Time-horizon is a very important aspect in understanding interest rate risk and the return characteristics of a fixed-rate investment. The primary concern for an investor is the change in the price of a bond given a sudden change in its yield-to-maturity. Reinvestment of coupon interest is a key factor in the investor’s horizon yield.

The bond duration is a primary measure of risk and convexity is a secondary risk measure. In comparing 2 bonds, it is assumed that “given change” is the same for both securities.

When the government par-curve is shifted up or down by the same amount to calculate effective duration and effective convexity, it is described as “parallel” yield curve shifts. Yield curves are rarely a straight line, so this shift may also be described as “shape-preserving” shift to the yield curve.

The term structure of bond yields (also called the “term structure of interest rates”) is typically upward sloping. The term structure of yield volatility is the relationship between the volatility of bond yields-to-maturity and times-to-maturity.

For instance, a central bank engaging in an expansionary monetary policy might cause the yield curve to steepen by reducing short-term interest rates. However, this policy might result in a greater volatility in short-term bond yields to maturity than in longer term bonds. Longer-term bond yields are mainly determined by future inflation and economic growth expectations. Such expectations are often less volatile.

Bond price changes are products of 2 factors: (1) impact per basis point change in the yield-to-maturity, and (2) number of basis points in the yield-to-maturity change. The first factor is duration or combination of duration and convexity, and the second factor is the yield volatility.

The estimated percentage change in the bond price depends on the modified duration and convexity as well as on the yield-to-maturity change.

QuestionAn investment bank needs to rank 3 bonds in terms of interest rate risk.

The modified duration and convexity statistics are annualized. ?Yield is the increase in the annual yield yield-to-maturity. How should the bonds be ranked in terms of interest rate risk (from the highest risk to the lowest)?

A. C has the highest degree of interest rate risk, followed by Bond A, and Bond B

B. B has the highest degree of interest rate risk, followed by Bond C, and Bond A

C. C has the highest degree of interest rate risk, followed by Bond B, and Bond A

SolutionThe correct answer is A.

Based on the assumed changes in the yield-to-maturity and the modified duration and convexity risk measures, Bond C has the highest degree of interest rate risk (a potential loss of 1.1938%), followed by Bond A, and then Bond B.

*Reading 54 LOS 54j:*

*Describe how the term structure of yield volatility affects the interest rate risk of a bond*