Hi, Does anyone have answer key to this attached PS?

Financial Economics Due: Tuesday, November 26, 2013 Problem Set 8 1. Consider the following bonds with face values of $1,000. The coupon bonds make semiannual coupon payments: Issuer BB&T Pacific Gas & Electric NBD Bancorp Years to Maturity 5 5 9 Coupon 2.30% 8.25% 8.25% Price (% of FV) 101.345 127.113 131.787 In class, we calculated duration for a bond with semi-annual coupons. With semi-annual coupons, we transform duration from years to semi-annual periods. For example, if a bond with semi-annual coupons has a yield to maturity of 2.48% and a duration of 1.956 years, we transform the duration to 1.956*2 = 3.912 semi-annual periods. Since the semi-annual yield on the bond is 2.48/2 = 1.24%, modified duration, D* = 3.912/1.0124 = 3.864 semi-annual periods. Then, if the semi-annual yield rises by 10 basis points, the percentage change in the price of the bond is -3.864*.001 = -.00386 = -.386% a. Calculate the yield to maturity, duration (in years), and modified duration (in semi-annual periods) for each bond. b. Consider the two bonds with the same maturity (5 years). For each bond, consider a rise in semi-annual yields of 12 basis points. Using modified duration to estimate the rate of capital loss, which bond has the highest rate of capital loss? For each bond, consider a decline in semi-annual yields of 12 basis points. Using modified duration to estimate the rate of capital gain, which bond has the highest rate of capital gain? Why is duration a better measure than maturity when calculating a bond's sensitivity to changes in interest rates? c. Consider the bonds with the same coupon rate. For each bond, consider an increase in semi-annual yields of 12 basis points. Using modified duration to estimate the rate of capital loss, which bond has the highest rate of capital loss? For each bond, consider a decrease in semi-annual yields of 12 basis points. Using modified duration to estimate the rate of capital gain, which bond has the highest rate of capital gain? 2. An 8-year to maturity bond with a face value of $1000, coupon of 6%, paid annually, is priced at 102 (% of face value). a. What is the yield to maturity, duration, and modified duration of the bond? b. On a graph with the percentage change in the price of the bond on the vertical axis and the change in yield to maturity (i, in percentage points) on the horizontal axis, graph the relationship between the change in yield to maturity and the percentage change in price for this bond (you should see a convex relationship). Do this in EXCEL. c. What is the relationship between the percentage change in the price of the bond and the bond's modified duration? Graph this relationship in your graph from part b. d. Consider a 25 basis point increase in yield to maturity. What is the percentage change in the price of the bond estimated by modified duration? What is the actual percentage change in the price of the bond? Consider a 300 basis point increase in yield to maturity. What is the percentage change in the price of the bond estimated by modified duration? What is the actual percentage change in the price of the bond? e. Consider a 25 basis point decline in yield to maturity. What is the percentage change in the price of the bond estimated by modified duration? What is the actual percentage change in the price of the bond? Consider a 300 basis point decrease in yield to maturity. What is the percentage change in the price of the bond estimated by modified duration? What is the actual percentage change in the price of the bond? f. For large increases in yield to maturity, does modified duration over- or underestimate the rate of capital loss? For large declines in yield to maturity, does modified duration over- or underestimate the rate of capital gain? When does modified duration give a good estimate of the percentage change in the price of the bond? 3. In this question, you will demonstrate the result of the liquidity preference theory. The current short-term (1 period) yield is i1,1 = 1%. Next period, the distribution of the 1 period yield is: i1,2 Probability 1.5% .25 2% .50 2.5% .25 a. The expected 1 period yield next period is the mean of the above distribution. Under the expectations hypothesis, what is the current long-term (2 period) yield? If the face value of the 2 period zero coupon bond is 100, what is the price of 2 period zero coupon bond today? b. The expectations hypothesis assumes that investors are risk neutral. Suppose that investors are risk averse and demand a higher yield to invest in the longer-term asset: i2,1 > [(1.01)(1.02)]1/2 - 1. If investors are risk averse, will the price of the 2 period bond be greater or less than the price in part a.? Consider a 1 period holding period and the following two strategies: Strategy 1: Invest in the 1 period bond today with a certain yield of i1,1 = 1% Strategy 2: Invest in the 2 period bond today and sell the bond at the end of one period. c. Consider Strategy 2: Since the expected 1 period yield next period is 2%, what is the expected selling price of the 2 period bond at the end of one period? What is the expected one period return of Strategy 2? Is the expected return greater than, less than, or equal to the certain return of Strategy 1? d. If investors are risk averse, which strategy will they choose and why? e. Since risk averse investors with a 1 period holding period will not demand the 2 period bond at the price of 97.0685, what will happen to the price of the bond? f. Suppose the price of the bond falls to 95.6474, and downward pressure on the price abates. What is the equilibrium yield on the 2 period zero coupon bond today? Demonstrate that the forward rate in period 2 implied by the yield curve exceeds the expected 1 period yield in period 2 (i.e., the liquidity preference theory). 4. The following are prices (percent of face value) of U.S. Treasury STRIPS (zero-coupon bonds) from trading on November 15, 2013: Maturity 1-year 2-year 3-year 4-year 5-year 6-year 7-year 8-year 9-year 10-year Price 99.905 99.435 98.184 96.651 94.331 90.857 87.346 83.442 78.917 74.264 a. Calculate the yield to maturity for each bond and graph the U.S. Treasury zero coupon bond yield curve. b. Calculate the implied forward rates for years 2 to 10 and graph the implied forward curve. c. Under the expectations hypothesis, what can you say about the path of future expected short-term interest rates on November 15, 2013? If real yields are expected to be constant, what can you say about market expectations of future inflation on November 15, 2013 under the expectations hypothesis? d. Does the expectations hypothesis support the following statement: Given the 301 basis point yield spread between the 10-year zero and the 1-year zero, a portfolio of 10-years zeros would be expected to experience higher returns over a ten year horizon, rather than buying 1-year zeros and reinvesting the proceeds into 1-year zeros at each maturity date. e. Suppose that we have information that there are liquidity/risk premiums, and that liquidity/risk premiums (measured in basis points) increase with maturity: Maturity (years) Liquidity Premium 2 10 3 25 4 45 5 70 6 100 7 140 8 190 9 240 10 290 Using this information, what does the yield curve imply about the expected future path of short-term interest rates in the U.S. on November 15, 2013 relative to your answer in part c.? Graph the expected future path of short-term interest rates in your graph for part c