The Banking View of Bond Risk Premia

• DOI: http://doi.org/10.1111/jofi.12949
• Author: VALENTIN HADDAD,DAVID SRAER
• Published date: 01 October 2020
• Date: 01 October 2020

THE JOURNAL OF FINANCE •VOL. LXXV, NO. 5 •OCTOBER 2020

The Banking View of Bond Risk Premia

VALENTIN HADDAD and DAVID SRAER∗

ABSTRACT

Banks’ balance sheet exposure to fluctuations in interest rates strongly forecasts ex-

cess Treasury bond returns. This result is consistent with optimal risk management,

a banking counterpart to the household Euler equation. In equilibrium, the bond risk

premium compensates banks for bearing fluctuations in interest rates. When banks’

exposure to interest rate risk increases, the price of this risk simultaneously rises. We

present a collection of empirical observations that support this view, but also discuss

several challenges to this interpretation.

BANKS ARE LARGE SOPHISTICATED INTERMEDIARIES in the market for inter-

est rate risk, but are absent from standard studies of the yield curve.1In this

paper, we show that banks’ balance sheet exposure to fluctuations in interest

rates strongly forecasts excess Treasury bond returns. We interpret this result

through the lens of banks’ risk management decisions, which tightly connect

their exposure to interest rate risk with the price of this risk. This connection

represents a banking counterpart to the classic household Euler equation. In

equilibrium, an increase in future bond returns compensates any increase in

banks’ exposure to interest rate risk.2This paper establishes this relationship

∗Valentin Haddad is with UCLA and NBER. David Sraer is with UC Berkeley, NBER, and

CEPR.We gratefully acknowledge the useful comments and suggestions of Stefan Nagel; an As-

sociate Editor; two anonymous referees; Tobias Adrian; Mikhail Chernov; Anna Cieslak; John

Cochrane; Arvind Krishnamurthy; Augustin Landier; Giorgia Piacentino; Monika Piazzesi; David

Thesmar; Dimitri Vayanos;as well as seminar participants at Kellogg, Princeton, the University of

Michigan, Stanford, the Federal Reserve Bank of New York, the UNC Junior Faculty Roundtable,

the NBER Summer Institute, CITE, the MFS meeting, the Adam Smith Conference, and the SED

Annual Meeting. We have read The Journal of Finance disclosure policy and have no conflicts of

interest to disclose.

Correspondence: Valentin Haddad, Anderson School of Management, UCLA, 110 Westwood

Plaza, Los Angeles, CA 90095; e-mail: valentin.haddad@anderson.ucla.edu.

1In 2014, private depository institutions (U.S.-chartered depository institutions, foreign bank-

ing offices, banks in U.S.-affiliated areas, and credit unions) held 3.2% of all outstanding Trea-

suries, 25% of agency and government-sponsored enterprise-backed securities, 12.3% of municipal

securities, 33.6% of mortgages, and 49.5% of all consumer credit.

2Importantly, this statement describes an equilibrium relation rather than a causal relation-

ship. The price and quantity of interest rate risk are jointly determined in equilibrium. However,

we sometimes follow the tradition of the literature on the household Euler equation, which tends

to describe equilibrium relations using a more causal language.

DOI: 10.1111/jofi.12949

© 2020 the American Finance Association

2465

2466 The Journal of Finance®

empirically, presents a collection of facts that further support this view, and

highlights challenges to this interpretation.

We start by constructing a measure of the average bank exposure to interest

rate risk. At the bank level, we follow Gomez et al. (Forthcoming) and use the

income gap as our measure of interest rate risk exposure. The income gap of

a financial institution corresponds to the difference between the book value of

all assets that either reprice or mature within one year and the book value of

all liabilities that mature or reprice within a year, normalized by total assets.

