Interest Rate Risk in Banking: A Survey∗

Guillaume Vuillemey†

July 22, 2016

Abstract

This paper surveys the theoretical and empirical literature on interest raterisk in banking. Theoretically, it considers the origins of interest rate risk andits allocation. Interest rate risk is non-diversifiable and does not originate fromthe banking sector, but from the potential time inconsistency between futureaggregate demand and supply of consumption goods. Empirically, we discussmeasurement and stylized facts. Banks bear part of total interest rate risk,but also engage in risk management and risk-sharing with non-financial agents.They transfer large amounts of risk to households and firms, by writing interestrate-contingent loan and deposit contracts. We consider the determinants ofthe aggregate exposure to interest rate risk and the pricing of marginal unitsof risk. Finally, interest rate policy, both conventional and non-conventional, isdiscussed.

J.E.L. Codes: E43, G21.

Keywords: Interest rate risk, Maturity mismatching, Interest rate, Investment,Consumption, Monetary policy.

∗I am grateful to the Chair ACPR/Risk Foundation: Regulation and Systemic Risk for supportingthis research.†HEC Paris. Email: vuillemey@hec.fr.

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1 Introduction

Interest rate risk arises as a major concern at times of negative or near-zero short-term

interest rates. However, it is also most relevant at any other time. As the intertemporal

price ratio, the term structure of interest rates is a primary determinant (and an

endogenous outcome) of virtually any choice involving intertemporal trade-offs, such

as consumption vs. saving decisions, financing and production plans, or portfolio

allocations. Yet, while interest rates are an input to most models in macroeconomics

and finance, the literature devoted specifically to interest rate risk is limited.

This paper surveys the theoretical and empirical literature on interest rate risk in

banking. It focuses particularly on its allocation, thus on exposures to it rather than on

its pricing.1 Exposures are crucially important, because interest rate risk is aggregate

in nature, as discussed below. This mere fact implies that it is not diversifiable, thus

that some agents have to bear it. A key question is whether banks, as intermediaries

between demanders and suppliers of funds at various maturities, are best able to bear

this risk, to what extent they are exposed to it or transfer it to the non-financial sector.

In this paper, I build upon the Diamond and Dybvig (1983) model of banking, and

on the major subsequent contribution by Hellwig (1994), to provide a comprehensive

theoretical view of interest rate risk, and to inform the empirical literature.

What is interest rate risk?

What is interest rate risk, and how does it arise? While it is often associated with

maturity mismatching, i.e., the intermediation of cash flows which differ in maturities

or repricing frequencies, interest rate risk does not ultimately originate from the bank-

ing sector. Several standard models of banking, such as Diamond and Dybvig (1983),

feature maturity mismatching without interest rate risk. In general equilibrium, in-

terest rate risk arises in the non-financial sector, from the possibly time-inconsistent

consumption and production decisions by households and firms.

Let us be precise. Banks are intermediaries between non-financial suppliers and

demanders of funds. On one side, firms invest in projects that have a short or a

long maturity, i.e., that return consumption goods sooner or later. On the other1Following Fama and Bliss (1987), there exists a separate literature relating the pricing of interest

rate risk to information contained in the yield curve. See Campbell and Shiller (1991) for a review.

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side, households have preferences for early or late consumption. Interest rate risk

arises from the interaction between the two, in which financial intermediaries play a

central role. There is interest rate risk whenever there is a risk that the maturity

structure of future aggregate production (supply of consumption goods) and that of

aggregate demand for consumption do not match. There is no reason why they should

systematically equalize. Indeed, future productivity and/or preferences are typically

unknown ex ante. Uncertainty about productivity implies that the ability to produce

real consumption at future dates is unknown. Uncertainty about preferences means

that the future marginal utility of consumption is also unknown.

Whenever the aggregate supply and demand for consumption goods do not match,

present consumption has to be traded off against future consumption. Consequently,

the interest rate (or, equivalently, the yield curve when multiple maturities are con-

sidered) has to adjust so as to induce agents to postpone or advance consumption.

In equilibrium, the yield curve equalizes the marginal utility of consumption across

dates, given the time structure of expected production and preferences. Two sym-

metric issues arise for households and firms. From the household perspective, there

is a risk that the preference for consumption is high when the supply of consumption

goods is low (because capital is invested in long-term assets that return consumption

later). In this case, some households will have to postpone consumption and engage

in “forced savings”, driving up the real interest rate. From the perspective of firms,

there is roll-over risk arising from the fact that households (as providers of savings)

may want to consume at times they need to attract funds for investment. In such

circumstances, the interest rate will also increase. If they fail to attract new savings,

firms may be forced to curtail investment or to liquidate long-term projects, which is

a costly way to provide consumption to impatient households.

Banks are a central link between households and firms. In the presence of aggregate

uncertainty, channeling savings from depositors with stochastic consumption needs to-

wards long-term investments necessarily creates interest rate risk. That banks engage

in such maturity transformation does not imply, however, that they are best able to

bear interest rate risk. A key question is therefore whether they provide insurance to

households against aggregate consumption shocks, or to firms against aggregate savings

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shocks. The contractual structure that links banks to their non-financial counterpar-

ties determines the amount of insurance that is provided. Banks can shield against

interest rate risk by writing contracts whose payoffs are contingent on the realized

interest rate. For example, variable-rate loan contracts can be written to provide the

bank with higher interest income when aggregate liquidity demand is high. Similarly,

variable-rate deposit contracts offer lower consumption to households in such states.

Overall, variable-rate contracts transfer interest rate risk to the non-financial sector.

In contrast, a bank retains interest rate risk by writing non-contingent (fixed-rate)

contracts.

Main findings

We review the theoretical literature on interest rate risk and relate it to empirical

work. The main takeaways from this survey can be summarized as follows.

1. Maturity mismatching per se does not create interest rate risk. When technology

or preference shocks are idiosyncratic, i.e., diversifiable, maturity mismatching

can be part of the optimal banking contract to finance long-term assets. It works

as an insurance mechanism and does not give rise to interest rate risk. For

interest rate risk to arise when long-term assets are financed out of short-term

savings, uncertainty about future technology or preferences has to be aggregate,

i.e., non-diversifiable.

2. Theory predicts that banks should bear no interest rate risk in a frictionless envi-

ronment, i.e., provide no insurance to households against aggregate consumption

risk. Interest rate risk should be fully born by agents in the non-financial sector.

The introduction of frictions can explain why banks bear non-zero interest rate

risk. Such frictions include moral hazard or the inability of bank managers to

commit their human capital.

3. In the data, banks retain some exposure to interest rate risk. Positive interest

rate shocks reduce bank equity value. Banks, however, engage in active risk

management, so that the interest rate sensitivity of net interest margins is low.

Off-balance sheet, hedging using interest rate derivatives is small in magnitude,

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due to limited net worth. On-balance sheet, large amounts of risk are transferred

to non-financial firms through variable-rate loans and to households through

variable-rate deposits. In the presence of financial constraints for non-financial

agents, these transfers have real effects.

4. While it can be achieved, perfect immunization against interest rate risk is usu-

ally not optimal. Some dependence of real outcomes (e.g., investment and con-

sumption decisions) on interest rates is desirable, as it makes it possible to achieve

better intertemporal smoothing.

5. Interest rate policy can alleviate bank funding constraints and avoid the costly

liquidation of long-term investment projects. Accommodative monetary policies,

however, impose costs to the non-financial sector. They operate by transferring

funds from households to banks at times aggregate demand for consumption is

high relative to the supply of consumption goods. This works against the provi-

sion of aggregate consumption insurance by banks to households. Expectations

of future interest rate policy also distort incentives ex ante, and leads to exces-

sive risk-taking. Finally, negative interest rates or low long-term interest rates

may impair the proper functioning of financial intermediation, even though more

empirical evidence is needed.

Relevance of interest rate risk

Interest rate risk is a relevant object of study for at least two strands of economics.

First, in macroeconomics, whether banks, other financial institutions or non-financial

agents bear interest rate risk is key to understanding the dynamics of real variables

in the face of aggregate preference or productivity shocks. It is also relevant to the

workings of monetary policy. For example, Brunnermeier and Sannikov (2012) high-

light that “asset holdings and interest rate sensitivities of these assets matter when

choosing between conventional or non-conventional monetary policy tools”.

Second, a proper understanding of interest rate risk is central to the literature on

banking and financial stability. Most of the recent literature on financial institutions

has instead focused on other sources of risk, such as solvency or liquidity risk. In an

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environment where both short-term and long-term interest rates have been at histor-

ically low levels for about eight years, a well-managed interest rate risk is arguably

a first-order concern for financial intermediaries (Bednar and Elamin, 2014; Begenau,

Piazzesi, and Schneider, 2015). Interest rate risk can impose severe losses onto finan-

cial intermediaries, as illustrated in the 1980s by the Savings & Loan crisis in the U.S.

(e.g., Kane, 1989; White, 1991; Curry and Shibut, 2000). Between 1986 and 1995,

1,043 thrift institutions had been closed, representing USD 519 Bn in assets.

Throughout the paper, we build on the seminal banking model by Diamond and

Dybvig (1983) and on its extension by Hellwig (1994) to allow for aggregate risk. That

interest rate risk is non-diversifiable is a key theme of this paper, and gives rise to most

of the questions which we review. We pay particular attention to the question whether

banks provide insurance to non-financial agents against interest rate shocks. A unique

model structure is able to generate rich predictions that can inform measurement and

a diverse body of empirical work. Relying on a single theoretical framework brings

the benefit of simplicity and consistency. We are not aware of any other encompassing

survey on interest rate risk in banking.2

We proceed as follows. In Section 2, we discuss the origins of interest rate risk.

Section 3 turns to its measurement and quantifies the extent of banks’ risk expo-

sures. Section 4 summarizes empirical work on risk-sharing between banks and their

non-financial counterparties, taking the aggregate amount of risk as given. Section 5

proceeds by endogenizing the amount of risk and by discussing the pricing of marginal

units of risk. Section 6 introduces interest rate policy and studies its effects on risk-

sharing across sectors and on the amount of risk.

