1)Consider a 2-year, risk-free bond with a coupon rate of 6% (annual coupons) and a face amount of $1,000.

1. What is price of this bond if the YTM is 5%? 6%? 7%?

 

 

 

 

2. If you buy the bond for $980, hold it to maturity and you reinvest the coupon payment at 6%, what is the annualized HPR on your investment?

 

 

3. If you buy the bond for $1,000 (YTM = 6%), then the yield increases to 7%, and you sell the bond immediately after the first coupon payment, what is your HPR?

 

 

4. You buy the bond for $1,000 (YTM = 6%), then the yield increases to 7%, and you sell the bond immediately after the first coupon payment. If you take the proceeds from the sale plus the coupon payment and buy a 1-year, zero-coupon bond with a yield of 7%, what is your annualized HPR over the 2-year period?

 

 

2. The yields on 1-year, 2-year and 3-year, risk-free, zero-coupon bonds are 2%, 2.5% and 3%, respectively.
   1. What is the value of a 3-year, risk-free bond with a coupon rate of 4% (annual coupons) and a face amount of $1,000?

 

 

1. 2. What are the 1-year and 2-year forward rates (f₁ and f₂)?

 

1. 3. Under the expectations hypothesis, what is the expected 1-year spot interest rate 2 years from now?

 

 

3. Consider the following 3 risk-free bonds, all with face amounts of $1,000: (i) a 1-year zero-coupon bond, (ii) a 2-year bond with a coupon rate of 6% (annual coupons), and (iii) a 2-year zero-coupon bond, all with yields of 6%.

a. What are the Macaulay durations of these 3 bonds? What are the modified durations?

 

 

             

b. If the yields on all 3 bonds rise immediately to 7%, what does the duration predict will be the percentage change in the bond price? What is the actual percentage change in the bond price?

 

4. Fill in the following payoff table (as a function of the stock price in 1 year) of a portfolio that is (i) long one share of stock, (ii) long one 1-year put with an exercise price of $50, (iii) short one 1-year call with an exercise price of $60, (iv) short one 1-year call with an exercise price of $80, and (v) short a 1-year zero-coupon bond with a face amount of $40.

 

 

 

 

 

 

 

 

             

5. Consider the following strategy: buy a call option, sell a put option, sell the underlying stock, and buy a risk-free security. Suppose the current stock price (S) is $110 and the strike price (X) is $100 for both the options, the face value of the risk-free security is also $100 (same as X), the time-to-expiration of the options is 1 years, and the risk-free rate is 0%. Is the strategy going to make arbitrage profits if the difference between the call and put option prices , C and P, respectively, is less than $10, i.e., C-P < $10?

 

 

6. Consider a stock with a current price of $100 that will be worth either $125 or $80 1 year from now. Assume r_f = 2%. What are the values and hedge ratios (deltas) of 1-year, atthe-money European call and put options? Note that you can check your answer using the binomial spreadsheet available on ANGEL, but you should do the problem by hand since you cannot use Excel on the final exam.