Part III Short Essays and Calculations: Show your work to get full credit. I. Co

Question

Part III Short Essays and Calculations: Show your work to get full credit. I. Consider a 4% coupon bond ABC maki ng annual coupon payments if it has 3 years until maturity and has a yield to maturity of 5%. (45 points) a. What is the Macaulay duration of this bond ABC? Show your work. (15 points) b. What is the modified duration of bond ABC? Show your work. (5 points) Given that this bond's convexity is 10.33, if the market yield increases by 200 basis points, what price would be predicted by the duration-with-convexity rule for this bond at this new yield? Show your work. (20 points) c.

Explanation / Answer

a. Macaulay Duration = Year* Sum of discounted cash flows/ PV of bond

= 2767.74/ 972.77

= 2.845

b. Modified duration = Macaulay duration/ (1+YTM/n)

2.845/ (1.05)

= 2.71

c. Convexity = 10.33

Change in interest = 2%

Convexity adjustment = 10.33*100*2%^2

= 0.4132

Price change = Duration* Interest change + Convexity adjustment

= 2.71* 2 + 0.4132

= 5.83 %

Predicted price = 972.77 * 105.83% = $1029.48

Year Cash flows Discount factor=1/1+r^n Discounted cash flow Year*Discounted cash flow 1 40 0.952380952 38.0952381 38.0952381 2 40 0.907029478 36.28117914 72.56235828 3 1040 0.863837599 898.3911025 2695.173307 PV of Bond 972.7675197 Sum of Year*discounted
cash flow 2767.735666

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