinancial borrower, originated by the bank, monitored by the bank, and carried to maturity — and the securities that Table 2.5 lists are the smaller half of what it owns. The dealer sector's largest asset is not a security at all: repo lending and securities borrowed are 44 percent of its financial assets, which is the balance sheet in §19.3's sentence about a machine for converting a security into cash and back, measured. The dealer's own inventory of Treasuries and agency paper is a fifth of its assets and a small fraction of the markets it makes, which is the arithmetic Figure 19.1 states in ratio form. Dealer securities are published as net long positions, and the sector's receivables from customers and from other brokers are inside the Z.1's miscellaneous block rather than broken out, so they sit in the residual band here rather than in one of their own. *Source: Financial Accounts of the United States (Z.1), tables L.111 and L.130, through the FRED mirror. Author's calculations.*

The mechanics of that machine — the T-accounts of repo, matched books, the dealer's inside and outside spread, and Mehrling's account of the dealer of last resort — are developed in *International Finance*, Chapter 2, and this chapter cross-references rather than rebuilds them. Chapter 16 §16.4 carries the bridge: dealers sit between the layers of the money hierarchy, funding inventory with repo, and a refusal to roll that funding forces inventory out into every market they make.

What this book needs from the dealer balance sheet is one point. A dealer's willingness to hold a claim is not a preference over payoffs. It is a function of how much space it has, and the price at which it will absorb a seller's flow is the price at which taking the position is worth the balance sheet it consumes. Chapter 11 §11.6's account of liquidity supply — spreads, depth, and price impact — is the same object measured at trade frequency; this chapter looks at it at the frequency of a capital ratio.

![Figure 19.8: A dealer's balance sheet](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-54d00bd80bd344904785ea79bdc0e21c4a91d62b%2Ffig_19_08_dealer_balance_sheet.png?alt=media)

**Figure 19.8: A dealer's balance sheet.** The whole of a repo-financed inventory, in two accounts drawn at the same size so that the one thing that moves is visible. On the left, a hundred dollars of securities funded by ninety-eight of repo and two of equity: the equity sliver *is* the haircut, since the lender advances the collateral's value less its haircut and the dealer must fund the difference. That is how a book runs at fifty to one without anybody extending unsecured credit. On the right, the haircut moves to five percent. Nothing about the securities has changed — same issuer, same coupon, same maturity — but holding the same inventory now requires five dollars of equity against the two the dealer has. It must find three more or sell down to forty. The second is what happens in practice, and it happens into the market whose move raised the haircut in the first place, which is the mechanism §16.5 states and the reason the March 2020 episode ended with a balance sheet that faces no haircut at all.

### The post-2008 shift

The market-making capacity of the dealer sector, relative to the size of the markets it makes, is substantially smaller than it was in 2007. Two regulatory changes are usually named.

The **supplementary leverage ratio** requires large US bank holding companies to hold equity against total assets without risk weighting, at 3 percent for covered institutions and higher for the largest banks under the enhanced version. Because the ratio is not risk-weighted, it charges the same capital for a Treasury security as for a leveraged loan. For a business whose stock in trade is holding enormous quantities of near-riskless collateral at thin spreads, that is close to a tax on the core activity. The **Volcker rule** prohibits proprietary trading while exempting market-making, but the exemption requires a dealer to document that its inventory does not exceed the reasonably expected near-term demands of clients — a requirement that a desk complies with by carrying less inventory.

Reasonable people disagree about how much of the shrinkage these two rules explain and how much is the ordinary consequence of higher capital everywhere. The magnitudes are not in dispute. Treasury debt held by the public has grown from roughly $5 trillion before the crisis to something in the mid-$20 trillions, while primary dealer net positions in Treasuries have remained in the low hundreds of billions. Dealer capacity per dollar of outstanding Treasuries has fallen by something like a factor of five. Figure 19.1 puts the arithmetic on the record. Duffie (2020) makes this ratio the center of his account of March 2020, and the arithmetic is hard to escape: a market five times larger, intermediated by a balance sheet that did not grow, will find its intermediary constraint sooner. A third post-crisis change relocated exposure rather than shrinking it: the mandate to clear standardized derivatives through **central counterparties** moved a large set of bilateral dealer positions, and the collateral posted against them, out of the dealers' books and into clearinghouses that now sit at the center of the network under margin regimes of their own.

![Figure 19.1: Dealer capacity against market size](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-f4495093337d7c731b6a57ab5aad253ccd23dfa1%2Ffig_19_01_dealer_capacity.png?alt=media)

**Figure 19.1: Dealer capacity against market size.** Treasury debt held by the public against two measures of primary dealer capacity — net outright Treasury positions, which §19.3's sentence names, and the Treasuries dealers finance through repo and securities lending, which is the quantity Duffie (2020, Figure 2) uses — and both ratios on a second panel. On the financing measure capacity per dollar of Treasuries fell from 48 per cent in 2007 to 11 per cent, a factor of 4.3 (5.8 measured to the 2022 low). On net outright positions the ratio rose, from -2.6 per cent to +1.6 per cent, because dealers ran short Treasury books before 2009. "Treasuries financed by dealers" is the FR 2004 securities-out line — repo plus securities lending, nominal Treasuries and TIPS, overnight and term; it is the quantity Duffie (2020, Figure 2) uses, and it begins in 2001. The weekly data are spliced across the reporting-form changes of July 2001 and April 2013; neither join moves the level by as much as one weekly standard deviation, so the April 2013 break is marked on both panels rather than adjusted for. *Source: Federal Reserve Bank of New York primary dealer statistics (FR 2004), weekly, spliced across the reporting-form changes of July 2001 and April 2013; US Treasury debt held by the public (FYGFDPUN), via FRED; author's calculations.*

The trade-off is real and this chapter does not resolve it. The regulations were adopted because dealer balance sheets in 2007 were funded in a way that made the sector itself the crisis. The cost is that the sector now has less room, and the room it has is exactly what a market needs when everyone wants to sell at once. That is one of the sharpest live questions in financial regulation, and it is also a set-up for the asset pricing question: if the intermediary sector's capacity is small relative to the claims it must absorb, then its capacity is a state variable that prices claims.

