Q1. The cash prices of six-month and one-year Treasury bills are $103.45 and $89.65. A 1.5 year bond that will pay coupons of $3.50 every six months currently sells for 95.45. A two-year bond that will pay coupons of $6.85 every six months currently sells for $90.95. Calculate the six, one-year, 1.5 year, and two-year zero rates.
Q2. The following table gives the prices of bonds:
Bond principal $ Time to maturity (yrs.) Annual coupon $ Bond price $
100 0.50 0.0 96.75
100 1.00 0.0 98.25
100 1.50 3.6 101.98
100 2.00 7.5 103.50
a. Calculate zero rates for maturities of 6 months, 12 months, 18 months, and 24 months.
b. What are the forward rates for the following periods?
i. 6 months to 12 months
ii. 12 months to 18 months
iii. 18 months to 24 months
c. What are the 6-month, 12-month, 18-month and 24-month par yields for bonds that provide semiannual coupon payments?
d. Estimate the price and yield of a 2-year bond providing a semiannual coupon of 5.15% per annum.
Q3. A 1-year long forward contract on a non-dividend paying stock is entered into when the stock price is $65.80 and the risk-free interest rate is 4.25% per annum with continuous compounding.
a. What is the forward price and the initial value of the forward contract?
b. Six months later, the price of the stock is $68.45 and the risk-free rate is still 4.25%, what are the forward price and the value of the forward contract?
Q4. Consider a five-year bond with a face value of $1000, and a 7.5% coupon rate (semi-annual payments). If the current yield to maturity is 9.25%, calculate:
a. the price of the bond
b. Macaulay duration
i. semi-annual duration
ii. Annualized duration
c. Modified duration
i. semi-annual duration
ii. Annualized duration
d. Convexity
i. semi-annual duration
ii. Annualized duration
e. The %change in bond price resulting from a change in the yield to maturity of +200 basis points using:
i. Modified duration
ii. Modified duration and convexity
f. The actual calculated price change in bond price due to +200 basis points in yield to maturity.
Q5. The three-month Eurodollar futures price for a contract maturing in five years is quoted as 93.65. The standard deviation of the change in the short-term interest rate in one year is 1.54%. Estimate the forward LIBOR interest rate for the period between 5.00 and 5.25 years in the future. To do so, proceed as follows:
a. Find the convexity adjustment
b. Find the futures rate using the quoted futures price with continuous compounding
c. Estimate the forward Libor rate.
Attachment:- Assignment Files.rar