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) Forward rate for year 2 = (1+0.035)^2/1.03- 1 = 0.040024 or 4.002%

Forward rate for year 3 = (1+0.0475)^3/1.035^2- 1 = 0.0729547 or 7.295%

b) Price of 2 year 6% annual coupon bond a year from now

P = 6/1.04 + 106/(1.04002*1.07295)

= $100.7598

c) The quoted price of Bond future = 100'14 = 100+14/32 = 100.4375

As the calculated price of the bond future is more than the quoted price, Investor should go long on the bond futures   

After one year, profit generated per bond = $100.7598- 100.4375 = $0.3223 per bond