2 The origins of interest rate risk

This section shows that interest rate risk does not stem from maturity mismatching per

se. It arises from aggregate shocks to technology or preferences when long-term assets

are financed and short-term consumption needs are uncertain. We also demonstrate

that perfect immunization against interest rate risk is, in general, not desirable.2Two surveys by Staikouras (2003, 2006) have a different focus, since they restrict attention to the

effects of interest rate changes on common stock returns of financial intermediaries.

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2.1 Model structure

We introduce the basic model structure. Then, we use it to consider both the Diamond

and Dybvig (1983) and the Hellwig (1994) models. The only difference between them

is whether there is aggregate risk or not.3

Time is divided in three periods, t = {0, 1, 2}. There is a continuum of unit mass

of consumers, all identical at t = 0 and endowed with one unit of a good. They have

preferences over consumption ct either at date 1 or 2 given by

u (c1) with probability λ (impatient type)

u (c2) with probability 1− λ (patient type),(1)

with u (.) increasing, strictly concave, and u′ (0) = ∞. Consumers are ex ante uncer-

tain about whether they value consumption at date 1 or 2. Due to the law of large

number, the fraction of date-1 consumers is exactly λ. There is no consumption at

date 0.

Date-0 endowments can be invested in short-term and long-term projects.

• Short-term investments at date 0 yield a per-unit return r1 at date 1, normalized

to r1 = 1. When financed at date 1, short-term investments yield r2 at date 2.

• Long-term investments at date 0 yield R > 1 at date 2, with no intermediate

payoff at date 1. If liquidated at date 1, the long-term asset yields a per-unit

salvage value ` < r1. The chosen level of liquidation at date 1 is denoted L.

Furthermore,

r1r2 < R, (2)

i.e., long-term investments are more profitable than short-term investments if

carried to maturity.

Assumption (2) is important to understand maturity mismatching and, later, inter-

est rate risk. Long-term investments are not similar to short-term investments that3We focus on a few salient features of these models, which make it possible to highlight the

respective roles of maturity mismatching and of interest rate risk. More detailed descriptions of theDiamond and Dybvig (1983) model, and of important subsequent contributions, can be found inTirole (2006, Chapter 12) or Freixas and Rochet (2008, Chapter 7).

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would simply “take longer” to return consumption; they are also more productive.

One interpretation is that the long-term technology is more capital-intensive, and

therefore requires more time-to-build. In contrast, the short-term technology yields

consumption goods quicker, but in lower quantities. If an investor were sure to have no

intermediate (i.e., date-1) consumption need, investment in the long-term technology

would always dominate. When preferences for consumption at each date are ex ante

uncertain, however, investing part of the endowment in the short-term technology is

necessarily part of the optimal plan. If, indeed, all endowments were to be invested in

the long-term asset, investors who turn out to be early consumers would be left with

no consumption goods available at t = 1. For long-term investments to be profitably

exploited, it has to be the case that some investors forego early consumption and de

facto engage in long-term savings (even if the timing of consumption is individually

unknown ex ante). The representative investor decides how to allocate savings be-

tween short-term investments k01 and long-term investments k02, subject to a budget

constraint, k01 + k02 = 1.

2.2 Maturity mismatching without interest rate risk

From this basic model structure, we turn to the Diamond and Dybvig (1983) model.

For our purposes, its key feature is that r2, the date-2 return on short-term investments

made at date 1, is known at date 0. Therefore, the only source of uncertainty in the

model comes from the timing of individual consumption. Importantly, this uncertainty

is purely idiosyncratic. There is no aggregate uncertainty: aggregate consumption at

date 1 in known from date 0.

To maximize ex ante expected utility, the first-best allocation features pooling of re-

sources across consumers. The autarkic allocation, in which each consumer maximizes

its expected utility, is inefficient, because investors lose the benefits from short-term

(respectively, long-term) investments if they turn out to be patient (resp. impatient)

consumers. In the first-best, there is no liquidation (L = 0) at date 1, because this is a

costly way to provide resources to early consumers, in a setup where aggregate date-1

consumption is known ex ante. With pooling of resources, the unique symmetric (i.e.,

that gives everyone at date 0 the same type-contingent consumption plan) optimal

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allocation solves

maxc1,c2,k01,k02

E [U ] = λu (c1) + (1− λ)u (c2) , (3)

under the budget constraints at dates 1 and 2, respectively

λc1 = k01, (4)

(1− λ) c2 = Rk02. (5)

The solution (c∗1, c∗2, k∗01, k∗02) is given by the constraints and the first-order condition

U ′ (c1)U ′ (c2) = R. (6)

Diamond and Dybvig (1983) show that the first-best allocation can be implemented

using a demand deposit contract in which the interest rate received by each consumer

depends on the date of withdrawal. We highlight two features of the optimal contract.4

First, it features maturity mismatching without interest rate risk. Provided λ 6= 1,

there is some level of investment in the long-term asset. Moreover, this long-term

investment never gets liquidated at date 1 under run-proof deposit contracts (which

can be shown to exist). The absence of interest rate risk is easily seen from the fact

that consumption levels c∗1 and c∗2 are known from date 0, and depend only on whether

each depositor turns out to be patient or impatient. They are not contingent on any

other aggregate variable.

Second, the optimal contract provides insurance against idiosyncratic consumption

shocks. To see this, we show that yield curve resulting from the contract is flatter than

the technological yield curve. Define the technological yield curve as the per-period

return on the short-term and on the long-term assets. The per-period yield on the

long-term asset, rLT , solves

(1 + rLT )2 = R, (7)

thus rLT =√R − 1 and rST = r1 − 1 = 0 < rLT . Turning to the yield curve implied

4Most of Diamond and Dybvig (1983)’s subsequent focus is on introducing asymmetric informationabout consumers’ types, thus incentive compatibility constraints. In the second-best, they showconditions under which a deposit contract is stable or subject to runs. Given our focus on interestrate risk, we do not review these discussions here.

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by the optimal allocation {r∗ST , r∗LT}, condition (6) implies5

1 < c∗1 < c∗2 < R. (8)

It follows that

rST < r∗ST and r∗LT < rLT , (9)

i.e., impatient consumers benefit from part of the returns made possible by the invest-

ment in the most productive long-term technology.6 The insurance that is provided

is against idiosyncratic consumption shocks only. The absence of interest rate risk,

despite maturity mismatching, is a direct consequence of the absence of aggregate

risk, in the form of either aggregate preference or productivity risk. From date 0, the

aggregate amount of date-1 consumption is known.

2.3 Maturity mismatching with interest rate risk

We introduce aggregate risk in the model, following Hellwig (1994). This gives rise

to interest rate risk. Instead of taking r2 as a constant, we assume there is aggregate

uncertainty about it. The date-2 return on short-term investments made at date 1

is now unknown at date 0 and publicly observed at date 1 only. It has a continuous

probability density function F with support [0, R/`). The upper bound, R/`, ensures

it is never optimal in the first-best to liquidate the long-term investment to invest in

the short-term project.

To obtain the first-best allocation, on which we focus, one solves

maxc1,c2,k01,k02,L

E [U ] = E [λu (c1) + (1− λ)u (c2)] , (10)

5A necessary condition is that consumers’ coefficient of relative risk aversion exceeds 1, i.e.,|cu′′ (c) /u′ (c)| > 1 for all c.

6Insurance, however, is incomplete, since c1 < c2. Sacrificing some insurance is optimal to takeadvantage of the upward-sloping technological yield curve.

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subject to the constraints

λc1 ≤ k01 + `L, for all r2, (11)

(1− λ) c2 ≤ R (k02 − L) + r2 (k01 + `L− λc1) , for all r2, (12)

k01 + k02 = 1, (13)

0 ≤ L ≤ k02 for all r2, (14)

where we note that c1, c2 and L are functions of r2. Inequalities (11) and (12) are

budget constraints at dates 1 and 2. The amount available for consumption at date 1

equals the return on the short-term asset (r1 = 1) plus the amount obtained through

the liquidation of the long-term asset, if any. This entire amount needs not be con-

sumed, because high realizations of r2 may be associated with reinvestment at date

1. Thus, constraint (11) needs not be binding. Constraint (12), in contrast, is always

binding, since consuming less than the amount produced is inefficient at date 2. Con-

sumption available at date 2 equals the amount of long-term investment that has not

been liquidated, plus the proceeds on any reinvestment in the short-term asset at date

1.

In the first-best, liquidating the long-term investment is always an inefficient way

to provide consumption or funds for reinvestment at date 1. We find the optimal

allocation using backward solution and write the problem arising at date 1, after r2 is

realized,

maxc1,c2

U = λu (c1) + (1− λ)u (c1) , (15)

subject to the budget constraint at date 2,

(1− λ) c2

r2= r1k01 − λc1 + Rk02

r2, (16)

in which (r1k01 − λc1) ≥ 0 is the amount reinvested at date 1.

The solution delineates two regions. Intuitively, there is an economy-wide trade-off

between providing insurance against liquidity needs and exploiting good reinvestment

opportunities at date 1. Insurance requires immunization of date-1 and date-2 con-

sumption levels against the realization of the aggregate factor r2. The exploitation of

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reinvestment opportunities, in contrast, commands some dependence of consumption

on r2.

A first region is one in which r2 is low and where there is no reinvestment at date

1. Impatient (resp. patient) investors consume all resources available at date 1 (resp.

date 2), i.e.,

c1 = r1k01

λand c2 = Rk02

1− λ. (17)

This solution provides perfect immunization against interest rate risk, i.e., the con-

sumption of both patient and impatient consumers does not depend on the realization

of r2. Equation (17) is the first-best solution for realizations of r2 below a threshold

r∗2. The need to provide insurance overrides that of exploiting short-term investment

opportunities at date 1, whose profitability is low. Thus, there is optimally no rein-

vestment at date 1 out of maturing short-term assets.

