Chapter 4 (Bond Price Volatility)
1.Consider a 30-year 3% coupon bond with semi-annual coupon payments. Currently, the price of the bond is $337.47. Based on the current yield to maturity, the bond has a duration of 12.2 years and convexity of 233.2 year2. Calculate the following for this bond:
a)Yield-to-maturity (YTM).
b)Modified duration.
c)Using modified duration only, estimate the percentage change in bond price when YTM goes DOWN by 2%.
d)Using modified duration AND convexity, estimate the percentage change in bond price when YTM goes DOWN by 2%.
e)Now calculate the actual price of the bond with the YTM decreasing by 2%. What is the actual percentage change in bond value?
f)Now compare your answers in part c) and d): which method leads to a more accurate estimate on the bond’s value change?
2.A financial analyst wants to estimate the modified duration and convexity of a 30-year 3% bond trading at par, using numerical approximation. Follow her steps below to compute the modified duration and convexity of this bond (assuming the bond pays coupons annually).
a)Calculate the bond price if yield-to-maturity goes UP and goes DOWN by 20 basis point.
b)Using numerical approximation, estimate the modified duration of this bond.
c)Using numerical approximation, estimate the convexity of this bond.
3.As of April 30, 1994, the Orange County Investment Portfolio was valued at $7.5 billion. The modified duration of the portfolio is around 7.4 years. Toward the end of 1994, the market interest rates rose by about 3%. Estimate the amount of loss of this portfolio.
Chapter 5 (Term Structure of Interest Rates)
4.An analyst gathered the following information (assuming annual compounding) to compute forward rates and to calculate bond prices.
Years to Maturity
Spot Rate
1
3%
2
4%
3
5%
Based on the data above, please compute:
One-year forward rates (F1,2) and (F2,3);
Two-year forward rate (F1,3);
Price of a 3-year 4% coupon bond (with coupons paid annually), assuming the par value is $1,000.
5.The following table lists the coupon rate of the par yield curve. (1 year rate is the yield to maturity on the zero coupon bond, others are based on coupon bond).