h) The bond price risk, that is, the relative change in price, P/P, can be easily written in terms of the modified duration:

= -D * y.

Carefully explain this equation and the terms in it. Why is there a minus sign? Then, using this equation, describe the impact of the modified duration on price risk.

i) The for mula for the modified duration in part h) is a linear approximation to the true equation. In fact, the line is actually a curve; this is called convexity Taking this into account, a more accurate description of bond price risk would be y + Convexity (Av)2 100 Actual Price Change Duration Approximation " 20 -40 -60 Change in Yield to Maturity (%) The linear approximation in part h) is shown as the dashed line in the plot, and the actual price change is shown as the solid line. Explain which investors would prefer: bonds with large or small convexity. i) The for mula for the modified duration in part h) is a linear approximation to the true equation. In fact, the line is actually a curve; this is called convexity Taking this into account, a more accurate description of bond price risk would be y + Convexity (Av)2 100 Actual Price Change Duration Approximation " 20 -40 -60 Change in Yield to Maturity (%) The linear approximation in part h) is shown as the dashed line in the plot, and the actual price change is shown as the solid line. Explain which investors would prefer: bonds with large or small convexity