c) Consider a bond with three years to maturity with a face value of $F. At the end of each year it pays a cash coupon of $C. Denote its yield to maturity by y. i. You buy the bond today for a price of $P, and sell it in one year (just after the payment of the coupon) for $P. If the yield to maturity does not change over time, write down expressions for P, and for P, in terms of C, F and y. [2 marks] ii. Define the return from holding the bond for that year in the normal fashion (i.e. the return is equal to the sum of its change in price over the period and any end of period cash payments, all divided by the initial price). Show how this return is related to the bond's yield to maturity. [4 marks] iii. Based on your preceding answer, discuss when yield to maturities are likely to be decent indicators of the returns from holding bond positions. [3 marks]