Question

An investor believes in the pure expectation hypothesis and observes the following yield curve:

Maturity (years)	Zero Coupon Yield	Forward Rate
1	3.00%	3.000%
2	3.50%
3	4.75%

1. Compute the forward rates for Year 2 & Year 3

2. According to this investor, how much should a 2-year 6% annual coupon bond be priced at a year from now?

3. You find the following information about a futures contract on a 2-year bond deliverable one year from now. The underlying deliverable is assumed to have two years to maturity and a 6% annual coupon rate. [Note: quotes are based on a tick size of 1/32nds]

Expiration	Last Quote	Change
One year from today	100’14	-0’16

         Based on this information, will the investor long or short the futures contract today? If she is correct in her assessment of the price of the bond one year from now, how much profit will she generate? (I want to know how much $$ profit per bond)

Answer 1

(a)

Let r: be the 1-year forward rate year 2

(1+3%)*(1+r) = (1+3.5%)^2

r = 4%

Let y be the 1-year forward rate year 3

(1+3.5%)^2)*(1+y) = (1+4.75%)^3

y = 7.30%

(a) Price of 2-year bond

Let P be the price

FV = 100

coupon = 6%*100 = 6

P = 6/(1+3%)^1+(100+6)/(1+3.5%)^2 = 104.78

a. Forward quote = 100'14 = 100+14/32 = 100.4375

F*: theoretical price of 2 year bond deliverable in 1-year

We will use the forward quotes derived above to price this bond

F* = 6/(1+4%)+(100+6)/((1+4%)*(1+7.3%)) = 100.7581

Since F*<F the forward quote is undervalued and should be bought

Arbitrage Profit = 100.7581-100.4375 = 0.3206 per 100 face value