There is, however, another region where positive reinvestment takes place at date

1. This is the case if r2 is larger than r∗2. In this case, the first-order condition to the

date-1 problem yields

u′ (c1) = r2u′ (c2) . (18)

Denote c∗1 (k01, k02, r2) and c∗2 (k01, k02, r2) the consumption levels at dates 1 and 2

that satisfy (18) when r2 ≥ r∗2. The consumption of date-2 consumers increases in

r2, as reinvestment becomes more attractive. The provision of liquidity insurance for

impatient consumers is traded off against the desire to exploit more profitable short-

term investment projects. The resource constraint at date 2, Equation (16), makes

it clear that the relevant discount factor between dates 1 and 2 is r2. The stochastic

realization of r2 thus determines the extent to which resources available at date 1

should serve the consumption needs of patient or impatient consumers. We pursue

with five results on interest rate risk.

First, perfect maturity matching is, in general, not optimal. The allocation in

Equation (17) provides immunization of early and late consumers against interest

rate risk, i.e., their consumption does not depend on r2. In this case, it can be

said that there is perfect maturity matching: all date-1 consumption is financed out

of short-term investments and all date-2 consumption out of long-term investments.

This allocation, however, is not optimal for high realizations of r2. In this case,

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immunizing early consumers against realizations of r2 would imply foregoing highly

profitable short-term investments between dates 1 and 2. For a high enough value of r2,

the cost of foregone investment is larger than the benefit from liquidity insurance. In

such cases, part of the resources available at date 1 are re-invested, implying that the

consumption of both patient and impatient consumers depends on r2. Perfect maturity

matching, even though doable, is not always optimal. There is an economy-wide trade-

off between investing in more productive longer-term technologies (that yield greater

future consumption), and the need to satisfy early/intermediate consumption demand.

A second remark relates to the allocation of interest rate risk between patient and

impatient consumers. Impatient consumers are better off when the realized value of r2

is low. This is because there is no reinvestment, and they obtain the consumption level

given in equation (17). They are exposed to high values of r2, i.e., to a flattening of the

technological yield curve, because there is reinvestment in this case and they consume

less than r1k01/λ. In contrast, patient consumers are better off when r2 is high, because

some of date-1 resources are then reinvested for their own profit. They are exposed to

low realizations of r2, i.e., to a steepening of the technological yield curve. In Hellwig

(1994)’s terminology, impatient consumers bears all the valuation risk on the long-

term investment, while the patient consumers bear all the reinvestment-opportunity

risk of short-term investment.

Third, risk is entirely born by patient or impatient consumers, not by the financial

intermediary. Together, maturity mismatching by financial intermediaries and aggre-

gate productivity risk (thus interest rate risk) do not imply that intermediaries are

exposed to interest rate risk. The key feature that immunizes the bank against interest

rate risk is that it writes state-contingent contracts, i.e., contracts whose pay-offs are

contingent on r2. These contracts can be interpreted as interest-bearing deposits in

which the promised rate is variable. Since there is pooling of resources across many de-

positors, however, it is still the case that some level of insurance against idiosyncratic

consumption risk is provided, as in Diamond and Dybvig (1983). But no insurance

against aggregate consumption risk is offered. Intuitively, being a pure intermediary

of funds, the bank improves allocations by pooling resources of individually uncer-

tain consumers. But since it does not itself engage in production, it cannot provide

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households with additional consumption – on top of what is produced by firms – when

aggregate consumption demand is high.

Fourth, interest rate risk arises from aggregate productivity risk, as the technolog-

ical return between dates 1 and 2 is unknown ex ante. It could equally well arise from

aggregate preference risk, with very similar results and implications. What matters

for interest rate risk to arise is the existence of ex ante aggregate uncertainty about

either the ability to produce future consumption (productivity risk) or about future

demand for consumption (preference risk), or both. A model in which interest rate

risk arises from aggregate preference risk is Diamond and Rajan (2012).

Fifth, the absence of liquidations at date 1 is a property of the first-best only. In the

presence of asymmetric information about depositors’ types (where late consumers can

in principle withdraw their deposit at date 1, even if they consume at date 2), the level

of investment in the short-term technology will be reduced relative to the first best.

A lower level of liquid funds within the bank at date 1 reduces the incentive of late

depositors to run. In such cases, partial liquidations at date 1 may be optimally used

to provide additional consumption to early consumers. The cost of early liquidations

has to be traded off against the incentive benefit of holding fewer liquid assets at date

1. In Section 6, we further discuss a related model in which positive but excessive

liquidations occur, and where interest rate policy can play a role.

3 Interest rate risk within the banking sector

We turn to the measurement of interest rate risk and review empirical evidence on

banks’ risk exposures. Data shows that financial intermediaries bear some interest

rate risk. We discuss theoretical reconciliations with Hellwig (1994)’s model, in which

all risk is transferred to non-financial agents. Finally, we introduce bank hedging by

means of interest rate derivatives.

3.1 Measurement of interest rate risk

The measurement of interest rate risk raises two main challenges. First, exposure to

interest rate risk is a high-dimensional object, which arises from the time structure of

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interest rate-sensitive assets and liabilities at a large number of maturities. It is thus

difficult to proxy by a simple statistic. We review three common measures of interest

rate risk, which deal with this dimensionality problem differently. The second challenge

pertains to the measurement of interest rate risk embedded in demand deposits.

3.1.1 Income gap

The income gap (also called “maturity gap” or “repricing gap”) is a popular measure

of interest rate risk, both in the academic literature (Flannery and James, 1984; Pur-

nanandam, 2007; Landier, Sraer, and Thesmar, 2015) and in practitioners’ textbooks

(Saunders and Cornett, 2008; Mishkin and Eakins, 2009). The construction of the in-

come gap relies on a breakdown of a bank’s assets and liabilities by maturity/repricing

buckets (e.g., below one year, between one and three years, etc.). The dimensionality

problem is overcome by deliberately restricting attention to one of these buckets only.

It is defined as

Income gap (i) = AIR (i)− LIR (i) , (19)

where AIR (i) and LIR (i) denote interest rate-sensitive assets and liabilities that ma-

ture or reprice within a bucket i. A negative value of the income gap means that the

bank holds more interest rate-sensitive liabilities than assets in this bucket. If so, an

increase in interest rate at maturity i reduces its interest income at this maturity. It is

exposed to refinancing risk. In contrast, a positive value of the income gap leaves the

bank vulnerable to decreases in the interest rate at maturity i, thus to reinvestment

risk.

As a measure of interest rate risk, the income gap has the appealing property

that, in first approximation, changes in net interest income in maturity bucket i are

proportional to it, i.e.,

∆NII (i) ≈ Income gap (i) ∗∆ri, (20)

where ∆NII (i) is the change in net interest income arising from assets and liabilities

in bucket i and ∆ri the change in the level of the interest rate at that maturity.

Intuitively, both assets and liabilities within one maturity bucket bear similar interest

15

rates. Assuming they are equal, the sensitivity of net interest income to interest rates

in a bucket is proportional to net assets within that bucket (i.e., assets minus liabilities,

which the income gap captures). In empirical work, a standard choice is the one-year

maturity bucket (i.e., all assets and liabilities that mature or reprice within one year).

Indeed, the one-year income gap can be readily computed for each U.S. bank holding

company from publicly available call reports data, which is not the case for other

maturity buckets. Practically, another advantage of the one-year gap is that it can

be interpreted as the interest rate sensitivity of a bank’s one-year ahead net interest

margin, which is a natural forecasting horizon.

There is ample evidence that the income gap is a satisfactory measure of interest

rate risk. Landier, Sraer, and Thesmar (2015) show that the sensitivity of bank profits

to interest rates increases significantly with their income gap.7 Flannery and James

(1984) show that the income gap correlates with the sensitivity of common stock

returns to interest rates. Banks with more long-term assets relative to short-term

liabilities experience more negative stock returns following an increase in interest rates.

However, the income gap has a number of limitations, due to its simplicity in

dealing with the dimensionality problem. It considers one maturity bucket only and

disregards gaps between interest rate inflows and outflows in all other parts of the

maturity spectrum. When computed for short-term maturity buckets, it is useful as

an indicator of the interest rate sensitivity of future cash flows, but provides a poor

view of (valuation-induced) interest rate risk arising from the mismatched structure

of assets and liabilities at longer maturities.

3.1.2 Duration

To address these concerns and capture valuation risk throughout the whole maturity

spectrum, measures of duration (inspired by the literature on the pricing of fixed-

income securities) can be computed. The duration is initially defined for a single

fixed-income security. A bank’s balance sheet is subsequently modeled as a portfolio of

fixed-income securities, whose average duration can be computed. Define the Macaulay7Landier, Sraer, and Thesmar (2015) also show that the income gap predicts the sensitivity of bank

lending to interest rates. They conclude that a bank’s exposure to interest rate risk is a importantdeterminant of the intensity of the lending channel.

16

duration D of a fixed-rate bond as

D =n∑

i=1tiCFie

−yti

V, (21)

where CFi is a cash flow (coupon or principal) to be received at date ti, y is the yield

to maturity for the bond, and V is the present value of all cash flows of the asset,

V = ∑ni=1 CFie

−yti . The Macaulay duration is the time-weighted present value of all

cash flows i ∈ {1, ..., n} to be received until maturity, normalized by the unweighted

present value of all cash flows. It is expressed in units of time.

To see why duration is a measure of interest rate risk, consider the derivative of

the present value of the bond with respect to the yield to maturity,

∂V

∂y= −

n∑i=1

tiCFie−yti

= −D · V, (22)

i.e., the change in bond value with respect to a small change in yield to maturity is

proportional to the Macaulay duration. On this basis, a number of related measures of

interest rate risk (convexity, DV01) can be computed (see Sundaresan, 2009). Applying

them to banks is straightforward theoretically, as assets and liabilities can be modeled

as a series of future cash inflows and outflows at various maturities.8 A measure of

bank exposure is the difference between the average duration of its assets and that

of its liabilities. Under the approximation that assets and liabilities are zero-coupon

(i.e., that the residual maturity equals the duration), a measure of duration gap can

be computed as

Duration gapit =∑

j mjAj

it∑j A

jit

−∑

k mkLk

it∑k L

kit

, (23)

where j and k index respectively several classes of assets and liabilities. mj and mk

denote the residual maturity (for fixed-rate instruments) or next repricing date (for

variable-rate instruments) of assets and liabilities, respectively.

