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NII and NPV Simulation: 

Are the Two Methods for Measuring IRR 

Consistent? By E. Mays, Senior Financial Economist 

(202)906-5729 

The two most common targets of 

interest rate risk management at 

depository institutions are net 

interest income (NII) and net 

portfolio value (the economic 

value of equity). Typically, regulators concentrate on the potential volatility of net portfolio 

value (NPV) as a measure of the 

institution’s risk. Although 

managers of institutions have 

begun increasingly to subject 

their portfolios to NPV scenario 

analysis, most place primary 

focus on the stabilization of nearterm NII. These two approaches 

are often viewed as completely 

different ways to measure interest rate risk and managers sometimes question the relevance of 

NPV analysis to risk management. 

In this Risk Management 

Release, we discuss the link 

between NII and NPV, and show 

that analyzing the effect of interest rate changes on the market 

value of a portfolio is consistent 

with analyzing the effect of rate 

changes on the net interest cash 

flows generated by that portfolio. 

The link Between NII 

and NPV 

NPV is equal to the estimated 

market value of an institution’s 

portfolio of assets, less the market value of its liabilities. The 

market value of any financial 

instrument may be estimated by 

summing the discounted present 

value of its future cash flows. 

Thus, NPV is the net present 

value of all future cash inflows 

from assets, minus the net present value of all future cash outflows from liabilities. 

Most savings institutions are 

exposed to rising interest rates 

(i.e., when interest rates increase, 

NPV and NII both fall). 

Although an increase in interest 

rates does not always result in an 

immediate decline in interest 

income, NPV is instantly impacted. 

Rising market interest rates 

cause investors to increase the 

yields they demand on financial 

assets, and as a result, the prices 

at which assets may be sold 

immediately declines. For a 

given change in rates, the decline 

in price for any particular financial asset is greater the further in 

the future the asset’s cash flows 

will be received (that is, the 

longer the duration of the asset). 

Because most savings institutions’ assets are longer-term than 

their liabilities, the result is that 

when rates rise, asset values 

decline more than those of liabilities, and NPV falls. Over time, 

the decline in the market value 

Office ot Thrift Supervision 

Risk Management Division 

Anthony G. Comyn, CFA 

Director, 

August 1995 
Office of Thritt Supervision 

of the portfolio will be reflected 

in NII. Because the liabilities are 

shorter term than the assets, they 

will reflect the higher market 

interest rates more quickly than 

the asset portfolio, and NII will 

be squeezed. The change in 

interest cash flows over the 

remaining life of the portfolio, 

discounted to the present using 

market interest rates, will be 

exactly equal to the decline in 

NPV. 

Consider a bank with no equity 

and $100 in assets. Assume the 

assets consist of a $100 five-year 

fixed-rate loan, with a yield to 

maturity of 10 percent, that pays 

interest semiannually at a rate of 

10 percent and principal at maturity. Assume further that the 

asset is funded with a one-year, 

10 percent CD. The CD pays 

interest semiannually and principal at maturity. In the current 

rate environment, the asset and 

liability are both worth par, or 

$100, and NPV is equal to zero. 

Now suppose market interest 

rates increase by 100 basis 

points, and the required yield on 

the two financial instruments 

increases to 11 percent. Under 

this scenario, the fixed-rate loan 

still pays interest at 10 percent. 

When its cash flows are discounted by 11 percent, the market value of the loan is $96.23, a 

loss of $3.77 from par. 

The CD, on the other hand, continues to pay a rate of 10 percent 

for the first year. When it “rolls 

over,” however, it must pay the 

market rate of 11 percent. 

Assuming the CD continues to 

fund the asset for its remaining 

term of four years, the stream of 

Table 1. Net Interest Income After 

1 Percent Increase in Rates 

Payment Interest 

Income 

Interest Net Interest 

Expense Income 

1 $5 $ 5.0 $ 0.0 

2 5 5.0 0.0 

3 5 5.5 -.5 

4 5 5.5 -.5 

5 5 5.5 -.5 

6 5 5.5 -.5 

7 5 5.5 -.5 

8 5 5.5 -.5 

9 5 5.5 -.5 

10 5 5.5 -.5 

Present Value -2.84 

cash flows, when discounted at 

11 percent, would have a value 

of $99.07, a loss of only $.93. 

Looking at the net effect of the 

rate shock on both sides of the 

balance sheet, we see that NPV 

after the rate shock would be 

equal to $2.84 ($96.23-$99.07). 