> **Box 19.2 — The supplementary leverage ratio, in the arithmetic**
>
> Section 19.3 says the supplementary leverage ratio "charges the same capital for a Treasury security as for a leveraged loan." That sentence is doing a lot of work, and the arithmetic is short enough to do properly.
>
> The ratio is capital over total leverage exposure, where the denominator is assets plus certain off-balance-sheet items and is **not** risk-weighted. Suppose a dealer buys a hundred million dollars of Treasury securities and finances them in repo. Under the risk-based rules the position attracts a zero risk weight and consumes essentially no risk-based capital. Under the leverage ratio it adds a hundred million to the denominator, and at a required ratio of five percent for the largest US holding companies it therefore requires five million dollars of equity — the same five million the same firm would need against a hundred million of leveraged loans.
>
> Now put a spread on it. Market-making in Treasuries earns a few basis points on turnover. Against five million dollars of equity, a position earning five basis points on a hundred million returns fifty thousand dollars a year before funding and costs, which is a return on the equity consumed of one percent. No desk survives that comparison against any other use of the same balance sheet, and the desk does not have to be shut down for it to shrink; it simply loses every internal capital allocation.
>
> That is the mechanism, and it has a natural experiment attached. On 1 April 2020, with the Treasury market dysfunctional, the Federal Reserve temporarily excluded Treasury securities and reserves held at Federal Reserve Banks from the denominator for holding companies, initially for a year. Dealer Treasury holdings expanded materially over the following months, and the exclusion was allowed to expire on 31 March 2021.
>
> Reasonable people disagree about whether that trade-off was struck correctly, and §19.3 does not resolve it. What the arithmetic settles is the shape of the question. A non-risk-weighted charge is a tax on holding safe assets in size, and holding safe assets in size is what a Treasury dealer does.

***

## 19.4 Nonbank Inventory

Banks and dealers are not the only levered holders, and after 2008 they are not the fastest-growing ones. Three nonbank forms matter for the ecology, and the point of this section is not the taxonomy — *International Finance*, Chapter 8 catalogues the shadow banking sector, and Chapter 9 covers the private credit channel — but that each is a distinct holder with a distinct constraint, and therefore a distinct row in the demand system Chapter 20 estimates.

**Money market funds** hold Treasury bills, repo, and short-dated credit, and issue a claim their holders treat as cash. Chapter 16 §16.4 locates them on the hierarchy: they sit one layer below deposits on the asset side and issue a claim at the deposit layer, with no capital buffer and no guarantee. Their constraint is the redemption right combined with a stable-value promise — Diamond-Dybvig with the run threshold reset by fund rules rather than by the sequential service constraint. Their pricing relevance is that they are among the largest holders of the shortest claims in the map, so their demand sets the price of money-market instruments and their retreat from a market removes the natural buyer of that market's paper.

**Securitization vehicles** hold loans and issue tranched securities against them. The vehicle is not levered in the ordinary sense — its liabilities are the tranches, and there is no margin call on a CLO's senior notes — but it is constrained in a different way: its ability to buy assets depends on whether the tranches can be sold, and the buyers of the tranches are themselves constrained institutions choosing on the basis of ratings and capital charges. When those buyers stop, the vehicle stops, and the loans that would have been securitized stay on a bank's balance sheet or are not made. Chapter 10 prices the tranches; the 2008 volume narrates what happened when the chain broke.

**Private credit vehicles** — closed-end funds and business development companies lending directly to mid-market firms — are the newest and, from a stability standpoint, the most interesting, because they are the one form in this list whose funding cannot run. Capital is committed, drawdowns are contractual, and there is no redemption right. That makes them the natural holder of illiquid credit, which is Chapter 18 §18.5's point and *International Finance* Chapter 9's subject. The constraint has been relocated rather than removed: it now sits with the insurers and pension plans that fund these vehicles, whose own capital charges and funding ratios determine how much commitment capital exists, and with the bank credit lines that finance the vehicles between capital calls.

The general lesson is the one this part keeps supplying. Each of these forms was created to hold a claim that somebody else could not hold cheaply, and each therefore inherits a constraint from the holder it displaced. Understanding what any of them does to prices requires knowing which constraint binds and when.

***

## 19.5 Intermediary Asset Pricing

### The idea

Everything so far has been institutional. This section is the chapter's argument, and it is short to state.

Chapter 3 derived $$p = E\[mx]$$ from a household's first-order condition, with $$m = \delta u'(c\_1)/u'(c\_0)$$. That derivation requires the household to be **marginal** in the claim — free to buy or sell a little more at the going price. For an enormous share of the claims in Chapter 2's map, no household is anything of the kind. A household does not hold credit default swaps, over-the-counter interest rate options, sovereign bonds of other countries, or commodity futures. It holds a mutual fund share, a pension entitlement, or a deposit. The entity that is actually marginal in those claims — that decides at the margin whether to hold one more of them and at what price — is a financial intermediary.

If the intermediary is the marginal investor, its Euler equation is the pricing equation, and $$m$$ is whatever appears in *its* first-order condition. Write $$\Lambda\_t$$ for the marginal value to the intermediary sector of one more dollar of equity capital at date $$t$$. Then

$$
m\_{t+1} = \delta\frac{\Lambda\_{t+1}}{\Lambda\_t}, \qquad 1 = E\_t\big\[m\_{t+1}R\_{i,t+1}\big]
$$

for every claim $$i$$ the sector holds, and, exactly as in Chapter 3,

$$
E\_t\[R\_{i,t+1}] - R\_{f,t} = -R\_{f,t}\mathrm{Cov}\_t\left(\frac{\Lambda \_{t+1}}{\Lambda\_t},R \_{i,t+1}\right).
$$

The structure is unchanged. What changed is the object in the covariance. A claim is expensive if it pays off when intermediary capital is *abundant* and cheap if it pays off when intermediary capital is *scarce* — because scarce capital is when a marginal dollar inside the intermediary is most valuable. This is the same logic as the consumption-based model with a different bad state. In Chapter 5 the bad state is when consumption is low. Here the bad state is when the levered sector's equity has been impaired.

That substitution has an empirical payoff that is easy to miss on first reading. Aggregate consumption is smooth, which is the source of the equity premium puzzle: a smooth $$m$$ cannot generate a large premium without absurd risk aversion. Chapter 5 §5.4's Hansen-Jagannathan bound puts a floor under the requirement — any admissible discount factor must have a coefficient of variation at least as large as the highest Sharpe ratio in the market — and consumption growth does not come close to clearing it. Intermediary equity is *not* smooth. It fell by a large fraction in 2008-2009 and again, more briefly, in March 2020. A discount factor built out of it is volatile enough to clear the bound without any heroic preference parameter.

It is worth being clear about what this argument does and does not assume, because the objection arrives immediately. Households in this economy are not irrational and they are not excluded from wealth. They hold the intermediary's liabilities — deposits, fund shares, insurance contracts — and their preferences show up in the price of *those* claims. What they do not do is stand ready to buy one more credit default swap at the going price if it becomes marginally attractive. The household Euler equation therefore holds for the claims households actually trade at the margin and fails, as an inequality rather than an equality, for the rest. Where it fails, the intermediary's holds instead, and the two are linked by the intermediary's own constraint. In the limiting case where the constraint never binds, the intermediary passes household preferences through untouched and the intermediary SDF reduces to the household's; the model nests the textbook one rather than contradicting it. That is why the interesting empirical action is concentrated in the states where capital is scarce, and why a factor built from intermediary balance sheets can look uninformative in a long calm sample and then explain most of what happens in a bad quarter.

