3 Congratulations, You're an Analyst You have just been hired as a junior analyst working for a bond trader. Your first assignment is to value a corporate bond paying semi-annual coupons at an annual rate of 9.5%, with a maturity of exactly 2 years. The bond has a face value of $1,000. A senior analyst has already processed the current Treasury price data and provided you with an up-to-date term structure chart, shown in Figure 1. You are told to treat this corporate bond similarly to government bonds; i.e. you will ignore all default, liquidity, and similar risks, which will be analyzed by more experienced colleagues. 3.1. The term structure of interest rates chart has a horizontal axis labeled "Maturity," and a vertical axis labeled "[Annual"] Yield. What kind of government bonds have their yields and maturities plotted on this chart? 3.2. From earlier problems you solved while in college, you learned to decompose more complex financial instruments into sums - or differences - of simpler instruments. Explain how you can decompose this corporate bond into a collection of zero-coupon bonds of different maturities, perhaps having atypical face values. Provide a brief statement explaining the decomposition and show, in a table, what would be the bond's maturities and face values, respectively. 3.3. You learned that in realistic settings cash flows that arrive later must be discounted at (usually) higher per-period interest rates. For each zero-coupon bond listed in part 3.2 above, use the term-structure chart and look up its corresponding yield. Next, compute the present value of each zero-coupon bond. Using these zero-coupon bond prices, and also relying your earlier insights, provide a computed (theoretical) price for your corporate bond. 3.4. You now have a price for your corporate bond - what is its yield? 3.5. You provide the result computed in item 3.4 to one of your colleagues, who explains that in the practice of your firm, in order to adjust for the risks that a bond like yours bears in addition to government bonds, its yield must be changed by 0.50% per year. The colleague did not say explicitly whether the yield should be increased or decreased. State whether the yield must be increased or decreased, explain why, and then compute the new bond price. Determine what is the percentage change in the bond price when comparing prices before and after the risk adjustment, respectively. 3.6. Now adjust the yield in the opposite direction to that you decided was necessary in part 3.5 above. Compute the new price and the percentage price change when comparing the original (riskless) price and the price after the newest change in yield. Compare the percentage changes in the price of the corporate bond when the yield has been increased and decreased by the same amount, respectively. Which relative change is bigger? Could you have predicted which change is bigger by examining any of the slides discussed in class, without resorting to formulas? 1 As you will note, the chart only uses "Yield" as a label for the vertical axis. The usual bond terminology expresses yields in annualized terms, and you should do the same in this class, as well as in other finance-related work that you do. We provide a reminder here, but you should not assume that similar reminders will also be present in the text of later homeworks or exams. The Term Structure of Interest Rates 6.0% 5.5% 5.0% Yield 4.0% 3.5% 3.0% 0 0.5 1 1.5 2 2.5 3 3.5 4 6.5 7 7.5 8 8.5 9 9.5 10 4.5 5 5.5 6 Maturity [Years] Figure 1: Term structure of interest rates on your first day as an analyst, as determined by a senior analyst using current government bond data. 3 Congratulations, You're an Analyst You have just been hired as a junior analyst working for a bond trader. Your first assignment is to value a corporate bond paying semi-annual coupons at an annual rate of 9.5%, with a maturity of exactly 2 years. The bond has a face value of $1,000. A senior analyst has already processed the current Treasury price data and provided you with an up-to-date term structure chart, shown in Figure 1. You are told to treat this corporate bond similarly to government bonds; i.e. you will ignore all default, liquidity, and similar risks, which will be analyzed by more experienced colleagues. 3.1. The term structure of interest rates chart has a horizontal axis labeled "Maturity," and a vertical axis labeled "[Annual"] Yield. What kind of government bonds have their yields and maturities plotted on this chart? 3.2. From earlier problems you solved while in college, you learned to decompose more complex financial instruments into sums - or differences - of simpler instruments. Explain how you can decompose this corporate bond into a collection of zero-coupon bonds of different maturities, perhaps having atypical face values. Provide a brief statement explaining the decomposition and show, in a table, what would be the bond's maturities and face values, respectively. 3.3. You learned that in realistic settings cash flows that arrive later must be discounted at (usually) higher per-period interest rates. For each zero-coupon bond listed in part 3.2 above, use the term-structure chart and look up its corresponding yield. Next, compute the present value of each zero-coupon bond. Using these zero-coupon bond prices, and also relying your earlier insights, provide a computed (theoretical) price for your corporate bond. 3.4. You now have a price for your corporate bond - what is its yield? 3.5. You provide the result computed in item 3.4 to one of your colleagues, who explains that in the practice of your firm, in order to adjust for the risks that a bond like yours bears in addition to government bonds, its yield must be changed by 0.50% per year. The colleague did not say explicitly whether the yield should be increased or decreased. State whether the yield must be increased or decreased, explain why, and then compute the new bond price. Determine what is the percentage change in the bond price when comparing prices before and after the risk adjustment, respectively. 3.6. Now adjust the yield in the opposite direction to that you decided was necessary in part 3.5 above. Compute the new price and the percentage price change when comparing the original (riskless) price and the price after the newest change in yield. Compare the percentage changes in the price of the corporate bond when the yield has been increased and decreased by the same amount, respectively. Which relative change is bigger? Could you have predicted which change is bigger by examining any of the slides discussed in class, without resorting to formulas? 1 As you will note, the chart only uses "Yield" as a label for the vertical axis. The usual bond terminology expresses yields in annualized terms, and you should do the same in this class, as well as in other finance-related work that you do. We provide a reminder here, but you should not assume that similar reminders will also be present in the text of later homeworks or exams. The Term Structure of Interest Rates 6.0% 5.5% 5.0% Yield 4.0% 3.5% 3.0% 0 0.5 1 1.5 2 2.5 3 3.5 4 6.5 7 7.5 8 8.5 9 9.5 10 4.5 5 5.5 6 Maturity [Years] Figure 1: Term structure of interest rates on your first day as an analyst, as determined by a senior analyst using current government bond data