**6**

# THE RISK OF CHANGING INTEREST RATES

The riskiness of bonds depends on an investor's horizon. Investors with a long horizon are concerned with the value of their portfolio at some distinct date. For these long horizon investors, the reinvestment rate for coupons and the interest rate at their horizon date are fundamental. For investors with a very short horizon, changes in interest rates over the very near term are important. The last part of this chapter will deal with long horizon investors. The beginning of this chapter will deal with short horizon investors.

## Duration

Macaulay's duration (DUR) is the most common measure of short-term bond price volatility and equals the percent change in bond price times one plus the interest rate for a change in interest rates:^{1}

The numerator of duration is (minus) the derivative of bond price with respect to yield to maturity times 1 + *y*. The derivative divided by the price is equal to the instantaneous percent change in price as interest rates change. Each term in the numerator is the present value of the cash flows in a particular period times the number of periods until those cash flows are received. This represents a weighted average maturity of the cash flows.

**Table 6.1** Duration calculations

The duration calculations can be illustrated ...