Yield Volatility

Prices of fixed income securities are affected by both the level of interest rates and the volatility of interest rates.

The risk of a default-free bond stems from two sources - interest rate shifts and risk of changes in the volatility of interest rates. The first type of risk is well-known. Managing interest rate risk requires measuring it first. Duration analysis has become an important tool, allowing portfolio managers to measure the sensitivity of their portfolios to changes in the level of interest rates.

The second type of risk is less familiar, although it can represent a major component of the total risk of a fixed-income portfolio. The greater the expected yield volatility, the greater the interest rate risk for a given duration and current value of a position.

Investment Horizon, Macaulay Duration, and Interest Rate Risk

The investment horizon is essential in measuring the interest rate risk of a fixed-rate bond.

When there is a parallel shift to the yield curve, the yield-to-maturity and coupon reinvestment rates are assumed to change by the same amount in the same direction. The Macaulay duration statistic identifies investment horizon so that the losses (or gains) from coupon reinvestment offset the gains (or losses) from market price changes.

The duration gap is the difference between the Macaulay duration and the investment horizon.

• When the investment horizon is greater than the Macaulay duration of the bond, coupon reinvestment risk dominates price risk. The investor's risk is to lower interest rates. The duration gap is negative.
• When the investment horizon is equal to the Macaulay duration of the bond, coupon reinvestment risk offsets price risk. The investor is hedged against interest rate risk. The duration gap is zero.
• When the investment horizon is less than the Macaulay duration of the bond, price risk dominates coupon reinvestment risk. The investor's risk is to higher interest rates. The duration gap is positive.