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FINA0804/3323 FINA0804/3323 Fixed Income Securities
Dr. Huiyan Qiu
Homework Assignment #3 Due: October 24, Monday, drop in TA ’s box by 6PM
1. Consider a convertible bond as follows: par value = $1,000; coupon rate = 9.5% market price of convertible bond = $1,000 conversion ratio = 37.383 estimated straight value of bond = $510 yield to maturity of straight bond = 18.7% Assume that the price of the common stock is $23 and that the dividend per share is $0.75 per year. a. Calculate each of the following (1) conversion value, (2) market conversion price, (3) conversion premium per share, (4) conversion premium ratio, and (5) premium over straight value. b. If the price of the common stock increases from $23 to $46. 1) What will be the approximate return realized from investing in the convertible bond? 2) What would be the return realized if $23 had been invested in the common stock? 3) Why would the return on investing in the common comm on stock directly be higher than investing in the convertible bond? c. If the price of the common stock declines from $23 to $8. 1) What will be the approximate return realized from investing in the convertible bond? 2) What would be the return realized if $23 had been invested in the common stock? 3) Why would the return on investing in the convertible conve rtible bond be higher than investing in the common stock directly? 2. An investment banking firm purchases $100 million of a 10-year 10 -year (fixed-rate) 8% coupon bond in the secondary market. (a) The firm issues $50 million of floaters and $50 million mi llion of inverse floaters. (The most popular split of floaters and inverse floaters is 50/50.) If the current short-term interest rate in the market is 5.75%, and this is paid on the floating-rate debt, how much coupon interest will be paid on the inverse floaters over the next 6-month 6 -month
Assignment 3
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FINA0804/3323 Fixed Income Securities
Dr. Huiyan Qiu
period? What is the coupon interest rate on the inverse floaters? (b) Answer the above two questions now assuming that the firm issues $75 million of floaters and $25 million of inverse floaters. 3. Following is a binomial interest rate tree. All rates given are one year spot rates and riskneutral probability is 50%. Consider a 3-year floating rate note with annual coupon rate set to equal to the 1-year interest rate plus 1%. What is the price of the 3-year floating rate note? Assume $1,000 par value.
4. Following table provides the information on the effective annual spot rates.
a. What are the six-month forward rates (effective annual number) for each period? Use excel to draw the spot rate curve and the forward curve. b. What is the price of a forward contract in which a 3-year 6% coupon bond will be delivered in year 3? Assume coupon is paid semiannually with $3 per payment and assume $100 par value. c. Suppose one year later, all spot rates increase by 10 basis points, what is the market value of the above forward contract then? 5. Suppose that bond ABC is the underlying asset for a futures contract with settlement six months from now. You know the following about bond ABC and the futures contract: (1) In the cash market ABC is selling for $80 (par value is $100); (2) ABC pays $8 in coupon
Assignment 3
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FINA0804/3323 Fixed Income Securities
Dr. Huiyan Qiu
interest per year in two semiannual payments of $4, and the next semiannual payment is due exactly six months from now; and (3) the current six-month interest rate at which funds can be loaned or borrowed is 6% (annual number). a. What is the theoretical futures price? b. What action would you take if the futures price is $83? c. What action would you take if the futures price is $76? d. Suppose that the borrowing rate and lending rate are not equal. Instead, suppose that the current six-month borrowing rate is 8% and the six-month lending rate is 6%. What is the boundary for the theoretical futures price? e. Suppose that bond ABC pays interest quarterly instead of semiannually. If you know that you can reinvest any funds you receive three months from now at 1% for three months, what would the theoretical futures price for six-month settlement be?