1. The following data are for zero coupon treasury bonds each with a face value of $1000. They are to be used for all parts of this question.
Maturity Price
1 Year 968
2 Year 940
3 year 921
a. What is the three year spot rate? Provide your answer as an annual rate assuming annual compounding.
b. What is the one year forward rate beginning two years from today? Provide your answer as an annual rate assuming semiannual compounding.
c. Suppose you had a three year Treasury bond that paid interest annually at a coupon rate of 4% per year and had a face value of $1000. Note that this bond pays only one coupon payment per year. What would you expect would be the value of the second coupon payment in the market if it were stripped from the bond?
d. What would you estimate as the yield to maturity for this three year bond (from part c)? Provide your answer as an annual rate assuming semiannual compounding.
2. You currently hold 10,000 shares of Scottsville Holding Co (SHC). The share price is $47.00. Your financial advisor has just made you aware of a new opportunity offered by a leading investment bank. The bank is offering to convert your 10,000 shares into a security that at the end of 3 years will have a minimum value of $500,000. In addition, if the share price of SHC in 3 years is greater than $47, you will get 35% of the total return over $47 in addition to the minimum, e.g., if the share price increases to $49, you will get 35% x (49-47) times 10,000 or $.70 x 10,000 = $7,000 plus the $500,000 minimum. However, if the stock price in two years is greater than $52 your payoff is capped at $17,500 plus the $500,000.
Assume that the annualized volatility for SHC stock is about 20% and that the three-year continuously compounded risk-free rate is 2.5%.
a. What is your estimate of the value of the security offered by the bank?
b. Assuming you can exchange your current shares for this new security, is the new security a financially attractive alternative?