2. Spot rates and forward rates (30 points):

Assume that the current yield curve for zero-coupon bonds (spot rates) is as follows:

y₁ = 0.4%, y₂ = 1%, y₃ = 1.5%.

a. What are the implied 1-year forward rates f₂ and f₃?

Assume that there is no uncertainty about future short rates, i.e. that future short rates (future 1 year yields) will be equal to current forward rates (so future short term interest rates will be equal to f₂ and f₃).

b. In that situation what will be the spot curve (that is, the yields to maturity on 1- and 2-year zero coupon bonds) in 1 year?

c. What is today's price of a 3-year zero coupon bond with par value of 1000?

- And IF y₃ change to 2% because of recovery

d. What is the price of this bond next year (remember, it is then a 2 year zero coupon bond)?What is the rate of return on this bond over the next year?

- And how does rise of interest y₃ change to 2% affect your expectations and returns?