Analyst

APPENDIX 1 TO CHAPTER

9

Duration Gap Analysis

An alternative method for measuring interest-rate risk, called duration gap analysis, examines the sensitivity of the market value of the financial institution’s net worth to changes in interest rates. Duration analysis is based on Macaulay’s concept of duration, which measures the average lifetime of a security’s stream of payments (described in the appendix to Chapter 4). Recall that duration is a useful concept, because it provides a good approximation, particularly when interest-rate changes are small, of the sensitivity of a security’s market value to a change in its interest rate using the following formula: %DP < 2DUR 3 where %DP 5 (Pt 1 1 2 Pt)/Pt 5 percent change in market value of the security DUR 5 duration i 5 interest rate After having determined the duration of all assets and liabilities on the bank’s balance sheet, the bank manager could use this formula to calculate how the market value of each asset and liability changes when there is a change in interest rates and then calculate the effect on net worth. There is, however, an easier way to go about doing this, derived from the basic fact about duration we learned in the appendix to Chapter 4: Duration is additive; that is, the duration of a portfolio of securities is the weighted average of the durations of the individual securities, with the weights reflecting the proportion of the portfolio invested in each. What this means is that the bank manager can figure out the effect that interest-rate changes will have on the market value of net worth by calculating the average duration for assets and for liabilities and then using those figures to estimate the effects of interest-rate changes. To see how a bank manager would do this, let’s return to the balance sheet of the First National Bank. The bank manager has already used the procedures outlined in the appendix to Chapter 4 to calculate the duration of each asset and liability, as listed in...