### ★ Where the constraint enters

The step from "the intermediary is marginal" to "the intermediary's capital ratio prices assets" requires a constraint; without one, the intermediary would simply pass through its clients' preferences and nothing new would be said.

He and Krishnamurthy (2013) supply it in the form of an **equity capital constraint**. Households cannot hold risky claims directly; they must invest through specialist intermediaries, and — because of a moral hazard problem in the intermediary's own management — they will contribute at most a multiple of the specialist's own equity stake. Outside equity is limited to a fixed multiple of inside equity, so the sector's total risk-bearing capacity is proportional to the specialists' own wealth. (He and Krishnamurthy write that multiple $$m$$; this book reserves $$m$$ for the discount factor, which is the object this section has just built, so the multiple is left unnamed here.)

Let $$\eta\_t$$ denote the intermediary sector's capital ratio: its aggregate equity divided by its aggregate assets. When $$\eta\_t$$ is high the constraint is slack, the intermediary prices claims as an unconstrained investor would, and household preferences come through undistorted. When $$\eta\_t$$ falls below the level at which the constraint binds, the Lagrange multiplier on the constraint enters the first-order condition alongside marginal utility, and the required return on every claim the sector must hold rises by an amount proportional to that multiplier and to the claim's exposure to intermediary capital.

Two predictions follow, and both are sharp. First, risk premia are a **decreasing and convex** function of $$\eta\_t$$: in the region where the constraint is slack, changes in intermediary capital do nothing; below the threshold, small further declines produce large increases in premia. The relation between intermediary health and risk premia is nonlinear, which is why the model can be quiet for years and then explain a great deal in a few weeks. Second, the model generates **time-varying volatility and correlation** endogenously: when the constraint binds, all claims held by the intermediary sector are exposed to the same state variable, so previously unrelated markets start moving together. He and Krishnamurthy calibrate the model to crisis episodes in mortgage and credit markets and reproduce both features.

The reader who skips this subsection loses the derivation and keeps the statement: *the intermediary's capital ratio is the state variable, the constraint binds in crises, and premia are nonlinear in it.*

![Figure 19.5: The intermediary capital ratio](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-811ce45ede821f255fa40d2198539aa3b731df8d%2Ffig_19_05_the_intermediary_capital_ratio.png?alt=media)

**Figure 19.5: The intermediary capital ratio.** The $$\eta\_t$$ of the paragraph above, on the series He, Kelly and Manela construct and post: the market equity of the primary dealers' holding companies over that equity plus their book debt, monthly since 1970. Read it as a state variable and not as a price. It spends years at a time on one side of its mean; it falls hard in exactly the episodes this book keeps returning to — the 1974 recession, the Volcker disinflation, LTCM, the crisis, the euro crisis — and the falls are much faster than the recoveries. The trough is 2.2 percent in February 2009, a fifth of the 1998 peak, and the ratio does not regain its mean until 2013. That asymmetry is what makes the constraint interesting: a variable that collapses in weeks and mends over years spends most of its time in one of two regimes, which is the empirical shape of a premium that is decreasing and convex rather than linear. One limitation, and it is a live one. The series the authors post ends in November 2018, so the episode this chapter opens with is not in it. Figure 26.4's dealer leverage, built on the Financial Accounts and running to the present, is the substitute — a coarser measure of the same object, available for the quarters this one is missing. *Source: He, Kelly and Manela, "Intermediary Asset Pricing: New Evidence from Many Asset Classes", posted factor file; NBER recession dates.*

The nonlinearity is also the model's most testable feature, and the place where it parts company with everything in Part II. A linear factor model says that a one-standard-deviation move in the factor changes premia by the same amount wherever it starts. He-Krishnamurthy says it does not: the same shock to intermediary capital is close to irrelevant in 2005 and enormous in late 2008. That prediction is why the model reads as an account of *crises* rather than of average returns, and why calibrating it means matching the behavior of spreads in a handful of episodes rather than the mean of a long sample. Its natural test assets are the ones where the intermediary is unambiguously the holder — mortgage-backed securities in 2008, corporate credit, and the arbitrage bases that widen when nobody has room on their balance sheet.

### Broker-dealer leverage as the priced factor

Adrian, Etula and Muir (2014) took the idea to the cross-section with an unusually economical implementation. Instead of estimating a structural model, they observe that if the intermediary's marginal value of wealth is the discount factor, then anything that moves with it is a candidate factor — and that broker-dealer **leverage** moves with it in a known direction.

The link is Adrian and Shin's procyclicality result, which Chapter 16 §16.5 states. Dealers actively manage leverage to a target: when asset prices rise and equity increases, they expand the balance sheet to restore leverage, and when prices fall they contract. Leverage therefore rises when balance sheet capacity is plentiful and the marginal value of a dollar of dealer equity is low, and falls when capacity is scarce and that dollar is precious. A discount factor that is decreasing in dealer leverage growth is the natural implementation, and linearizing gives a single-factor model in which the factor is the growth rate of aggregate broker-dealer leverage $$L\_t$$, constructed from the Financial Accounts' security brokers and dealers table.

The result is the striking part. A single factor, built from one free quarterly series in the Z.1, prices the twenty-five size and book-to-market portfolios with a cross-sectional fit on the order of three-quarters of the variation in average returns — comparable to the Fama-French three-factor model, which has three factors constructed from the very returns being explained, and far better than the consumption CAPM. It also prices momentum portfolios, which the Fama-French model notoriously does not, and it carries over to portfolios of Treasury bonds and corporate bonds sorted on maturity and rating. For a book that spent Chapter 6 on the factor zoo, the appeal of a factor with a stated economic mechanism and no free construction choices should be obvious.

Two honest caveats. The measured series is book leverage of the broker-dealer *subsidiaries* reported in the Financial Accounts, and that reporting perimeter has changed as dealers moved activity into holding companies; the series is not a clean read on the same institutions across the whole sample. And a single-factor model that fits this well on portfolios sorted by characteristics needs to be checked against the multiple-testing discipline of Chapter 6 §6.4 like any other.

### The intermediary capital ratio across asset classes

He, Kelly and Manela (2017) provide what is, for the purposes of this book, the decisive test. They build the factor directly from the theory rather than from leverage: the state variable is the **capital ratio** of the holding companies of the New York Fed's primary dealers, measured as market equity divided by market equity plus book debt, and the pricing factor is the innovation in that ratio. Primary dealers are the right population because they are the counterparties through which the Treasury, agency, repo, and much of the derivatives market actually clears.