While duration-based measures have the advantage over the income gap that they8For interest rate bearing securities, such as variable-rate loans, cash flows should not be considered

until maturity, but until the next repricing date, as there is no more interest rate risk relevant forpresent value calculations after that date.

17

incorporate risk over the whole maturity spectrum, their main limitation is that data

requirements to compute them are large. As such, they are difficult to compute from

public data. Using a partial breakdown of the residual maturity of assets and lia-

bilities provided in the call reports, English et al. (2013) compute the duration gap

of U.S. banks. Before that, most discussions of duration-based measures work with

highly stylized bank balance sheets (e.g., Kaufman, 1984). Such measures are not yet

commonly used in the empirical banking literature.

Importantly, the interpretation of duration as a measure of interest rate risk is

different from that of the income gap. The income gap captures the interest rate

sensitivity of cash flows within a given maturity bucket. In contrast, the duration gap

captures the interest rate sensitivity of net worth (or equity value), since all future

cash in- and out-flows are discounted. It has to be interpreted in terms of total equity

value change.

Given this difference, is one of the two measures economically more relevant? In

a frictionless environment, only the duration gap should be a relevant measure of

interest rate risk. Indeed, net worth should then be the relevant state variable for

a bank’s capital structure decision, regardless of the timing of future cash flows. By

capturing the net effect of changes in the term structure of interest rates on net worth,

the duration gap is a sufficient statistic. In contrast, for a given level of net worth,

the exact timing of cash flows can matter in the presence of financial frictions (see,

e.g., Tirole, 2011). For example, low cash flows can give rise to liquidity problem

even for solvent banks, i.e., for institutions whose equity value remains positive. This

can be the case if long-term cash flows are not perfectly pledgeable. Short-term cash

flows also matter if banks are regulated based on their level of book equity (which is

affected by short-term cash flows) rather than on the market value of their equity. In

such cases, the income gap can provide additional valuable information on top of the

duration gap. Empirically, the extent to which the income gap and the duration gap

correlate has not been documented precisely.

18

3.1.3 Factor models

Factor models make it possible to construct measures of risk interpretable in terms of

total bank value (as is the case for duration), while reducing data requirements. Bege-

nau, Piazzesi, and Schneider (2015) overcome the dimensionality problem by exploiting

the low factor structure in interest rates. The argument proceeds in two steps. First,

it is well-established that a small number of factors are sufficient to describe prices of

fixed-income securities (see, e.g., Litterman and Scheinkman, 1991). It follows that a

small number of spanning bonds are sufficient to describe quantities of interest rate

risk within possibly large portfolios. The balance sheet of a bank (a portfolio of many

fixed-income positions) can thus be represented as a portfolio of such spanning bonds.

On this basis, time-varying measures of interest rate risk can be obtained.9 Begenau,

Piazzesi, and Schneider (2015) illustrate this methodology by measuring the exposure

of U.S. bank holding companies to interest rate risk over a 20-year period. Consistent

with existing empirical evidence (see below, Section 3.2.1), they find that bank value

decreases when interest rates go up.

3.1.4 Interest rate risk exposure of demand deposits

Apart from the dimensionality problem, another empirical challenge is to measure the

interest rate exposure of demand deposits. Deposits are the largest source of bank

funding. As described in Hanson, Shleifer, Stein, and Vishny (2015), the average bank

in the U.S. finances 76% of its assets with deposits. Furthermore, they document little

variation in deposit funding in both the cross-section and the time-dimension over a

period of 115 years. Given the importance of deposits, the literature devoted to the

measurement of their exposure to interest rate risk is surprisingly small.

Demand deposits are usually defined as “non-maturing liabilities”. Contractually,

they bear no explicit maturity and can be withdrawn on demand. Considering that

all demand deposits have a one-day maturity is, however, simplistic (Kaufman, 1984),

as deposits tend to be sticky in the data. Therefore, a first empirical challenge comes

from the difficulty to assign a maturity profile to deposits, in order to construct a

replicating portfolio of bonds with fixed maturities, whose interest rate sensitivity9A related approach had already been suggested by Piazzesi and Schneider (2010), who use Flow

of Funds data to measure the exposure of the U.S. household sector to interest rate risk.

19

can be assessed. A second challenge is that deposit rates are set in an imperfectly

competitive market. Empirically, deposit rates tend to be lower and to adjust more

slowly to market rates in more concentrated markets (Berger and Hannan, 1989). As

pointed out by Hutchison and Pennacchi (1996), market rates cannot be used as a

proxy for deposit rates.

To address these two issues, the literature has converged towards models where

(i) market rates, (ii) deposit rates and (iii) deposit volumes are three factors driving

the interest rate exposure of deposits (Kalkbrener and Willing, 2004; Nyström, 2008).

The inclusion of both market rates and deposit rates makes it possible to capture

imperfect competition in the deposit market, since the wedge between the two can

be large. Incorporating deposit volumes is necessary to account for the slow-moving

nature of deposits. Volumes are therefore often modeled using autoregressive speci-

fications, e.g., through partial adjustment equations (O’Brien, 2000). For valuation,

most papers follow the arbitrage-free approach of Jarrow and van Deventer (1998),

who show that non-maturing liabilities are equivalent to an exotic interest rate swap,

where the principal depends on the past history of market rates. Demand deposits

can be valued as such. An intuition for this equivalence result is that the amount of

deposits left within a bank at a given date (analogous to the principal amount of the

replicating swap) depends on the history of deposits inflows and outflows, which is

itself a function of past market rates (relative to deposit rates). Models built along

these lines can be fitted to data. As an example, Janosi, Jarrow, and Zullo (1999)

estimate the Jarrow and van Deventer (1998) model using U.S. data.

3.2 Interest rate risk bearing by banks

Research on banks’ exposure to interest rate risk dates back at least to Samuelson

(1945). Relying on a duration-based approach (see Section 3.1.2), his paper highlights

a tension between two effects. First, it argues that “a rise in interest rates hurts the

banking system if the average time period of its inpayments exceeds that of its out-

payments”, which is the case if banks engage in maturity mismatching. However, the

stickiness of deposits leads Samuelson (1945) to conclude that “the banking system as

a whole is immeasurably helped rather than hindered by an increase in interest rates”.

20

In this section, we reformulate the exposition of these two forces by distinguishing the

effect of interest rate increases on bank value and on cash flows. We highlight two ro-

bust results. First, bank equity value is negatively related interest rates. Second, cash

flows at short time horizons from assets and liabilities in place are positively related

to interest rates. This apparent paradox echoes Samuelson (1945)’s argument.

3.2.1 Interest rates and bank equity value

Following the Savings & Loan crisis in the 1980s, a large literature investigated the

effect of interest rate shocks on the valuation of bank equity. These works were part

of a larger research stream showing that the inclusion of an interest rate factor in

an otherwise standard one-factor market model adds substantial explanatory power.10

In the case of banks, two questions are worth answering. First, whether bank value

increases or decreases on average following a positive shock to interest rates. Second,

whether cross-sectional variation in the sensitivity of stock returns to interest rates is

related to bank balance sheets.

A seminal paper answering both questions is by Flannery and James (1984), who

use a two-stage approach. In the first-stage, a bank’s stock return is regressed on the

market return and on an interest rate factor. For each bank, the coefficient on the

latter variable gives an “interest rate beta”. The second stage exploits cross-sectional

variation by regressing bank-specific interest rate betas on bank characteristics, in

particular measures of maturity transformation. Similar two-stage approaches have

subsequently been used in a number of other studies.

In the first stage, Flannery and James (1984) find that stock returns react nega-

tively to increases in interest rates. After them, a large number of papers, including

Aharony, Saunders, and Swary (1986), Yourougou (1990), Akella and Greenbaum

(1992), Lumpkin and O’Brien (1997) and Choi and Elyasiani (1997) have observed a

similar relation. That bank value is decreasing in interest rates is a robust stylized

fact.

In the second stage, Flannery and James (1984) find that cross-sectional variation10In an influential paper, Fama and Schwert (1977) find that common stock returns are negatively

related to the expected and unexpected components of the inflation rate. Sweeney and Warga (1986)build a two-factor model, using the market return and changes in yields of long-term governmentbonds as factors. Their empirical evidence suggests that the interest rate factor is priced.

21

in interest rate betas is well-explained by the income gap (see Section 3.1.1), which

they interpret as a measure of maturity transformation. Banks with more short-term

liabilities relative to short-term assets have a more negative interest rate beta. Their

stock price declines more in response to positive innovations to interest rates. This

finding has been confirmed by a number of papers, including Akella and Greenbaum

(1992) and Lumpkin and O’Brien (1997), even with slightly different measures of

maturity transformation.

Recently, this research stream has been revisited and expanded by English, Van den

Heuvel, and Zakrajsek (2013). Overall, their results are very consistent with those by

Flannery and James (1984), but they provide contributions in a number of dimensions.

First, they rely on intraday stock price data on FOMC announcement days. One

advantage of high-frequency data is that it enables better identification of pure interest

rate surprises. With data at a lower frequency, indeed, an endogeneity concern is

that changes in the general level of interest rates correlate with other changes in

macroeconomic factors which themselves drive bank stock returns. This concern is

absent for intraday interest rate surprises. Second, they look not only at innovations

to the level of interest rates, but also to the slope of the yield curve. They find negative

stock returns following an unanticipated increase in the level of interest rates or a

steepening of the yield curve. Finally, when relating estimated interest rate betas with

bank characteristics, English, Van den Heuvel, and Zakrajsek (2013) confirm that stock

returns are more negative for banks with a higher degree of maturity mismatching. An

additional and new finding is that stock returns are more negative following positive

interest rate innovations for banks relying more on core deposits. Their interpretation

is that the stock market prices the fact that interest rate increases triggers outflows

of deposits from the banking sector, which affect proportionally more banks that rely

heavily on deposits.

3.2.2 Interest rates and bank cash flows

From bank equity value, which arises from the whole term structure of assets and

liabilities, we turn to discussing the interest rate sensitivity of short-term cash flows and

profitability. In the presence of financial frictions, such as the imperfect pledgeability

22

of long-term assets, short-term cash flows can be crucially important (see discussion in

Section 3.1.2). Empirical evidence on the interest rate sensitivity of bank cash flows is

less stark than that on equity value. There is some evidence that positive innovations

to interest rates increase bank interest margins on average at short horizons. Most

papers, however, highlight that net interest margins are very stable over time and that

comovement with interest rates is low.

