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