The test is what makes it decisive. They price the major asset classes at once — US equities, US government and corporate bonds, foreign sovereign bonds, equity index options, credit default swaps, commodities, and foreign exchange. The intermediary capital factor carries a positive and economically large price of risk in essentially all of them, and — the point that matters — the estimated price of risk is of similar magnitude across classes, which is what a single stochastic discount factor is supposed to deliver and what no consumption-based or equity-factor model has ever delivered.

Consider which asset classes those are. Households do not hold credit default swaps. They do not write over-the-counter index options, trade the sovereign debt of other governments, or take positions in commodity futures. In those markets the intermediary is not merely *a* marginal investor; it is the only plausible one. A factor built from dealer equity that prices claims households never touch, with the same price of risk that it earns in the equity market households do touch, is close to a smoking gun for the intermediary view. It is very hard to tell a story in which dealer capital is a proxy for household marginal utility in the CDS market.

**Table 19.2: Three implementations of the intermediary discount factor**

|                | He-Krishnamurthy (2013)                            | Adrian-Etula-Muir (2014)                               | He-Kelly-Manela (2017)                                                                 |
| -------------- | -------------------------------------------------- | ------------------------------------------------------ | -------------------------------------------------------------------------------------- |
| Object         | Structural model                                   | Single traded-sector factor                            | Single traded-sector factor                                                            |
| State variable | Capital ratio $$\eta\_t$$ of the specialist sector | Growth in broker-dealer leverage $$L\_t$$              | Innovation in primary dealers' capital ratio $$\eta\_t$$                               |
| Measurement    | Calibrated, not directly measured                  | Book leverage, broker-dealer subsidiaries              | Market equity / (market equity + book debt), holding companies                         |
| Data source    | —                                                  | Financial Accounts (Z.1), L.130                        | CRSP/Compustat on the primary dealer list                                              |
| Test assets    | Crisis spreads in credit and mortgage markets      | Size, value, momentum; bond portfolios                 | Many asset classes at once: equities, bonds, sovereigns, options, CDS, FX, commodities |
| Headline       | Premia decreasing and convex in $$\eta\_t$$        | Cross-sectional fit comparable to three equity factors | Positive price of risk of similar magnitude across all classes                         |

*Source: Author's construction from the three papers cited.*

Read the last column as the argument and the first as the reason to believe it. He-Krishnamurthy says why intermediary capital should be a state variable; He-Kelly-Manela shows that a factor built to that specification prices claims across markets that share nothing except their intermediary.

One tension in the literature deserves to be stated rather than smoothed over, because a student will otherwise notice it and conclude that something is wrong. Adrian, Etula and Muir's factor is *leverage growth*, which is high in good times. He, Kelly and Manela's factor is the *capital ratio*, which is also high in good times — and the capital ratio is roughly the reciprocal of leverage. Both are found to carry positive prices of risk, which cannot both be describing the same object. The reconciliation runs through measurement: book leverage of broker-dealer subsidiaries and market-based capital ratios of holding companies behave very differently, particularly during 2008-2009, when book equity moved slowly and market equity collapsed. The two literatures agree on the mechanism and disagree on which balance-sheet measure captures it. That disagreement is not settled, and honest teaching says so.

![Figure 19.6: Broker-dealer leverage](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-be1da9f10487a8b105bcfd6b87bfd8b703dd8a6d%2Ffig_19_06_broker_dealer_leverage.png?alt=media)

**Figure 19.6: Broker-dealer leverage.** The series behind Adrian, Etula and Muir's factor: total financial assets of the US broker-dealer sector as a multiple of its own equity. It rises through the 1990s and 2000s to forty-seven times in 2008, collapses in eighteen months, and has sat between fifteen and twenty ever since. Two readings, and the second is the one this chapter needs. The pro-cyclicality is the point of the factor — leverage rises when asset prices rise, because a dealer marking a levered book to market gets equity it did not raise, and falls the same way — which is why *growth* in this series, rather than its level, is what carries a price of risk. And the post-2009 level is the constraint of §19.3 stated as a number: the balance sheet that had to absorb March 2020 was running at a third of its 2008 leverage against a Treasury market five times larger, which is Figure 19.1's ratio seen from the liability side. The caveats §19.5 states apply to every point on the line: this is book leverage of the broker-dealer subsidiaries, whose reporting perimeter moved as activity shifted into holding companies, and book equity moved slowly in 2008 while market equity collapsed. *Source: Financial Accounts of the United States (Z.1), table L.130, security brokers and dealers, via the FRED mirror; author's calculations.*

### What is established, and what is not

The evidence behind this chapter is uneven, and the line is worth marking, as Chapter 20 §20.5 marks it for the demand system.

**Table 19.3: The state of the evidence on intermediary asset pricing**

| Claim                                                                                                                                                  | Status                                                                                                                                                                 |
| ------------------------------------------------------------------------------------------------------------------------------------------------------ | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| Balance-sheet capacity, not news about payoffs, is what priced Treasuries in March 2020                                                                | **Widely accepted.** The temporary exclusion of Treasuries and reserves from the leverage ratio identifies the constraint from the policy side                         |
| Dealer capacity per dollar of Treasuries outstanding has fallen since 2007                                                                             | **Established** in direction on the financing measure — 48 percent to 11, Figure 19.1 — and **contested in size**, since net outright positions give the opposite sign |
| The leverage ratio and the Volcker rule, rather than higher capital everywhere, are what shrank market-making capacity                                 | **Contested.** Section 19.3 states the disagreement and does not resolve it; the magnitudes, not the attribution, are what is agreed                                   |
| Intermediary equity is volatile enough for a discount factor built from it to clear the Hansen-Jagannathan bound                                       | **Established** as a fact about the series; whether that discount factor is the right one is the rest of this table                                                    |
| A dealer-capital factor carries a positive price of risk of similar magnitude across asset classes households never touch                              | **Widely accepted**, on one carefully specified factor tested across many classes at once (He-Kelly-Manela)                                                            |
| Whether the mechanism is carried by book leverage growth or by the market capital ratio — near-reciprocal measures, both found to be positively priced | **Contested**, and unsettled; §19.5 states the tension rather than smoothing it                                                                                        |

*Source: Author's assessment of the literature discussed in §§19.3 and 19.5.*

### Whose $$m$$, revisited

Chapter 3 §3.7 asked whose marginal utility appears in the pricing equation and declined to answer "the representative household." Two answers are now on the table, and they are not competitors so much as claims about different markets.

**The wealthy household.** Chapter 5 §5.7's answer: equity risk is borne overwhelmingly by the top of the wealth distribution, whose consumption is far more volatile and far more correlated with equity returns than the aggregate, and using their consumption in place of aggregate consumption shrinks the equity premium puzzle by a large factor without closing it.

