HW2 Fin305 - HW2 PDF

Preview

Summary

HW2...

Description

1. Consider the following bond: $1,000 par value 8% coupon rate (semi-annual coupons) 4% interest rate. What is its invoice price when there are 3.99 years to maturity? Find the clean price.

Accrued interest = (annual coupon/# of payments per year)*(days since last coupon/days separating last coupon payment)

= (80/2) * (3.65/[.49*365]) = .802

Half year yield = Full Year Yield/2 

4%/2 = 2%

Total Periods (semi-annual) = bond maturity * 2

3.99*2=7.98 periods

Present Value of Bond: 40/.02 (1 - (1/1.02)^8) + (1000/(1.02)^8)

= 2000[.147] + 853.49 = 293.019 + 852.49 = 1146.41

B(7.98) = 1.02^(8-7.98) x B(8) = 1.02^.02 x 1146.41 Invoice price = 1146.76

Accrued Interest: = 80/2 x 3.65/182 = 40 x .02 = .802

Flat Price (clean): = invoice price - accrued interest = 1146.76 - .802 = 1145.96

2. Suppose there are two bonds, a 30-year zero coupon bond and a 2-year zero coupon bond. Currently, the discount rate, y, is 4%. Suppose we are short $1000 in par value of the 30-year zero coupon bond. How much of the 2-year zero coupon bond do we need to buy to be approximately immunized from changes in interest rates?

Short:

Price for 30 year bond: 1000/(1.04)^30 = 308.32

Modified Duration for 30 yr bond= 30/1.04 = 28.85

∆B30 = 308.32(-MD30*∆y)

Long: Price of 2 year bond: X MD2 = 2/1.04 = 1.92

∆B15 = x(-MD10*∆y)

Solution: 

308.32(-28.85*∆y) = x(-1.92 *∆y)



X = (308.32(-28.85*∆y))/(-1.92 *∆y) = (302.32(28.85))/1.92 X = 4632.93...