THE IMPACT OF THE CAPITAL MARKET
CHAPTER 12 RISK MANAGEMENT
12.3 INTEREST RATE RISK MANAGEMENT
of basis points than long-term interest rates.Basis riskrefers to the risk of changes in rates for instruments with the same maturity but pegged to a di¡erent index. For example, suppose a bank funds an investment by borrowing at a 6-month LIBOR and invests in an instrument tied to a 6-month Treasury Bill Rate (TBR). The bank will incur losses if the LIBOR rises above the TBR.
Additional risks are currency and equity risk. In the case of foreign currency lending (including bonds), the bank faces currency risk in addition to interest rate risk. Currency risk in this case arises because of changes in the exchange rate between the loan being made and its maturity. Banks also engage in swaps where they exchange payments based on a notional principal. One party pays/receives payments based on the performance of the stock portfolio and the other party receives/pays a ¢xed rate. In this case the bank is exposed to both equity risk and interest rate risk.3
The bank deals with interest rate risk by conducting various hedging operations. These are:
1. Duration-matching of assets and liabilities.
2. Interest rate futures, options and forward rate agreements.
3. Interest rate swaps.
Duration-matching is an internal hedging operation and, therefore, does not require a counterparty. In the use of swaps and other derivatives, the bank is a hedger and buys insurance from a speculator. The purpose of hedging is to reduce volatility and, thereby, reduce the volatility of the bank’s value. We will examine the concept of duration and its application to bank interest rate risk management.
Box 12.1 provides a brief primer to the concept of duration.
Since banks typically have long-term assets and short-term liabilities, a rise in the rate of interest will reduce the market value of its assets more than the market value of its liabilities. An increase in the rate of interest will reduce the net market value of the bank. The greater the mismatch of duration between assets and liabilities, the greater theduration gap.
IfVis the net present value of the bank, then this is the di¡erence between the present value of assets (PVAmarket value of assets) less the present value of liabilities (PVLmarket value of liabilities). As shown in Box 12.1 the change in the value of a portfolio is given by the initial value multiplied by the negative of its duration and the rate of change in the relevant rate of interest. Consequently, the change of the bank is equal to the change in the value of its assets less the change in the value of its liabilities as de¢ned above. More formally, this can be expressed as:
dV ½ðPVAÞðDAÞdrA ½ðPVLÞðDLÞdrL ð12:1Þ We can see from expression (12.1) that, if interest rates on assets and liabilities moved together, the value of assets matched that of liabilities and duration of assets and liabilities are the same, then the bank is immunized from changes in the rate of interest. However, such conditions are highly unrealistic. The repricing of assets, which are typically long-term, is less frequent than liabilities (except in the case of variable rate loans). Solvent banks will always have positive equity value, so PVA>PVL, and the idea of duration-matching goes against the notion of what a bank does, which is to borrow short and lend long. However, a bank is able to use the concept of duration gap to evaluate its exposure to interest rate risk and conduct appropriate action to minimize it.
By de¢nition, the duration gap (DG) is de¢ned as the duration of assets less the ratio of liabilities to assets multiplied by the duration of liabilities. This is shown in equation (12.2):
DG ¼DA PVL
PVA
DL ð12:2Þ
whereDAandDLare durations of the asset and liability portfolios, respectively.
INTEREST RATE RISK MANAGEMENT 187
BOX 12.1 Duration
Duration is the measure of the average time to maturity of a series of cash flows from a financial asset. It is a measure of the asset’s effective maturity, which takes into account the timing and size of the cash flow. It is calculated by the time-weighted present value of the cash flow by the initial value of the asset, which gives the time-weighted average maturity of the cash flow of the asset. The formula for the calculation of durationDis given by:
D¼Xn
t
Ct=ð1þrÞtðtÞ P0
or D¼ C P0
Xn
t
t
ð1þrÞt ð12:1:1Þ whereCis the constant cash flow for each period of timetovernperiods and r is the rate of interest andP0is the value of the financial asset. An example will illustrate. Consider a 5-year commercial loan of £10 000 to be repaid at a fixed rate of interest of 6% annually. The repayments will be £600 a year until the maturity of the loan when the cash flow will be interest £600 plus principal £10 000.
Table 12.1 shows the calculations.
Table 12.1
PeriodðtÞ Cash flow Present value of cash flowt
1 600 566.0377
2 600 1067.996
3 600 1511.315
4 600 1901.025
5 10 600 39 604.68
SUM 44 651.06
Duration yearsD¼44 651:06
10 000 ¼4:47 years<5 years. Such a measure is also known asMacaulay duration. An extended discussion of the use of duration in banks’ strategic planning can be found in Beck et al. (2000). However, in reality, the cash flow figures will include the repayments of principal as well as interest, but the simple example above illustrates the concept.
Duration can also be thought of as an approximate measure of the price sensitivity of the asset to changes in the rate of interest. In other words, it is a measure of the elasticity of the price of the asset with respect to the rate of interest. To see this, the value of the loan (P0) in (12.1.1) is equal to its present value, i.e.:
P0¼Xt¼n
t¼1
Ct
ð1þrÞt ð12:1:2Þ