**The constrained dealer.** This chapter's answer: for claims that households do not hold at all, the marginal investor is a levered intermediary, and the relevant $$m$$ is the marginal value of its equity capital. This answer works in exactly the markets where the first cannot apply, and it explains episodes — March 2020, the 2008 CDS-bond basis, persistent violations of covered interest parity — in which prices moved with no news about consumption or cash flows.

**The third answer is Chapter 20's**, and it subsumes both. Demand-system asset pricing does not choose a marginal investor at all. It estimates a demand curve for every holder — households by wealth group, mutual funds, pensions, insurers, dealers, foreign investors — and derives prices from market clearing. The intermediary SDF of this chapter is what that system produces when the dealer's demand curve is the steep one and everyone else's is vertical; Chapter 5 §5.7's wealthy household is what it produces when the wealthy household's is the steep one. Which holder is marginal becomes an estimated quantity rather than an assumption, which is the most complete answer this book has to Chapter 3's question.

***

## 19.6 The Balance-Sheet-Constrained Core

The investor ecology of Part IV has a center, and it is the sector this chapter has described. Households (Chapter 14) supply the saving. Funds, insurers, and pensions (Chapters 16-18) hold the claims and are constrained by mandates, capital charges, and redemption terms. Banks and dealers sit underneath all of them, providing the funding that levered holders use, the market-making that makes any of these positions exitable, and the collateral transformation that lets one holder's asset become another's cash. That is why a constraint on this sector propagates to every other row in the ecology, and why its capital ratio prices claims that its own clients never see.

The division of labor between this chapter and Chapter 16 is worth stating plainly. Chapter 16 §16.5 supplied the **mechanism**: constrained capital moves prices, through fire sales, margin spirals, and the leverage cycle. This chapter supplied the **pricing consequence**: if the constrained holder is the marginal investor, its shadow value of capital is the stochastic discount factor, and that discount factor can be measured and tested. The first is a story about propagation; the second is an asset pricing model. Neither replaces the other, and the empirical content of the second is what makes the first more than a description of crises.

Two forward pointers close the chapter. Chapter 11 §11.6 asks who supplies liquidity trade by trade, and shows that the spread and the depth a dealer quotes are the same balance-sheet capacity measured at a much higher frequency — the microstructure face of §19.3. And Chapter 26 takes up risk constraints as a regulatory and managerial object: value at risk and its failure modes (§26.3), stress testing (§26.4), and, in §26.6, the margin and capital rules that make an institution's own risk measure the thing that forces it to sell — which is also where §19.5's $$\Lambda\_t$$ acquires a mechanism. That is the regulatory face of the same phenomenon, and it closes the loop on why a capital requirement designed to prevent a crisis can tighten inside one.

The capstone is next. Chapter 20 stops asking which holder is marginal and starts estimating all of them at once.

***

## Elsewhere in the Series

* **The dealer system, repo T-accounts, matched books, and the dealer of last resort** — *International Finance*, Chapter 2. Section 19.3 uses the dealer's balance sheet and cross-references its mechanics; Chapter 16 §16.4 carries the bridge.
* **Money markets, repo, and the instruments dealers fund themselves with** — *International Finance*, Chapter 4.
* **The nonbank and shadow-banking taxonomy** — *International Finance*, Chapter 8. **Private credit as an intermediation channel** — *International Finance*, Chapter 9. Section 19.4 keeps only the constraint each form carries.
* **Lender of last resort, deposit insurance design, resolution regimes, and the safety-net architecture** — *International Finance*, Chapters 15 and 16. Section 19.2 keeps the Diamond-Dybvig application and defers everything institutional.
* **Banking institutional detail, money creation, and the macroeconomics of credit supply** — *Institutionalist Macroeconomics*, Chapter 11.
* **The crisis episodes themselves** — the 2008 crisis volume: the repo run, Bear Stearns, Lehman, the money-market run, and the emergency facilities are narrated there.
* **The canonical constrained-capital statement** — this book, Chapter 16 §16.5. **Liquidity supply at trade frequency** — Chapter 11 §11.6, which prices §19.5's shadow value of capital as a quoted spread and a quoted depth. **Risk constraints as a pricing mechanism, and what makes §19.5's shadow value of capital move** — Chapter 26 §26.6. **The demand system that nests this chapter's answer** — Chapter 20.
* **The Treasury market, safe assets, and the convenience yield** — this book, Chapter 9, which treats the March 2020 episode from the claim's side rather than the dealer's.

***

## Summary

1. **March 2020 is the chapter in one episode.** Treasury yields rose during the largest flight to safety since 2008 because the dealers who intermediate the market were full — of basis-trade inventory, of corporate bonds nobody would bid for — and could not expand. The Fed's Treasury holdings rose by something on the order of $1 trillion in about a month, and it temporarily exempted Treasuries and reserves from the leverage ratio, which identifies the binding constraint as balance sheet rather than willingness.
2. **Intermediaries exist to economize on monitoring and to transform liquidity.** Diamond's delegated monitoring explains why the monitor is debt-funded and diversified; Diamond-Dybvig explains why the debt is demandable. Both features make the intermediary a large, levered holder, which is the property that matters for prices.
3. **The run is an equilibrium, not a panic.** In the worked example ($$\pi = 0.25$$, $$R = 2$$, $$\gamma = 2$$) the demand deposit contract pays 1.2815 early and 1.8123 late against autarky's 1 and 2 — genuine insurance. But if everyone withdraws, only 78 percent are served, and waiting is no longer a best response once more than 56 percent head for the door. Nothing about the assets changed in either equilibrium.
4. **Deposit insurance selects the good equilibrium and, in the model, is never used.** Its cost is moral hazard, which is what capital requirements are for. The lender of last resort and the rest of the safety net belong to the companion volume.
5. **Dealer capacity shrank relative to the markets it intermediates.** Treasury debt held by the public grew roughly fivefold after 2007 while primary dealer positions did not, under a non-risk-weighted leverage ratio that charges the same capital for a Treasury as for a leveraged loan and a market-making exemption that rewards carrying less inventory. That ratio is the setup for both the March 2020 episode and the pricing theory.
6. **If the intermediary is marginal, its shadow value of capital is the SDF.** Writing $$m\_{t+1} = \delta\Lambda\_{t+1}/\Lambda\_t$$ leaves the pricing equation intact and changes the bad state: a claim is cheap if it pays badly when intermediary capital is impaired. Intermediary equity is volatile in a way aggregate consumption is not, which is why the resulting discount factor can generate large premia without extreme risk aversion.
7. **He-Krishnamurthy makes the capital ratio the state variable.** An equity capital constraint that binds only when the sector is weak generates risk premia that are decreasing and convex in the capital ratio, plus endogenous spikes in volatility and cross-market correlation.
8. **The empirical implementations work, and the strongest evidence is where households are absent.** Broker-dealer leverage growth prices the size, value, and momentum cross-sections about as well as three constructed equity factors (Adrian-Etula-Muir), and the primary-dealer capital ratio carries a similar positive price of risk across equities, bonds, sovereigns, options, CDS, commodities, and FX (He-Kelly-Manela). That a dealer-capital factor prices credit default swaps at the same price of risk it earns in equities is the strongest single argument for the intermediary view. The unresolved tension is that the two implementations use measures — book leverage and market capital ratio — that are near-reciprocals and are both found to be positively priced.