This measure, commonly used by both banks and bank regulators, is readily

available at the quarterly frequency for the 1986 to 2014 period through FR

Y-9C filings of Bank Holding Corporations (BHC) to the Federal Reserve. The

income gap provides a relevant quantification of the net exposure of banks’ in-

come to interest rate risk. Gomez et al. (Forthcoming) show that the sensitivity

of banks’ profits to interest rates increases significantly with their income gap.3

We use the average income gap across banks with more than $1bn of total as-

sets as our measure of financial intermediaries’ interest rate risk exposure.

We run regressions of one-year excess returns on Treasuries—borrow at the

short rate, buy a long-term bond—on the average income gap available at the

beginning of the period. The estimated coefficient is significant for all bond

maturities. With this single predictor, we find R2values of 20% on average

across maturities. A battery of robustness checks shows that this result does

not spuriously derive from the persistence of our forecasting variable in a small

sample. Additionally, the forecasting power of the average income gap for Trea-

suries’ excess returns is not affected by the inclusion of macroeconomic factors

known to predict bond returns (Ludvigson and Ng (2009)). The robust corre-

lation between bonds’ excess returns and the average income gap, depicted in

Figure 1, is the main contribution of the paper. This finding offers prima facie

evidence of the role of financial intermediaries in asset pricing (e.g., He and

Krishnamurthy (2013), Brunnermeier and Sannikov (2014)).

We interpret this finding through the lens of a simple equilibrium restriction

on the yield curve following Greenwood and Vayanos (2014). This equilibrium

restriction must hold in a large family of economies. In the model, banks trade

assets of different maturities to maximize their expected profits while man-

aging their risk. When banks hold more long-term assets, they must absorb

additional interest rate risk. They will do so only if the market compensation

for this risk increases. Such compensation can be observed in, for instance,

Treasury bond returns.4In equilibrium, banks’ income gap, that is, the sen-

sitivity of banks’ profits to variation in the short rate, is negatively correlated

3Purnanandam (2007), Begenau, Piazzesi, and Schneider (2015), and English, den Heuvel, and

Zakrajsek (2012) also document that financial intermediaries do not fully hedge their exposure to

interest rate risk. Di Tella and Kurlat (2017) build a model to explain why banks optimally expose

their balance sheets to movements in interest rates.

4While a large share of the exposure of banks to interest rate risk comes from non-Treasury

assets, Treasuries constitute a simple and stable way to measure this price of risk. Hanson (2014)

and Malkhozov et al. (2016) follow a similar measurement approach in the context of mortgage-

backed security supply.

The Banking View of Bond Risk Premia 2467

−0.1 −0.05 0 0.05 0.1 0.15

Excess Returns

0.05 0.1 0.15 0.2

Income Gap

1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 2015q1

Date

Income Gap

3xr2xr

5xr4xr

Figure 1. Average income gap and future bond excess returns. This figure plots the time

series of banks’ income gap and future bond excess returns. The bank-level income gap is computed

from the quarterly Consolidated Financial Statements (Files FR Y-9C) and corresponds to the

difference between the dollar amount of assets that reprice or mature within one year and the

dollar amount of liabilities that reprice or mature within one year, all scaled by total consolidated

assets. “Income Gap” is the average income gap, computed across all U.S. bank holding companies

with total consolidated assets of $1 bn or more. rx nis the excess one-year return of zero-coupon

bonds of maturity n, using data from Gurkaynak, Sack, and Wright (2007) (Color figure can be

viewed at wileyonlinelibrary.com)

with bond risk premia. Since long-term Treasuries are more sensitive to the in-

terest rate than short-term Treasuries, this correlation between banks’ income

gap and risk premia is larger, in absolute value, for bonds of longer maturities.

These qualitative predictions echo our main findings. We confirm that they

hold quantitatively as well. Fitting the model to the data also allows us to es-

timate banks’ willingness to take risk, a key input for our theory and more

generally for macroeconomic models with financial intermediation.

Our analysis departs from the classic, frictionless view of the market for in-

terest rate risk. This view has received mitigated empirical success so far.5

In contrast, several recent papers provide convincing evidence that not all

5See Duffee (2018), Gürkaynak and Wright (2012), Beeler and Campbell (2012), and Schneider

(2017) for discussions of these issues.