Chapter 8
Managing Interest Rate Risk: Economic Value of Equity
Chapter Objec ves
1. Demonstrate the importance of measuring interest rate risk in terms of price sensitivity of assets,
liabilities, and stockholders’ equity.
2. Demonstrate how the economic value of equity (EVE) analysis focuses on interest rate risk over
longer time periods as opposed the static GAP and earnings sensitivity analysis.
3. Demonstrate applications of Macaulay’s duration, modi)ed duration, and effective duration in
estimating price sensitivity.
4. Introduce Duration Gap and duration-based models of interest rate risk.
5. Describe how sensitivity analysis is applied to a bank’s economic value of equity (EVE).
6. Document the strengths and weaknesses of GAP versus duration gap analysis.
7. Critique various strategies to manage earnings and EVE in terms of what a bank’s bets are versus the
prevailing yield curve.
Key Concepts
1. Duration is an approximate elasticity measure of how much the market value of a security or
portfolio will change when the level of interest rates changes. The longer is duration, the greater the
relative price sensitivity.
2. For securities with options, analysts typically estimate an “effective” duration. This calculation
recognizes that cash 9ows on the security may change when interest rates change as the underlying
options are exercised.
3. The economic value of equity (EVE) is a plug figure representing the market value of assets minus the
market value of liabilities. It does not equal market capitalization (share price times the number of
shares outstanding). Thus, by itself the EVE figure does not equal the true value of the bank.
4. Duration Gap (DGAP) measures the comparative price sensitivity of a bank’s assets versus the price
sensitivity of its liabilities when the target measure of performance is the market value of
stockholders’ equity (EVE). DGAP equals the weighted average duration of assets minus the product
of a bank’s liabilities to assets ratio and the weighted average duration of liabilities.
5. A positive DGAP indicates that, on average, assets are more price sensitive than liabilities. Thus,
when interest rates rise (fall), assets will fall proportionately more (less) in market value than
liabilities and EVE will fall (rise) accordingly. A negative DGAP indicates that liabilities are more price
sensitive than assets. Thus, when interest rates rise (fall), assets will fall proportionately less (more)
in value than liabilities and the MVE will rise (fall).
6. EVE sensitivity analysis effectively involves the same steps as earnings sensitivity analysis. In this
case, however, the bank focuses on the relative durations of assets and liabilities, how much the
durations change in different interest rate environments, and what happens to the market value of
equity across different rate environments.
7. Generally, if a bank is liability sensitive in the sense that net interest income falls when rates rise and
vice versa, it will likely have a positive DGAP suggesting that assets are more price sensitive than
liabilities, on average. If a bank is asset sensitive in the sense that net interest income rises when
rates rise and vice versa, it will likely have a negative DGAP suggesting that liabilities are more price
sensitive than assets, on average.
8. DGAP analysis has the advantage of focusing on all cash 9ows from the underlying assets and
liabilities and not just cash 9ows that are expected to arise over short time intervals. Interest rate
risk can be summarized in one measure for the entire portfolio.
9. EVE sensitivity analysis focuses on long-term interest rate effect because it incorporates the present
values of all expected cash 9ows. However, it is a liquidation analysis. The value for EVE is measured
as the market value of assets minus the market value of liabilities. As such, it ignores other factors
that affect the value of the firm, such as franchise value, contingent liabilities, the value of
o*-balance sheet activities, etc. Given the longer-term focus of EVE analysis, it is not uncommon for
EVE sensitivity results to differ from earnings sensitivity results. For example, a bank with signiticant
long-term mortgage holdings will typically have a positive DGAP especially in a rising rate
environment. As such, EVE will fall when rates rise. Yet, earnings sensitivity analysis may show an
increase in expected net interest income over 1 year when rates rise given a bank’s ability to widen
its spread temporarily as the bank raises asset base rates before increasing rates on liabilities.
10. It is difficult to consistently alter either GAP or DGAP and increase earnings or the economic value of
stockholders’ equity. Whenever management chooses to change asset and liability maturities
and/or durations in anticipation of rate changes, it is placing a bet against forward rates from the
yield curve.
11. The general level of interest rates and the shape of the yield curve appear to follow the U.S. business
cycle. In expansionary stages, rates rise until they reach a peak as the Federal Reserve tightens credit
availability. In contractionary stages, rates fall until they reach a trough when the U.S. economy falls
into recession. portfolio managers should consider this information when making choices regarding
the maturities and durations of assets and liabilities and how to price them.
Teaching Sugges ons
This chapter follows conceptually from the material introduced in Chapter7 on GAP and earnings
sensitivity. It is important to point out that both GAP/Earnings Sensitivity and Duration Gap/EVE
Sensitivity models are two ways of looking at the same type of phenomena. GAP and Earnings
Sensitivity analysis focus on rate sensi vity. Duration gap and EVE Sensitivity focus on price sensi vity.
Carefully distinguish between the two. An asset or liability that is extremely rate sensitive is not very
price sensitive. If the asset or liability is extremely price sensitive, it is not very rate sensitive. Earnings
sensitivity analysis focuses on short-term income effect and is important to bankers in their budgeting
as well as their risk assessment. EVE sensitivity analysis focuses on longer-term interest rate effect on
aggregate firm value. It is closely tied to ensuring that the bank remain solvent.
An example of the relationship between GAP and duration gap is helpful. Consider a bank that borrows
federal funds overnight to buy 30-year zero coupon Treasury bonds. The liability is extremely rate
sensitive as it reprices every day. It is not price sensitive because it will always trade near par. The zero
coupon T-bond, however, is extremely price sensitive because it has a 30-year Macaulay’s duration, but
is not rate sensitive because the rate will not change for 30 years. The bank will have a negative GAP
with this transaction and a positive DGAP.
Work carefully through the examples applying duration measures to emphasize the price sensitivity of
individual assets and liabilities. Then work through the First Savings Bank example. Focus on the output
represented by the variability in EVE in Exhibit 8.6. The percentage change in EVE and the absolute
change in EVE across different rate environments indicate how much risk a bank has assumed.
Finally, work with students to help them understand the importance of prevailing yield curve information
in managing GAP and duration gap. Many students will believe that banks can simply adjust the rate
sensitivity or price sensitivity of assets and liabilities to take advantage of perceived changes in interest
rates. Emphasize that this involves placing an explicit interest rate bet. Work through examples to
document what that specific bet is.