To a first-order approximation, the relation between interest rates and cash flows

can be documented using the income gap. As seen in Equation (20), changes in

a bank’s net interest income at a one-year horizon are proportional to its one-year

income gap. Landier, Sraer, and Thesmar (2015) follow this approach and document

that the average income gap of U.S. bank holding companies, defined in Equation

(19), is positive, i.e., that BHCs hold more short-term interest rate sensitive assets

than liabilities. Therefore, bank cash flows should increase in response to a positive

rate surprise for banks with a positive gap. They test this hypothesis and find that

it is strongly supported by the data. Consistent with these results, English, Van den

Heuvel, and Zakrajsek (2013) also find that an increase in the short-term interest rate

boosts banks’ net interest margins.

Rather than focusing on interest rate shocks, a few papers quantify the interest rate

sensitivity of banks’ net interest margins in a longer perspective, throughout various

interest rate environments.11 Most highlight that margins tend to be stable over time.

Based on a small sample of 15 U.S. institutions, Flannery (1981) finds no significant

effect of interest rate fluctuations on bank profitability. His interpretation is that banks

hedge operationally, by matching the average maturity of their assets and liabilities.

Using larger samples, a number of papers come to the sample conclusion. Studying

commercial banks in a sample of 10 industrial countries, English (2002) finds that they

have managed their exposure so that changes in the yield curve have limited effects

on their net interest margins.11A separate literature explicitly models banks’ net interest margins. In the seminal paper by

Ho and Saunders (1981), banks are modeled as dealers receiving stochastic deposit flows and loandemands. Net interest margins are akin to a bid-ask spread that banks charge to get compensationfrom holding long or short positions in the money market. In this model, the variance of interestrates is an important determinant of a bank’s margin. The model by Ho and Saunders (1981)has subsequently been extended by Allen (1988) and Angbazo (1997), and tested by Saunders andSchumacher (2000) using a sample of U.S. and European banks.

23

Taken together, these findings seem hard to reconcile. If the increase in margins

following positive interest rate shocks is short-lived, it can still be compatible with the

stability of margins over time. That banks reshuffle their balance sheet in response

to shocks can create stability of margins. The existence of an imperfectly competitive

deposit market can also be a source of bank resilience when adverse interest rate shocks

occur. Overall, however, more work is needed to jointly rationalize (i) negative stock

returns when rates increase, (ii) increasing short-term cash flows when rates increase

and (iii) stable net interest margins in the long-term.

3.3 Theoretical reconciliations

A conclusion from the preceding section is that banks have open exposure to interest

rate risk, which they take by writing non-contingent contracts. The Hellwig (1994)

model cannot explain why banks take on such contracts, either in the form of fixed-rate

loans or of demand deposits. We highlight two possible reconciliations of the theory

with the data.

First, as highlighted by Hellwig (1994, 1998), the problem in Equation (10) does

not incorporate moral hazard on the bank side. It assumes that the investment and

liquidation policies (k01, k02 and L) are part of the optimal contract between the

bank and its depositors, and are enforceable as such. In contrast, if banks have some

discretion over their investment policy once they have collected funds from depositors,

they may take excessive risk, e.g., by writing non-contingent contracts.12 Moral hazard

in the context of the Hellwig (1994) model has not been examined so far. It raises the

open question whether the induced distortions of investment are primarily detrimental

to early or late consumers, i.e., whether valuation risk or reinvestment-opportunity

risk (as defined in Section 2.3) are becoming relatively more important, and how this

affects the optimal contract ex ante. Often modelled in the context of banks (e.g.,

Holmström and Tirole, 1997), and possibly reinforced by deposit insurance (Keeley,12Behavioral biases can give rise to a premium on fixed-rate relative to variable-rate loans, or vice

versa. Koijen, Van Hemert, and Van Nieuwerburgh (2009) find that households try to time the marketwhen choosing between fixed-rate and adjustable-rate mortgages. They show that a simple decisionrule based on the average of recent short-term interest rates explains a sizable part of the variationin types of mortgage origination. In this context, banks can write contracts to earn the premiumarising from the fact that households do not solve complex investment problems.

24

1990) or implicit bailout guarantees (Farhi and Tirole, 2012), moral hazard is likely

to play a critical role to understand banks’ exposure to interest rate risk.

While moral hazard distorts a bank’s asset allocation, the fact that banks take

non-contingent liabilities can be explained by other frictions. A prominent model

where non-contingent demand deposits emerge as the optimal contract is that by

Diamond and Rajan (2001). In the spirit of Hart and Moore (1994), the friction

making long-term assets illiquid is that their best users cannot commit to employing

their specialized human capital so that assets yield their highest payoffs. The lack of

commitment implies that assets cannot be used as collateral to their full value. In the

case of banking, a plausible interpretation is that bankers hold specialized information

and monitoring skills about the firms with which they have engaged in a relationship.

Diamond and Rajan (2001) highlight that this friction has an important implication

when the bank may be faced with a need for liquid funds before long-term projects

mature. In the face of a liquidity need, little cash can be obtained by selling the

project or pledging it as collateral, due to the lack of commitment of the banker. The

only way for him to borrow against the full value of the project is by offering ex ante a

non-contingent promise to liquidity to its financiers, in the form of a demand deposit

contract. If this contract is not contingent on the aggregate state, it commits the

banker to deploy his human capital in the future. Indeed, such a capital structure is

subject to runs if the banker does not behave, leading to inefficient liquidation. The

threat of a run implies that the banker has no choice but to use his specific skills.

Consequently, it enables him to face intermediate liquidity needs by borrowing against

the project’s future cash flows. With lack of commitment by bank managers, non-

contingent demand deposit contracts are the optimal way of financing a bank. They

dominate state-contingent contracts in this context. In the presence of aggregate

uncertainty, however, they leave the bank exposed to non-zero interest rate risk.13

13There is no aggregate uncertainty, thus no interest rate risk, in Diamond and Rajan (2001).Diamond and Rajan (2012), whose model is discussed below in Section 6.1, introduce aggregateuncertainty in a model where the lack of commitment by managers gives rise to non-contingentdeposit contracts.

25

3.4 Interest rate risk-sharing through derivatives

Interest rate risk arising from the joint structure of assets and liabilities can be hedged

off-balance sheet, in derivatives markets. The interest rate derivatives market is large

in notional terms, with an outstanding gross exposure of USD 434 trillion as of end-

2015 (BIS, 2016).14 97% of these contracts are used by financial intermediaries. Inter-

est rate derivatives come in the form of several contract types, primarily swaps (which

account for more than 70% of gross exposures), but also futures, forwards or options.

A plain-vanilla interest rate swap stipulates the exchange of a floating rate (e.g., the

Libor) against a fixed rate (the swap rate) for a given period of time. Payments are

made periodically until maturity, and are computed as percentages of the notional

amount of the contract (see Hull (2014) for an introduction and Fleming, Jackson, Li,

Sarkar, and Zobel (2012) for a description of contract characteristics based on U.S.

data). Even though they provide hedging benefits for particular institutions, deriva-

tive markets do not reduce the aggregate exposure to interest rate risk. They make

it possible, however, to transfer risk to agents who are best able to bear it and get

compensated for it.

In this respect, Vuillemey (2015) points to a puzzling fact. While bank equity

value is decreasing in the level of interest rates (see Section 3.2.1), a large part of U.S.

banks take derivative exposures for hedging which pay off when interest rates are low.

Therefore, they are net payers on their derivative exposures when their net worth is

low. This fact is prevalent over time, suggesting that it does not arises only from short-

term anomalous behaviors. One interpretation is that banks are constantly engaging in

some form of speculation, possibly driven by moral hazard. These exposures, however,

are explicitly reported as hedging exposures. Instead, Vuillemey (2015) builds a model

in which taking such exposures can be part of the optimal hedging strategy even for

banks whose market value is decreasing in the level of interest rates. In this model,14This large number is partially misleading, since a sizable part of gross exposures arises from

market making and, as such, does nos create net exposures (see Peltonen, Scheicher, and Vuillemey,2014, for related evidence in the CDS market). In the U.S. banking data, exposures to interest ratederivatives are broken down between exposures “held for trading” and “held for purposes other thantrading”, i.e., hedging. In aggregate, derivatives held for trading represent the bulk of gross exposures,from 90 to 99%. As shown by Rampini, Viswanathan, and Vuillemey (2015), the top-5 banks accountfor about 96.0% of all exposures for trading, and the top-10 banks for more than 99.7% of suchexposures. For banks outside the top-10, exposures for hedging purposes are much more importantthan exposures for trading.

26

swaps are valuable only for insurance motives, since they make it possible to transfer

funds to future states in which financing constraints may bind. Banks can find it

optimal to hedge both increases or decreases in interest rates. Intuitively, they want

to hedge increases in rates because their financing capacity is reduced in such states.

However, they also want to hedge decreases in rates, because optimal lending, and the

associated need for funds, are larger in such states. Depending on bank characteristics,

one force overrides the other. Therefore, they can take both pay-fixed or pay-float

swap positions, consistent with data. Finally, because derivatives hedging makes it

possible to alleviate financial constraints, banks in the model are able to better achieve

their optimal lending policy. The main predictions about lending are consistent with

empirical findings by Purnanandam (2007), who uses U.S. data to show that derivatives

users are able to shield their lending policy against monetary policy shocks.

Given that interest rate derivatives can be traded by constrained financial insti-

tutions to better achieve their optimal lending policy, two basic facts can be seen

as puzzling from the vantage point of corporate risk management theory. In theory,

Froot, Scharfstein, and Stein (1993) show that financial constraints give rise to effec-

tive risk aversion even for risk neutral institutions, which should therefore engage in

risk management. In their model, where hedging is frictionless, two main predictions

arise. First, banks should completely hedge the tradable risks they face. Second, more

constrained institutions should hedge more, and unconstrained institutions should not

hedge.

