20 On December 30 2009 there were the following prices and c

20

On December 30, 2009, there were the following prices and coupon (assume annual coupons) rates for Treasury securities: Maturity Price Coupon 1 990.85 4.50% 2 981.78 4.25 3 972.65 5.25 4 978.48 5.00 What is the two year rate in one year? Select one: a. 3.42% b. 8.01% c. 7.76% d. 3.81%

Solution

A) Let us consider 1 year rate first

Time to maturity=1 year

Price=981.78

Coupon=4.25%
Enter the above details and Caluclate YTM (in caluclator)

YTM=5.46% (1 year)

Consider two year bond info now

Time to maturity=2 years

Price=990.85

Coupon=4.50

Enter the above details and Caluclate YTM (in caluclator)

YTM=5.23% (2 years)

For 3 yearbond

T=3 years

Price= 972.65

Coupon=5.25

Enter the above details and Caluclate YTM (in caluclator)

YTM = 6.27 (3 years)

Now forward rate (two year rate in 1 year is)

(1+6.27%)^3/(1+5.23%)^2 -1

=(1.0627^3/1.0523^2)-1

= 8.2 (approx)

So answer which is near is B) 8.01%