***

## Key Terms

* **Delegated monitoring**: The Diamond (1984) rationale for intermediation — one agent monitors borrowers on behalf of many savers, and funds itself with debt against a diversified portfolio so that no one need monitor the monitor
* **Liquidity transformation**: Issuing a claim that is redeemable on demand against assets that lose value if liquidated early; the bank's second function and the source of its fragility
* **Run equilibrium**: In Diamond-Dybvig, the second equilibrium of the demand deposit game, in which each depositor withdraws because she expects others to. It requires no news about asset values and no irrationality
* **Sequential service constraint**: The rule that depositors are paid in the order they arrive, which is what makes a run individually rational for those near the front of the queue
* **Dealer**: An intermediary that quotes two-sided prices and absorbs the timing difference between buyers and sellers onto its own balance sheet, financing the resulting inventory in short-term secured markets
* **Repo (repurchase agreement)**: A sale of a security combined with an agreement to repurchase it, economically a collateralized loan with a haircut; the dealer sector's principal funding instrument
* **Balance-sheet capacity**: The quantity of claims an intermediary can hold given its equity and the capital, leverage, and margin constraints it faces; the scarce resource in every episode in this chapter
* **Intermediary SDF**: The stochastic discount factor $$m\_{t+1} = \delta\Lambda\_{t+1}/\Lambda\_t$$, in which $$\Lambda\_t$$ is the marginal value of a dollar of intermediary equity capital rather than a household's marginal utility
* **Leverage factor**: The growth rate of aggregate broker-dealer leverage, used by Adrian, Etula and Muir (2014) as a single priced factor on the argument that dealer leverage is high precisely when the marginal value of dealer wealth is low
* **Intermediary capital ratio**: Aggregate equity over aggregate assets of the intermediary sector; the state variable in He-Krishnamurthy and, measured on primary dealers' holding companies, the pricing factor in He-Kelly-Manela

***

## Readings

### Required

* Diamond, D. and P. Dybvig (1983). "Bank Runs, Deposit Insurance, and Liquidity." *Journal of Political Economy* 91(3): 401-419. *The model of §19.2 in four pages of algebra; read it for the structure of the argument, which recurs in every runnable institution in this book.*
* He, Z. and A. Krishnamurthy (2013). "Intermediary Asset Pricing." *American Economic Review* 103(2): 732-770. *The equity capital constraint, the capital ratio as the state variable, and the nonlinearity that lets the model be quiet for years and then explain a crisis.*

### Recommended

* Freixas, X. and J.-C. Rochet. *Microeconomics of Banking*. MIT Press. *The natural next book, and the depth reference this chapter deliberately does not duplicate — what Foucault, Pagano and Röell are to Chapter 11. Delegated monitoring, runs, credit rationing, competition among banks, and regulation, all derived rather than described. Sections 19.1 and 19.2 compress two models out of a field that has a textbook.*
* Adrian, T., E. Etula and T. Muir (2014). "Financial Intermediaries and the Cross-Section of Asset Returns." *Journal of Finance* 69(6): 2557-2596. *One free quarterly series from the Financial Accounts, and a cross-sectional fit comparable to three constructed equity factors.*
* He, Z., B. Kelly and A. Manela (2017). "Intermediary Asset Pricing: New Evidence from Many Asset Classes." *Journal of Financial Economics* 126(1): 1-35. *The test across many asset classes at once, including the ones households never touch. The factor series is posted publicly.*
* Diamond, D. (1984). "Financial Intermediation and Delegated Monitoring." *Review of Economic Studies* 51(3): 393-414. *Why the delegated monitor is debt-funded and diversified — the two features §19.1 carries forward.*
* Leland, H. E. and D. H. Pyle (1977). "Informational Asymmetries, Financial Structure, and Financial Intermediation." *Journal of Finance* 32(2): 371-387. *The pre-Diamond answer to §19.1's question: intermediaries exist because an informed agent can signal the quality of what it originates by retaining a stake in it. Read next to Diamond (1984) to see that delegated monitoring was one answer among several, and note that the retained-stake mechanism is what post-2008 securitization rules eventually mandated.*
* Petersen, M. A. and R. G. Rajan (1994). "The Benefits of Lending Relationships: Evidence from Small Business Data." *Journal of Finance* 49(1): 3-37. *Delegated monitoring's empirical payoff, measured on firms small enough that the relationship is the whole story. Availability of credit, more than its price, is what the relationship buys — the source for the second half of §19.1.*
* James, C. (1987). "Some Evidence on the Uniqueness of Bank Loans." *Journal of Financial Economics* 19(2): 217-235. *A short result students can check: announcing a bank credit agreement moves the borrower's share price, announcing a comparable public issue does not. If the bank were only a conduit for funds, the two announcements would be the same event.*
* Gorton, G. and A. Winton (2003). "Financial Intermediation." In G. M. Constantinides, M. Harris and R. M. Stulz (eds.), *Handbook of the Economics of Finance*, Volume 1A, Chapter 8. North-Holland. *The field survey, and the natural step past the two models §19.1 and §19.2 keep. Its organizing question — why the intermediary's liability is fragile by design rather than by accident — is the one this chapter carries into §19.5.*
* Bond, P. (2004). "Bank and Nonbank Financial Intermediation." *Journal of Finance* 59(6): 2489-2529. *The boundary of §19.4 drawn formally: what distinguishes an intermediary funded by depositors from one funded by the investors whose claims it originates, and why the two coexist rather than one displacing the other.*
* Duffie, D. (2020). "Still the World's Safe Haven? Redesigning the US Treasury Market After the COVID-19 Crisis." Hutchins Center Working Paper, Brookings Institution. *The opening episode in its clearest published account, with the dealer-capacity ratio that organizes §19.3.*
* Copeland, A. (2012). "Evolution and Heterogeneity among Larger Bank Holding Companies: 1994 to 2010." Federal Reserve Bank of New York *Economic Policy Review* 18(2): 83-93. *The composition data behind §19.3's claim about what banks and dealers hold, from the supervisory series, and the evidence that the sector's largest firms became less alike rather than more.*
* Kroszner, R. S. (1999). "Can the Financial Markets Privately Regulate Risk? The Development of Derivatives Clearinghouses and Recent Over-the-Counter Innovations." *Journal of Money, Credit and Banking* 31(3): 596-618. *Central counterparties as a private solution to counterparty risk, written before the post-2008 clearing mandate made them public infrastructure. Background for §19.3's third change, and for the question of what happens when the institution that absorbs everyone else's counterparty risk is itself constrained.*

