1.A financial institution has an investment horizon of two years 9.33 months (or 2.777 years). The institution has converted all assets into a portfolio of 8 percent, $1,000, three-year bonds that are trading at a yield to maturity of 10 percent. The bonds pay interest annually. The portfolio manager believes that the assets are immunized against interest rate changes.
a.Is the portfolio immunized at the time of bond purchase? What is the duration of the bonds?
b.Will the portfolio be immunized one year later?
c.Assume that one-year, 8 percent zero-coupon bonds are available in one year. What proportion of the original portfolio should be placed in these bonds to rebalance the portfolio?
2.Consider a 12-year, 12 percent annual coupon bond with a required return of 10 percent. The bond has a face value of $1,000.
a.What is the price of the bond?
b.If interest rates rise to 11 percent, what is the price of the bond?
c.What has been the percentage change in price?
d.Repeat parts (a), (b), and (c) for a 16-year bond.
e.What do the respective changes in bond prices indicate?
3.Consider a five-year, 15 percent annual coupon bond with a face value of $1,000. The bond is trading at a yield to maturity of 12 percent.
a. What is the price of the bond?
b. If the yield to maturity increases 1 percent, what will be the bond’s new price?
c. Using your answers to parts (a) and (b), what is the percentage change in the bond’s price as a result of the 1 percent increase in interest rates?
d.Repeat parts (b) and (c) assuming a 1 percent decrease in interest rates.
e.What do the differences in your answers indicate about the rate-price relationships of fixed-rate assets?
4.Follow Bank has a $1 million position in a five-year, zero-coupon bond with a face value of $1,402,552. The bond is trading at a yield to maturity of 7.00 percent. The historical mean change in daily yields is 0.0 percent, and the standard deviation is 12 basis points.
a. What is the modified duration of the bond?
b. What is the maximum adverse daily yield move given that we desire no more than a 5 percent chance that yield changes will be greater than this maximum?
c. What is the price volatility of this bond?
d.What is the daily earnings at risk for this bond?
5.Export Bank has a trading position in Japanese yen and Swiss francs. At the close of business on February 4, the bank had ¥300 million and Sf10 million. The exchange rates for the most recent six days are given below:
Exchange Rates per U.S. Dollar at the Close of Business
2/4 2/3 2/2 2/1 1/29 1/28
Japanese yen 112.13 112.84 112.14 115.05 116.35 116.32
Swiss francs 1.4140 1.4175 1.4133 1.4217 1.4157 1.4123
a.What is the foreign exchange (FX) position in dollar equivalents using the FX rates on February 4?
b.What is the definition of delta as it relates to the FX position?
c.What is the sensitivity of each FX position; that is, what is the value of delta for each currency on February 4?
d.What is the daily percentage change in exchange rates for each currency over the five-day period?
e.What is the total risk faced by the bank on each day? What is the worst-case day? What is the best-case day?
f.Assume that you have data for the 500 trading days preceding February 4. Explain how you would identify the worst-case scenario with a 95 percent degree of confidence?
g.Explain how the 5 percent value at risk (VAR) position would be interpreted for business on February 5.
h.How would the simulation change at the end of the day on February 5? What variables and/or processes in the analysis may change? What variables and/or processes will not change?