In recent work, Rampini, Viswanathan, and Vuillemey (2015) show that these

predictions are counterfactual. First, risk management is limited in the data. In the

U.S., only 7.4% of banks and 50.8% of bank holding companies (BHCs) engage in some

form of interest rate hedging. Conditional on using derivatives, the extent of hedging

is also rather small, with a gross exposure to total assets equal to 7.5% of bank assets

on average (5.8% for BHCs). Second, more constrained institutions hedge less, not

more. This is true using a variety of measures of financial constraints, and also holds

within banks over time.

To solve these puzzles, recent advances in corporate risk management theory are

useful. Rampini and Viswanathan (2010) relax two assumptions from Froot et al.

27

(1993). First, since both financing and hedging involve promises to make payments

in the future, both should be subject to the same financial constraints in order for

these promises to be credible. This implies that both hedging and financing require

net worth, so that a trade-off between both arises. Second, there are concurrent

investment opportunities at the time hedging decisions are taken. When hedging,

a bank not only foregoes financing, but also investment. Consequently, the main

prediction about the relation between net worth and hedging is reversed. Foregoing

investment opportunities is more costly at the margin for more constrained institutions,

which therefore hedge less, not more. This prediction is consistent with stylized facts.

Empirically, Rampini, Viswanathan, and Vuillemey (2015) go one step further and

test this prediction. Instrumenting bank net worth with local house prices, they show

that institutions facing a negative net worth shock reduce hedging substantially. Their

conclusion is that the financing needs associated with hedging are a substantial barrier

to interest rate risk sharing in derivatives markets.

4 Interest rate risk sharing between the banking

and the non-financial sectors

Banks intermediate funds between households and non-financial firms. Each time

banks write interest rate-contingent contracts (as in Hellwig (1994)’s model), in the

form of variable-rate loans or deposits, they hedge themselves against interest rate

fluctuations and transfer interest rate exposure to the non-financial sector. This section

discusses interest rate risk sharing through a lending and a deposit-taking channel.

4.1 Risk sharing through the lending channel

A stylized fact in the U.S. is that most bank loans to non-financial firms are issued at a

floating rate.15 Ippolito, Ozdagli, and Perez (2015) show that 76% of the debt of U.S.

firms that borrow only from banks has a floating rate. Using data from the Federal

Reserve’s Survey of Terms of Business Lending, Vickery (2008) finds that 54% of all15This is also the case in the Euro area, where 85% of lending to non-financial corporates is at a

variable rate (Gambacorta, 2008). In the U.K., most long-term loans bear a floating rate.

28

sample loans are at floating rates, and also documents sizable heterogeneity across

loan types (the share of floating-rate contracts is 39% for equipment loans, but rises

to 72% for lines of credit). When lending at a floating rate, banks shield themselves

against interest rate fluctuations by transferring interest rate risk to their borrowers. A

pervasive question is whether this contractual structure is driven by demand or supply

factors. A large part of the literature on corporate debt structures takes the firm’s

perspective and focuses on demand-driven (i.e., firm-driven) factors.16 In contrast, a

few papers have recently recognized that banks play an active role in affecting firms’

decisions to take on fixed-rate or floating-rate debt.

Kirti (2015) demonstrates that bank-driven factors are first-order determinants of

fixed vs. floating debt structures. Theoretically, his hypothesis is that banks find it

advantageous to lend at floating rates, because they mostly have floating-rate liabil-

ities. Matching the interest rate exposure of their assets with that of their liabilities

amounts to engaging in operational risk management. He finds several pieces of ev-

idence supporting this hypothesis. First, banks holding more floating-rate liabilities

make more floating-rate loans. Second, they also hold more floating-rate securities.

Third, they quote lower prices for floating-rate loans relative to fixed-rate loans. In

addition to cross-sectional evidence, Kirti (2015) suggests that the correlation between

the structure of bank deposits and that of bank assets prevails in the time dimension:

during periods in which deposits were mostly non-interest bearing, interest rates on

corporate loans were structured so as to be less sensitive to short-term benchmark

rates. Overall, these results suggest that banks are actively managing their exposure

to interest rate risk.

Ippolito, Ozdagli, and Perez (2015) provide direct evidence that the floating-rate

debt structure transfers interest rate risk to firms and has real consequences in the

presence of financial frictions. They show that firms using more bank debt display

a stronger sensitivity of their stock price to monetary policy, implying cash transfers

between a firm’s equity holders and the creditor bank when the short rate rises. Banks16Papers in this literature mostly revolve around two competing theories: hedging and market

timing theories. If firms are hedging, they should select the exposure of their debt to offset thecorrelation of their cash flows with interest rates (see Vickery, 2008, for empirical evidence). If firmsengage in market timing, they should borrow at a floating rate when they perceive it is cheap relativeto fixed-rate borrowing, and vice versa (Faulkender, 2005). We do not discuss these demand-drivenexplanations in further details and instead focus on supply-driven (i.e., bank-driven) channels.

29

are thus hedged against interest rate increases, i.e., against states in which aggregate

liquidity is low. On the firm side, higher interest expenses will reduce the firm’s internal

funds, possibly increasing its need for external funds at times they are scarcer and more

costly. For financially constrained firms, internal and external funds are not perfect

substitutes; the latter are more costly. Consistent with the theory of investment

under financial constraints, they find that constrained firms with more bank debt

have a stronger sensitivity of their cash holdings, sales and fixed capital investment to

monetary policy. These results provide evidence that interest-rate contingent contracts

between banks and firms indeed shift interest rate risk to the non-financial sector and

have real consequences.

Risk-sharing through the lending channel also takes place vis-à-vis households,

primarily through mortgages. Similar in that respect to the literature on corporate

debt, the literature on household finance (e.g., Koijen, Van Hemert, and Van Nieuwer-

burgh, 2009) mostly focuses on demand-driven factors to explain the relative share of

adjustable-rate mortgages (ARMs) and fixed-rate mortgages (FRMs). Recent papers,

however, highlight the importance of supply-side factors in explaining the ARM/FRM

share. Foà, Gambacorta, Guiso, and Mistrulli (2015) show that the choice between

ARMs and FRMs is not only driven by the relative price of the two mortgage types,

but that bank characteristics play a role in the contract choice. Fuster and Vickery

(2014) show that the share of FRM issuance is lower when mortgages are difficult to

securitize, suggesting that lenders are reluctant to retain interest rate risk associated

with prepayment options. Together, these findings provide evidence that banks en-

gage in active operational risk management, by transferring interest rate risk to the

household sector whenever it is inconvenient for them to retain it.

4.2 Risk sharing through the deposit-taking channel

Banks also shield their balance sheet against interest rate fluctuations by entering

state-contingent debt contracts with savers, in the form of interest-bearing deposits.

Doing so, they transfer aggregate interest rate risk to the non-financial sector, primarily

households. Few papers investigate the nature of deposit contracts between banks and

their depositors.

30

Empirically, one challenge arises from the imperfectly competitive nature of the

deposit market. Banks in more concentrated areas offer lower deposit rates and raise

them at a slower pace when market rates rise (Berger and Hannan, 1989; Neumark

and Sharpe, 1992). They also offer more non-interest bearing deposits. The fact that

competition drives the nature and terms of deposit contracts in the cross-section makes

it more difficult to single out the effect of banks’ active decisions to transfer risk to

depositors.

Building on the earlier literature on deposit competition, Drechsler, Savov, and

Schnabl (2015) go some way in this direction. They show that increases in the Fed

funds rate induce banks to widen the spread they charge on deposits, which ultimately

induces deposits to flow out of the banking system. The documented effect is econom-

ically sizable, given the importance of deposits for bank funding, and given that banks

earn large spreads on checking and savings deposits. For example, the spread between

the Fed funds rate and the savings deposit rate has been larger than 2 percentage

points on average over the 1997-2008 period. Using local variation in the degree of

bank competition, Drechsler, Savov, and Schnabl (2015) are able to give a causal inter-

pretation to the relation between higher market rates, higher deposit spreads and lower

deposit supply. Importantly, they are able to rule out demand channels, indicating

that monetary policy works through changes in banks’ willingness to supply deposits

rather than through changes in household demand for deposits. Overall, their findings

suggest that banks are less willing to take on the risk associated with interest-bearing

deposits when market rates are higher.

Relatedly, Girotti (2015) investigates the substitution between interest-bearing and

non-interest bearing deposits. He shows that banks lose non-interest bearing deposits

when market rates increase, which are substituted by issuing more interest-bearing

deposits. The interest rate to be paid increases with the deposit amount to be substi-

tuted, implying that banks may choose not to fully substitute. In such cases, they will

curtail lending. While not providing direct evidence that banks engage in operational

interest rate risk management by supplying the type of deposits that best suits them,

the fact that they do not fully substitute across deposit types when market condi-

tions change indicates that such concerns may be at play. If so, interest rate risk is

31

transferred to households via deposit contracts whenever it is inconvenient for banks

to retain it.

5 The quantity of interest rate risk

The preceding section took the quantity of interest rate risk as given, and discussed its

allocation. The amount of risk, however, is endogenous. The exposure to interest rate

risk can be limited by increasing the share of savings that is invested in short-term

assets or, for firms, by issuing more long-term debt. Such operational immunization of

interest rate risk, comes at a cost, because short-term assets are usually less productive

than long-term assets, or because long-term debt is typically more costly than short-

term debt.

5.1 Theory

To discuss the quantity of interest rate risk, it is useful to close the solution of the

Hellwig model (Section 2.3). So far, the consumption plan has been solved for after

taking k01 and k02 as given. Doing so was possible, because the problem can be given

a recursive interpretation (i.e., optimally choosing the allocation of resources between

projects, given the optimal consumption plan as a function of k01 and k02). We now

solve for the optimal investment in long-term and short-term assets

maxk01,k02

[ ∫ r∗2

0

[λu

(r1k01

λ

)+ (1− λ)u

(Rk02

1− λ

)]dF (r2) (24)

+∫ R/`

r∗2

[λu (c∗1 (k01, k02, r2)) + (1− λ) c∗2 (k01, k02, r2)] dF (r2)],

under the constraint that k01 + k02 = 1. The first term corresponds to expected

utility when there is no reinvestment at date 1, which occurs if r2 is low enough. In

this case, consumption levels at dates 1 at 2 do not depend on r2. The second term

corresponds to high realizations of r2, in which case reinvestment takes place, and both

consumption levels depend on the realized value of r2.