***

## Discussion Questions

1. **Does March 2020 refute the safe-asset status of Treasuries?** One reading is that a security whose price falls in a flight to safety is not a safe asset. Another is that Treasuries remained perfectly safe as claims — no payment was ever in doubt — and what failed was the market-making technology that converts them into cash on demand. Argue both. Then say what observable would distinguish them, and whether your answer changes the case for exempting Treasuries from the leverage ratio permanently.
2. **Whose** $$m$$**, with three candidates.** Chapter 3 §3.7 asked the question, Chapter 5 §5.7 answered "the wealthy household," this chapter answers "the constrained dealer," and Chapter 20 answers "estimate all of them." For each of the following claims, say which answer you would use and why: a large-cap US equity, a five-year credit default swap on an investment-grade name, an off-the-run thirty-year Treasury in March 2020, and a municipal bond. Is there any claim for which all three answers coincide?
3. **The run threshold and the deposit contract.** In §19.2 the bank chose $$c\_1 = 1.2815$$, which made the run threshold $$\nu^{\ast} = 0.561$$. A more generous contract offers more insurance and a lower threshold. Sketch the trade-off the bank faces between insurance and fragility, and explain why a bank left to itself will not choose the contract that eliminates runs. What does deposit insurance do to this trade-off, and what does it do to the bank's incentive to choose $$c\_1$$?
4. **The two factors point opposite ways.** Adrian-Etula-Muir price assets with dealer *leverage growth*; He-Kelly-Manela price them with the dealer *capital ratio*, which is roughly the reciprocal. Both report positive prices of risk. Propose two explanations — one about measurement (book versus market, subsidiary versus holding company), one about economics (whether leverage is chosen or imposed). What data would settle it?
5. **Capacity and regulation.** Suppose the empirical claim in §19.3 is right and dealer capacity per dollar of Treasuries has fallen by a factor of five since 2007. List three policy responses (a permanent leverage-ratio exemption for Treasuries, central clearing of Treasury cash and repo trades, a standing central bank repo facility) and, for each, say which part of the March 2020 mechanism it addresses and what new problem it creates. Which one relocates the constraint rather than relieving it?

***

## Problems

**Problem 1 — The deposit contract with different parameters.** Using the setup of §19.2 with power utility and $$\gamma = 2$$, so that $$c\_2 = \sqrt{R}c\_1$$ and $$c\_1 = \sqrt{R}/\[(1-\pi) + \sqrt{R}\pi]$$: (a) compute $$c\_1$$ and $$c\_2$$ for $$\pi = 0.25$$, $$R = 1.5$$; (b) compute the fraction of depositors the bank can serve in a full run; (c) compute the run threshold $$\nu^{\ast}$$. You should find $$c\_1 = 1.1596$$, $$c\_2 = 1.4202$$, a served fraction of 0.862, and $$\nu^{\ast} = 0.587$$. Explain in one sentence why a lower $$R$$ makes the bank less fragile.

**Problem 2 — Why log utility gives no insurance.** Repeat the optimization of §19.2 with $$u(c) = \ln c$$. Show that the solution is $$c\_1 = 1$$ and $$c\_2 = R$$ for any $$\pi$$ and any $$R$$ — that is, the bank offers exactly the autarky allocation and provides no liquidity insurance at all. Explain the result in terms of the offsetting income and substitution effects at $$\gamma = 1$$, and say what it implies about which parameter governs how much liquidity transformation a bank does.

**Problem 3 — Suspension of convertibility.** Suppose the bank announces at date 0 that it will pay $$c\_1$$ to at most a fraction $$\pi$$ of depositors at date 1 and will refuse all further withdrawals. Assuming the fraction of impatient depositors is known to be exactly $$\pi$$, show that a patient depositor's payoff from waiting is unaffected by what other patient depositors do, and hence that the run equilibrium disappears. Now suppose the impatient fraction is random, with mean $$\pi$$. Explain why the suspension rule now imposes a cost in the good state, and relate your answer to why deposit insurance dominates suspension as a policy.

***

## Selected Solutions

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

**Problem 1.**

(a) At $$\gamma = 2$$ the first-order condition $$u'(c\_1) = Ru'(c\_2)$$ reads $$c\_1^{-2} = Rc\_2^{-2}$$, so $$c\_2 = \sqrt{R}c\_1$$; substituting that into the budget constraint gives the formula quoted in the problem. With $$\pi = 0.25$$ and $$R = 1.5$$, $$\sqrt{R} = 1.224745$$, so $$c\_1 = 1.224745/(0.75 + 1.224745 \times 0.25) = 1.224745/1.056186 = 1.1596$$ and $$c\_2 = 1.224745 \times 1.1596 = 1.4202$$, both to four decimals. Against autarky's 1 and 1.5, the impatient depositor gains 16.0 percent and the patient one gives up 5.3 percent — genuine insurance, but less of it than the 28 and 9 percent of Table 19.1, where $$R = 2$$.

(b) The bank holds one unit of the long technology per depositor and that unit is worth 1 if interrupted at date 1, so a full run lets it serve $$1/c\_1 = 1/1.1596 = 0.8624$$ of its depositors. **86.2 percent** are paid 1.1596 and the remaining 13.8 percent receive nothing, against 78.0 and 22.0 percent in the worked example.

(c) $$\nu^{\ast} = (R - c\_1)/\[c\_1(R-1)] = (1.5 - 1.1596)/(1.1596 \times 0.5) = 0.3404/0.5798 = 0.5871$$. **58.7 percent** of depositors must be heading for the door before waiting stops being a best response, against 56.1 percent at $$R = 2$$.

A lower $$R$$ narrows the gap between the two dates' consumption that the contract exists to insure, so the optimal $$c\_1$$ falls toward 1, the bank liquidates less of the long asset per early withdrawal, and it can therefore absorb a larger share of withdrawals before the patient depositor's continuation value drops below what the queue is paying. Fragility is not a separate design parameter that a prudent bank could dial down on its own: it is the price of the insurance, and at $$R = 1.5$$ there is less of both.

