You observe the following market information regarding three bonds.

Bond A is a pure discount bond with one year to maturity being traded at $952.38

Bond B is a 8% coupon bond with two years to maturity traded at $1033

Bond C is a 3 years coupon bond with yield to maturity of 9% traded at par.

The face value of all of the bonds in this question is assumed to be $1000.

(a) What is the term structure of spot rates up to year 3?

(b) What is the forward year for the third year (rate at which you can borrow at year 2 and repay at year 3)?

(c) Suppose you nd out that a 5% coupon bond with maturity of 2 years is being traded at $900. Can you make any arbitrage prots by forming a portfolio that consists only of this bond and bonds A and B? If so, explain what trades the strategy involves. (The arbitrage strategy can involve non-integer units of bonds as well)

(d) A year from now, the price of Bond C is expected to change to either $1020 or $950 with probabilities 70% and 30%, respectively. Assuming that the one year forward rate a year from now will surely be 9%, what is the expected return for an investor who buys a 2 years zero-coupon bond today?