Fixed Income

1. [6pts] Given a five-year, 8% coupon bond with a face value of $1,000 and coupon payments made annually:

a. [1.5pts] What is the bond value if it is trading at the yield of 6%?

b. [1.5pts] What is the bond value if it is trading at the yield of 8%?

c. [1.5pts] What is the bond value if it is trading at the yield of 10%?

d. [1.5pts] Comment on the price and yield relation you observe. What are the percentage changes in value when the yield goes from 6% to 8% and when it goes from 8% to 10%?

2. [4pts] Suppose an investor bought a 10-year, 10% annual coupon bond at par (face value of $1,000 and paying coupons annually) and then sold it 3.5 years later at a yield of 8%. 

a. [1pts] What is the full price?

b. [2pts] What is the accrued interest the investor would receive when he sold the bond? (Use a 30/360-day count convention)

c. [1pts] What is the clean price?

3. [6pts] A zero-coupon Treasury bill maturing in 150 days is trading at $98 per $100 face value. Determine the following rates for the T-bill:

a. [2pts] Dealers annual discount yield? (use 360-day count convention)

b. [2pts] Yield to maturity? (Use an actual 365-day count convention)

c. [2pts] Logarithmic return (use an actual 365-day count convention)

4. [4pts] Calculate both Macaulay and modified durations of the eight-year, 8.5% coupon bond given a flat yield curve at 10%.