**Problem 2.**

With $$u(c) = \ln c$$ the first-order condition $$u'(c\_1) = Ru'(c\_2)$$ reads $$1/c\_1 = R/c\_2$$, so $$c\_2 = Rc\_1$$. The budget constraint is $$c\_2 = R(1 - \pi c\_1)/(1-\pi)$$. Setting the two equal gives $$Rc\_1(1-\pi) = R(1 - \pi c\_1)$$, hence $$c\_1(1-\pi) + \pi c\_1 = 1$$, so $$c\_1 = 1$$ and $$c\_2 = R$$. Both $$\pi$$ and $$R$$ have dropped out of the answer: the log-utility bank offers exactly the autarky allocation, at every parameter value, and provides no liquidity insurance at all.

The general case shows what is special about $$\gamma = 1$$. Power utility gives $$c\_2 = R^{1/\gamma}c\_1$$, and the same substitution yields

$$
c\_1 = \frac{\kappa}{(1-\pi) + \kappa\pi}, \qquad \kappa \equiv R^{(\gamma-1)/\gamma},
$$

so $$c\_1 > 1$$ if and only if $$\kappa > 1$$, which holds if and only if $$\gamma > 1$$. Setting $$\gamma = 2$$ recovers §19.2's $$\kappa = \sqrt{R}$$. The cleanest way to see the knife-edge is to evaluate the first-order condition *at* the autarky allocation: it requires $$u'(1) = Ru'(R)$$, which under power utility is $$1 = R^{1-\gamma}$$. That holds exactly at $$\gamma = 1$$. For $$\gamma > 1$$ the left side is larger, so the bank wants to move consumption from date 2 to date 1 and liquidity insurance is positive; for $$\gamma < 1$$ it wants to move consumption the other way and the contract insures in reverse, paying the impatient depositor *less* than she could get alone.

The income and substitution effects are the same statement in another vocabulary. A higher $$R$$ makes date-2 consumption cheaper, which pulls the contract toward paying the patient depositor more; it also makes the depositor better off in expectation, which pulls consumption up at both dates. The elasticity of intertemporal substitution $$1/\gamma$$ is the exchange rate between them, and at $$\gamma = 1$$ they cancel exactly — the same cancellation that leaves a log-utility consumer's saving rate independent of the interest rate.

**Table 19.4: Liquidity insurance and fragility as risk aversion varies** ($$\pi = 0.25$$, $$R = 2$$)

| Relative risk aversion | $$c\_1$$ | $$c\_2$$ | Served in a full run | Run threshold $$\nu^{\ast}$$ |
| ---------------------- | -------- | -------- | -------------------- | ---------------------------- |
| 0.5                    | 0.5714   | 2.2857   | all                  | none                         |
| 1 (log)                | 1.0000   | 2.0000   | all                  | none                         |
| 2                      | 1.2815   | 1.8123   | 0.780                | 0.561                        |
| 5                      | 1.4689   | 1.6874   | 0.681                | 0.362                        |

*Source: Author's calculation from the first-order condition and the budget constraint of §19.2.*

So the parameter that governs how much liquidity transformation a bank does is the curvature of the depositor's utility, not the productivity of the technology. Raising risk aversion from 1 to 5 lifts the early payout from 1 to 1.4689 and drops the run threshold from "never" to 36 percent, while $$R$$ is held fixed throughout. The insurance and the fragility are one object seen twice — which is Discussion Question 3's point, and the reason a bank left to itself will not choose the run-proof contract.

***

## Data Exercise: Dealer Balance Sheets and the Price of Intermediary Capital

**Part A — Primary dealer positions and repo (free data).** The Federal Reserve Bank of New York publishes weekly primary dealer statistics — positions by instrument and maturity, financing (repo and reverse repo), and transaction volumes — free from its markets data page, with history back to the late 1990s.

1. Download the series for dealers' net outright positions in US Treasury securities, and the total value of Treasury debt held by the public from FRED. Plot the ratio of the two, quarterly, from 2000 to the present.
2. Locate the pre-crisis peak and the most recent value. By what factor has dealer position capacity per dollar of outstanding Treasuries changed? Compare your number with the claim in §19.3 and account for any difference — note in particular that net positions net long against short, which is not the same as gross inventory capacity.
3. Overlay dealer repo financing. Does the funding series move with the position series, and does the relationship change after 2008? State what a break would and would not establish about the leverage ratio.
4. Zoom to weekly frequency for January through June 2020. Date the peak in dealer Treasury positions, and compare it with the dates in the opening episode.

**Part B — The 2020 episode in prices and the Fed's balance sheet (free data).** All series here are on FRED.

1. Plot the ten-year Treasury constant-maturity yield (`DGS10`) and the S\&P 500 daily from February 1 to April 30, 2020. Mark March 9, March 15, and March 23. Describe in two sentences what a flight-to-quality model predicts for that window and what actually happened.
2. Add the Fed's total assets (`WALCL`, weekly) and its holdings of Treasury securities. Compute the change over the four weeks after March 15 and compare it with the magnitude stated in the opening episode.
3. Optional: add a market-liquidity proxy, such as the ICE BofA MOVE index or a Treasury-market noise measure if you can obtain one, and say what it adds that the yield alone does not.

**Part C — The intermediary capital factor (free data, if available for download).** He, Kelly and Manela have posted their intermediary capital ratio and factor series on their academic pages; check availability before building the exercise around it.

1. Retrieve the quarterly intermediary capital ratio and its innovation series. Plot the ratio from 1970 to the present and mark the four largest drawdowns.
2. Construct the Adrian-Etula-Muir leverage factor yourself from the Financial Accounts (Z.1), table L.130, security brokers and dealers: leverage is total financial assets divided by the difference between total financial assets and total liabilities. Take log changes and seasonally adjust as the authors do.
3. Correlate the two factors. Report the sign. Then re-read §19.5's paragraph on the tension between them and say which of your two series behaved more plausibly during 2008-2009 and during 2020.
4. Using Ken French's twenty-five size and book-to-market portfolios, run a two-pass Fama-MacBeth cross-sectional regression (mechanics in Appendix A) with each factor in turn. Report the estimated price of risk, its $$t$$-statistic, and the cross-sectional $$R^2$$. Compare with the CAPM and the Fama-French three-factor model on the same test assets.

**Part D ★ (if you have WRDS).** Rebuild the He-Kelly-Manela capital ratio from primary source data: take the current list of New York Fed primary dealers, match their publicly traded holding companies in CRSP and Compustat, and construct market equity divided by market equity plus book debt, aggregated across the sector. Compare your series with the posted one. Document every matching decision — the dealer list changes over time, several dealers are subsidiaries of foreign banks, and how you handle entry, exit, and non-US parents will move the series. Then state, in one paragraph, how much of the published factor's performance you regard as robust to those choices.