We highlight four features of the solution to Equation (24). First, the attractiveness

of the short-term investment is enhanced by the illiquidity of the long-term investment.

32

Investment in the short-term technology exceeds the level which would prevail if the

long-term asset could be liquidated at date 1 for its present value Rk02/r2. The illiq-

uidity of long-term investment implies that the short-term technology becomes more

valuable to produce intermediate consumption. Abstracting from the model, an im-

plication of this result is that overly enthusiastic expectations about future liquidation

values may lead to larger, and possibly excessive, interest rate risk-taking ex ante.

This may be the case if the effect of private liquidations on other market participants

is not internalized, leading to a pecuniary externality through fire sales (see Lorenzoni

(2008) for a model illustrating this mechanism and Shleifer and Vishny (2011) for a

survey on fire sales).

Second, there are two features of the long-term technology that make it attractive.

It is more attractive whenever the technological yield curve at date 0 is steeper, i.e.,

when R is larger relative to r1. Moreover, even when the technological yield curve is

relatively flat (when R is low), the long-term technology is still attractive as a way to

safely provide consumption to patient investors at date 2. Absent this technology, their

consumption level would be fully contingent on r2, which is not a desirable feature for

agents valuing insurance.

Third, the level of short-term investment, k01, is higher than that which would

prevail if reinvestment at date 1 were not allowed. The possibility to reinvest at date

1 increases the attractiveness of short-term investments. Reinvestment provides an

additional option to achieve better consumption smoothing in the presence of aggregate

uncertainty. That short-term investments are desirable due to their option value is

consistent with richer models of liquidity premia, such as Holmström and Tirole (2001).

Finally, we highlight that if agents are more risk-averse, insurance will be valued

more relative to the opportunity to reinvest at date 1. If so, the threshold above

which reinvestment takes place, r∗2, is higher, and reinvestment is less frequent. There

is immunization against interest rate risk in a larger number of states.

5.2 The pricing of a marginal unit of interest rate risk

Its aggregate nature implies that any additional unit of interest rate risk has to be

born by someone and must be priced to reflect the willingness or ability of marginal

33

investors to bear it. A few recent studies shed light on these issues. The main question

is whether the pricing of risk, as reflected in the term structure of the real interest rate,

is sensitive to the aggregate quantity of risk. The major challenge facing empirical work

is that there is usually no exogenous variation in the aggregate quantity of interest

rate risk. Economy-wide, it is an endogenous equilibrium outcome. From the banking

sector’s perspective, the existing literature provides no clear guidance as to what can

be regarded as a truly exogenous shock to interest rate risk born by intermediaries.

A recent contribution by Haddad and Sraer (2015) highlights the role of banks as

central intermediaries in the market for interest rate risk. If banks cater to firms’ and

households’ demand for fixed-rate or variable-rate loans and deposits, they are left

with a net exposure to interest rate risk that depends on these demand factors. Pro-

vided banks meet non-financial agents’ demand for specific deposit and loan contracts,

the aggregate component of this demand shock can be considered exogenous for the

banking sector as a whole.17 For banks to accommodate such shifts in demand, the

equilibrium price of a marginal unit of interest rate risk must go up. Therefore, the

main hypothesis in Haddad and Sraer (2015) is that an increase in banks’ average ex-

posure to interest rate risk should forecast an increase in bond risk premia. They find

evidence consistent with this hypothesis: the average income gap of U.S. banks fore-

casts the one-year excess return on Treasuries, even after controlling for traditional

predictors of bond returns. While focusing directly on the banking sector, Haddad

and Sraer (2015) only provide a robust correlation, but no identification. Following

their work, a question to be answered is how variation in bank’s income gap transmits

to bond risk premia, given that banks are fairly small investors in the bond market

relative to other institutional investors.

Not studying banks per se, a related contribution by Hanson (2014) has the advan-

tage that it can more directly exploit (arguably exogenous) variation in the aggregate

quantity of interest rate risk. He finds a large effect of the quantity of interest rate risk

on its pricing. Exploiting the fact that most home mortgages in the U.S. are fixed-rate

loans with an embedded option to prepay without penalty, he shows that declines in17An important question to understand banks’ exposure to interest rate risk is whether their residual

on-balance sheet exposure is driven by firms’ and depositors’ demand, or whether they choose aparticular exposure level and pass residual exposure onto the non-financial sector. The literatureprovides evidence that both play a role (see Section 4).

34

long-term interest rates increase the value of the prepayment option, thus reducing

the effective duration of mortgage-backed securities (MBS). This setup is well-suited

to study the pricing implications of changes in the aggregate quantity of interest rate

risk, because changes in aggregate MBS duration act as large supply shocks to the

quantity of risk for bond market investors. Theoretically, if the risk tolerance of these

investors is limited, the term premium (i.e., the expected return of a riskless long-term

bond over a risk-free short-term bond, as reflected, for example, in the U.S. Treasury

yield curve) must increase to compensate them for bearing additional interest rate

risk. Relating measures of MBS duration and excess government bond returns, Han-

son (2014) finds strong empirical support for these predictions: bond term premia

are high at times aggregate MBS duration is high, and variation in bond risk premia

can be explained by changes in MBS duration, even after controlling for traditional

forecasting variables.

Other shocks to the aggregate quantity of interest rate risk born by bond mar-

ket investors that are arguably relatively exogenous are large-scale asset purchases

(LSAPs) by central banks, conducted as part of their quantitative easing (QE) poli-

cies. There are several channels through which LSAPs are likely to affect asset prices,

including a signaling channel, a capital constraints channel and a scarcity channel (see

Krishnamurthy and Vissing-Jorgensen, 2013, for a review). Given our focus on interest

rate risk, one channel, the so-called “duration risk premium channel”, is of particular

interest. To the extent LSAPs remove long-duration assets from the portfolio of pri-

vate bond market investors, an open question is whether such policies can affect the

market-wide price of interest rate risk, namely the risk premium that bond investors

charge for bearing duration risk. While this question has not received a full treatment

yet, Krishnamurthy and Vissing-Jorgensen (2013) find no evidence that this effect is

at work. A potential explanation is that fixed-income markets are highly segmented.

35

6 Interest rate policy and interest rate risk

We turn to a discussion of interest rate policy, restricting attention to the literature

relevant for banking sector stability.18 We start with theoretical works, before review-

ing empirical evidence on the effects of accommodative monetary policies on bank

stability.

6.1 Theory of interest rate policy

We base our discussion of the theoretical literature on Diamond and Rajan (2012).

Their model has the advantage that it shares common features with those by Diamond

and Dybvig (1983) and Hellwig (1994). The main additional result to be gained from

the literature on interest rate policy is that market allocations can be distorted by

public (central bank) intervention, even if it is restricted to borrowing and lending

at market rates. Interest rate policy has real effects by changing consumption and

saving decisions, as well as investment and liquidation decisions. It can implement

allocations which cannot be obtained through market forces. As such, it can be an

efficient instrument ex post, but also undermines the disciplining effects of market

contracting ex ante.

In Diamond and Rajan (2012), as in the models discussed in Section 2, savings

are used to finance long-term projects whose liquidation at interim dates is inefficient.

There is aggregate risk, in the form of uncertainty about future household endowments.

Some households may have an unexpectedly high need to withdraw deposits from the

bank for consumption purposes, either because their current endowments are low,

or because they anticipate high future endowments and withdraw funds to smooth

consumption. This risk cannot be diversified away. Therefore, the banking sector is

under stress whenever withdrawals exceed liquid funds; in such cases, the aggregate

demand for consumption goods is larger than the aggregate supply. When this is the18There is a large literature in macroeconomics on interest rate policy. Most contributions over the

past three decades follow from the incorporation of monetary policy in general equilibrium modelswith frictions, such as sticky prices. Woodford (2003) gives a prominent account of this literature andfocuses on monetary policies taking the form of rules governing the short-term nominal interest rate(rather than, for example, the money supply). The banking sector is not a central object of interestin this area of study, which therefore falls outside the scope of this survey. A few recent papersincorporate a financial sector in macroeconomic models (see Brunnermeier and Sannikov (2014) andBrunnermeier, Eisenbach, and Sannikov (2013) for a survey).

36

case, the real interest rate rises to equate demand and supply of consumption goods,

and long-term investment projects need to be liquidated. As a consequence of higher

real interest rates, bank net worth drops. Indeed, the value of its present liabilities

(demand deposits) remains unchanged, while that of its long-term assets decreases, as

they get discounted by a larger factor. Consistent with empirical evidence, a higher

interest rate is associated with lower bank value (see Section 3.2.1).

The feature of its capital structure that exposes a bank to interest rate risk (in

contrast with Hellwig (1994)’s model, in which it is fully transferred to non-financial

counterparties) is that its liabilities are non-contingent promises to liquidity. The

bank cannot give lower repayments to depositors in states where aggregate demand

for consumption is high, i.e., when the short rate rises. Deposits are thus costly to

serve in such states, where flexibility would be valuable. Non-contingency is rational-

ized as in Diamond and Rajan (2001, see Section 3.3). The purpose of government

intervention is to restore state-contingency at the interim date, thus to implement

an allocation which is not achievable through private contracting. This requires an

instrument to transfer resources from households to banks. An important premise is

that the planner (the central bank) can access households’ endowments; in doing so,

it restores state-contingency by providing banks with more funds when they are illiq-

uid. An accommodative monetary policy is one such instrument, which can preserve

the solvency of the banking sector by raising its net worth. An implementation of

this policy is through central bank lending to banks, possibly out of forced borrowing

from households. Even though it can be desirable ex post, this policy is costly for

both early and late consumers. For early consumers, preventing the early liquidation

of long-term projects necessarily comes at the cost of lower consumption at interim

dates. Late consumers are penalized by earning a lower return on savings. Overall,

accommodative interest rate policy constitutes a transfer of resources from consumers

to banks.