Now, let’s take a look at NII. 

Had market rates not increased, 

the institution’s interest income 

would have been $0 since it was 

paying 10 percent on the loan 

and its funding cost was 10 percent. Table 1 shows the institution’s NII after the 100 basis 

point rate increase. For the first 

two payments (one year), NII is 

not impacted. After the CD 

resets to the market rate of 11 

percent at the end of the first 

year, the institution’s NII is $-.5 

in each subsequent semiannual 

period. The present value of the 

NII stream, discounted at the 

market rate of 11 percent is $2.84. 

Note this exactly equals the 

decline in NPV that resulted 

from the rate increase.l 

As the example suggests, minimizing the exposure of NPV to 

interest rate shocks is consistent 

with reducing the volatility of 

future NII over the life of the 

portfolio. A strategy that minimizes the volatility of near-term 

NII, however, may or may not 

reduce the interest rate volatility 

of NPV. In the example, oneyear NII is immunized from 

changes in rates since the institution’s liability does not reprice 

for one year. If short-term NII is 

immunized but NPV is negatively impacted in a particular interest rate scenario, longer-term NII 

will clearly be negatively affected. 

1 This result holds true for an institution with equity if the value of equity is included in the future cash flows, and is discounted at an appropriate rate. 
Why Changes in NPV 

Are Not Always 

Reflected in NII 

While changes in NPV are driven by expected future NII, they 

do not provide a perfect forecast 

of future NII. There are a number of reasons for this. First 

among them is the fact that an 

institution may significantly 

alter its portfolio composition. 

NPV analysis estimates the effect 

of rate changes on the current 

portfolio at a point in time. 

Subsequent modifications in the 

composition of the portfolio will 

cause the relationship between 

changes in NPV and future 

changes in NII to be altered. 

For example, suppose NPV 

analysis indicates that an institution’s portfolio will decline in 

value by $1 million if interest 

rates increase 100 basis points 

then remain constant. If the 

institution did not make any 

future changes to the portfolio, 

then over the remaining life of 

the portfolio, it could expect to 

experience declines in income 

equal to $1 million on a present 

value basis. 

If, however, the institution 

makes any significant changes in 

the types of assets or liabilities it 

holds, the institution’s net 

income stream could differ significantly from that projected 

based on the NPV analysis. One 

typical example is the institution 

that, when faced with a rate 

increase, attempts to bolster 

near-term income by obtaining 

shorter-term deposits or borrowings which typically are lower 

cost than longer-term funds. 

Through this strategy, institutions can increase income in the 

short term, but at the cost of 

increasing risk to future rate 

increases. 

by the NPV analysis fo;the original rate increase will not be 

A second assumption on which 

exact consistency between 

changes in NPV and changes in 

future NII depends, is that after 

the interest rate shock, rates 

remain constant. If, after rates 

increase, they subsequently fall, 

the full decline in NII nroiected 

Risk Management Series 

borne out. Institutions sometimes minimize the importance 

of analyzing the risk to longterm income and NPV by counting on future rate changes to be 

favorable ones. 

If rates remain stable or ‘fall, 

institutions can “ride out” the 

rate shock with little or no effect 

on NII; if rates rise further, the 

damage to NJ1 will be worse. A 

lesson of the thrift crisis is that 

trusting interest rates to return to 

more favorable IeveIs within a 

reasonable time interval may be 

wishful thinking. 

Even though any change in NPV 

that results from an interest rate 

shock may not be fully reflected 

in NII for the reasons discussed 

above, NPV analysis does tell us 

the direction an institution’s 

long-term NII is heading unless 

other factors intervene. Because 

none of us can predict the future 

course of interest rates, it is 

important for managers to consider the effect of rate changes on 

NPV when making portfolio 

decisions. 

Bank Regulators Adopt NPV Emphasis in Capital Regulation 

X-X-* 

The bank regulatory agencies (FDIC, OCC, and Federal Reserve Board) have amended their capital 

standards to specify that they will “include, in their evaluations of a bank’s capital adequacy, an 

assessment of the exposure to declines in the economic value of a bank’s capital due to changes in 

interest rates.” 

They have also published a proposal to adopt a supervisory model to measure IRR based on the 

decline in the economic value of a bank. The banking agencies’ focus on economic value (as opposed 

to NII) is comparable to the OTS’ NPV approach. After they gain experience with the proposed 

model, they intend to adopt a rule that would establish a capital charge for interest rate risk based 

on the level of a bank’s measured interest rate exposure. 

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