Another cost of interest rate policies is the distortion of incentives. As such, it can

be detrimental ex ante. In Diamond and Rajan (2012), the inefficiency comes from the

lack of internalization of the costs of interest rate intervention by banks and depositors.

Therefore, expectations of future low interest rates if the banking sector is illiquid can

37

increase the future need for low interest rates. This is because banks then have a

lower incentive to preserve liquid resources. Expectations of future accommodative

policy yields over-investment in long-term projects, whose value will be sustained by

intervention when liquidity is scarce. Anticipating this outcome, banks will hold more

illiquid loans and have excessive leverage ex ante. They take on excessive interest rate

risk. Anticipation of intervention brings about the need for intervention in a larger

number of states. To prevent excessive long-term investment ex ante, Diamond and

Rajan (2012) propose that the central bank maintains higher short-term interest rates

(above market-determined rates) in normal times. Such a policy would induce greater

investment in short-term assets (which pay off more on a per-period basis) and lower

investment in long-term assets, whose cash flows get discounted by a larger factor.

A related argument is made by Farhi and Tirole (2012), who show that banks’

choices of maturity mismatching are strategic complements in the presence of imper-

fectly targeted support to financial institutions. Intuitively, the central bank policy

is decided based on the aggregate maturity mismatch of the whole banking sector.

Because interest rate policies involves costs which are akin to a fixed cost (subsidized

financing of unworthy projects by unconstrained entities and overall incentive to en-

gage in greater maturity mismatching), the central bank will not find it optimal to

intervene if the aggregate maturity mismatch is too low. In such case, it is ill-advised

for a bank to be in the minority of institutions in need for relaxed financing constraints

when aggregate liquidity is low. In contrast, if the aggregate maturity mismatch is

high, which occurs if many banks are highly leveraged, the central bank has no choice

but to intervene. In this case, a bank has no incentive to maintain a low leverage ex

ante, as this would be akin to choosing a lower rate of return.

Both Diamond and Rajan (2012) and Farhi and Tirole (2012) compare interest rate

policies with alternative transfer policies (e.g., recapitalization or direct bailouts). In

both papers, the theoretical difference between the two policy instruments is whether

the intervention reduces borrowing costs for all banks, or whether it boosts the net

worth of institutions that benefit from a targeted transfer. In Diamond and Rajan

(2012), interest rate policy strictly dominates unconstrained transfer policies, which

make the system worse-off. This is because unconstrained bank bailouts undermine

38

the discipline induced by private contracts; banks make larger promises to households

so as to benefit from ex post rent extraction. In Farhi and Tirole (2012), the planner

is faced with asymmetric information when implementing transfer policies, i.e., the

financial condition of a bank is not observed. While it introduces distortions, interest

rate policy is always used. Its key advantage is that it primarily benefits institutions

with actual borrowing needs. It is therefore more akin to a market-driven solution,

which reduces rent extraction. Transfer policies can be used as a supplement targeted

towards strategic institutions.

6.2 Distortive effects of low short-term policy rates

There is little debate about the fact that banks can be tremendously helped by accom-

modative interest rate policies in times when liquidity needs are high. By construction,

such policies transfer funds from the non-financial sector to banks, at times the value

of liquidity is high for them. Chodorow-Reich (2014) provides evidence that banks

were helped by expansionary monetary policy in 2008-2009.

A few recent papers speak to the more difficult question of the distortive effects

of monetary policy. To obtain identification, the main empirical challenge is that

the interest rate environment (the monetary policy stance) is endogenous to local

economic conditions. To face this issue, Maddaloni and Peydro (2011) use the Euro

area, where there is a single monetary policy but diverse local economic conditions.

This constitutes a setup in which there is exogenous cross-sectional variation in local

monetary policy conditions, which may be too accommodative for some countries and

too restrictive for others. Such variation can be measured using Taylor rule residuals.

They find robust evidence that low short-term interest rates soften lending standards

for both firms and households. They do not find such evidence for low long-term

interest rates.

A number of papers make related points. Jimenez, Ongena, Peydro, and Saurina

(2014) use matched bank-firm data from the Spanish credit register, which comprises

all outstanding loans as well as loan applications. Controlling for demand factors at

the firm level, they find that poorly capitalized banks expand credit to riskier firms

following a rate cut. Ioannidou, Ongena, and Peydro (2015) find similar results by

39

using an alternative identification strategy. They exploit the almost complete dollar-

ization of the banking system in Bolivia, together with the absence of synchronization

of its local economic conditions with those of the U.S. In this context, variation in the

federal funds rate can be considered exogenous with respect to the local interest rate

conditions.

We highlight, however, that all these empirical studies are primarily focused on

identifying the causal effect of low interest rates on credit risk-taking, not interest rate

risk-taking. The variables of interest are measures of loan quality, such as borrower

credit rating or past loan performance. We are not aware of any study that explicitly

consider the effect of low interest rates on the share of fixed-rate vs. floating-rate

origination, on repricing frequencies (for floating-rate loans) or maturities (for fixed-

rate loans), which would provide more direct evidence that interest rate risk is higher.

A few papers (Delgado, Salas, and Saurina, 2007; Jimenez, Ongena, Peydro, and

Saurina, 2014) find that loan maturity increases during periods of monetary expansion.

In the absence of detailed information on loan types (fixed or floating-rate), these

results need not signal increased interest rate risk; they can be interpreted as another

dimension of credit risk-taking.

6.3 Non-conventional interest rate policies

A nascent area of research concerns non-conventional interest rate policies. These

are primarily of two types: either policies aimed at lowering long-term interest rates

(purchases of long-term assets, such as quantitative easing, or QE) or commitments

to preserve short-term interest rates at a low level for a long period (“forward guid-

ance”).19 In macroeconomics, non-conventional measures are often seen as a way to

amplify accommodative policies when the short rate is at its zero lower bound. There-

fore, it is seen as the continuation of conventional interest rate policies. In our view,

in contrast, from the perspective of the literature on risk in banks, one of the main19In macroeconomics, the literature on monetary policy at the zero lower bound follows from the

Japanese situation at the end of the 1990s, and has been revived after the global financial crisis. SeeEggertsson and Woodford (2003) and Bernanke, Reinhart, and Sack (2004) for early contributions.Since this literature is not primarily focused on the effect of non-conventional policies on interestrate risk in the banking sector, we do not review it and instead refer the reader to the overview byWoodford (2012).

40

questions to be answered, both theoretically and empirically, is whether the effects of

non-conventional policies differ from that of conventional policies. While research on

this issue is still limited, we summarize a few contributions suggesting it is indeed the

case.

One important friction that may kick in for banks at the zero lower bound is that

they can no longer fully pass through market interest rates to deposit rates. This can

be the case either because depositors withdraw funds to hold cash when deposit rates

become negative, or because of behavioral biases by which banks cutting deposit rates

below zero would be severely penalized in a competitive environment. Empirically,

Heider, Saidi, and Schepens (2016) provide evidence that deposit rates do not adjust

one-for-one to market rates when these rates become negative. Therefore, while the

profitability of bank assets drops, expenses on liabilities remains fairly constant. If

banks cannot substitute with other sources of income (non-interest income, in the form

of fees), the compression of banks’ margins could impair financial stability. This effect

runs against the main effect of conventional policies, by which banks are helped by

cuts in the short rate. Heider, Saidi, and Schepens (2016) also show that banks which

are more reliant on deposit funding, and therefore more affected by negative rates,

react by granting new loans to riskier borrowers.

Therefore, an important concern is whether non-conventional policies can have

unintended consequences by impairing the proper functioning of financial intermedi-

aries. With respect to zero interest rates, a compelling example, while not pertaining

to banks per se, is provided by DiMaggio and Kacperczyk (2016). They show that

the size of the money fund industry shrank in the U.S. after the zero lower bound

hit. Money market funds became more likely to exit the market and to invest in

riskier asset classes. With respect to low long-term interest rates, related concerns

can appear. While the main goal of non-conventional policies is to boost investment

by lowering long-term rates, a low term spread also possibly reduces the willingness

of banks to supply such credit. In theory, going back to the Diamond and Dybvig

(1983) model, there is no more benefit from financial intermediation when the yield

curve becomes flat, since there is no more benefit from pooling resources to exploit

long-term projects. Consistent with this view, English, Van den Heuvel, and Zakrajsek

41

(2013) show that bank equity value falls when the yield curve flattens. Alternatively,

as a way to preserve profitability on long-term loans, banks may turns to riskier loans.

In this respect, a few recent works study the transmission of non-conventional

monetary policies, in particular large-scale asset purchases, to bank lending and to real

outcomes. Several of these studies, for example Kandrac and Schlusche (2016), find

that, following QE programs, banks benefiting from more central bank reserves engage

in more, but riskier, lending. Here, risk primarily captures credit risk, not interest

rate risk. Whether banks respond by increasing or decreasing the duration of their

loans remains unclear. Relatedly, Chakraborty, Goldstein, and MacKinlay (2016) and

DiMaggio, Kermani, and Palmer (2016) highlight that the nature of asset purchases

matters for the transmission of unconventional policies. More work is needed, however,

to properly understand the ensuing changes in bank risk.

7 Conclusion

The current interest rate environment, characterized by sustained near-zero or negative

interest rates in most developed economies, generates renewed academic and policy

attention about interest rate risk management. So far, research on interest rate risk

in banking is still limited, but attracts a growing interest. We have summarized the

main conclusions from this survey in Section 1. A number of important questions are

yet to be investigated and answered.

Theoretically, modeling the allocation of interest rate risk in the presence of fric-

tions inducing positive risk-bearing by banks would allow for a better understanding

of risk-sharing and financial fragility. Empirically, access to more granular data should

make it possible to better measure interest rate risk at the bank-level in the future. On

this basis, the distribution of interest rate risk within the banking sector and across

sectors could be better described. Another promising area of research relates to the

effects of interest rate risk and interest rate policy on real outcomes, primarily in-

vestment and consumption decisions. In the respect, the effects of quantitative easing

policies on the quantity and distribution of interest rate risk are of particular interest.

42

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