Suppose you buy a bond with the following characteristics.

Maturity Coupon Yield Price

$4$ years $10\%8\%106\mathrm{.}73$

Coupons are paid semi$-$annually. Your investment horizon is $3$ years.

a$)$ Calculate the total coupon income, reinvestment income, price appreciation$/$depreciation and holding period return from this bond if the following path of forward rates is given: after $6$ months the rates increase to $8\mathrm{.}25\%,$ after $18$ months they increase to $8\mathrm{.}5\%,$ in the third year they increase to $9\%,$ and in the fourth year they fall back to $8\mathrm{.}5\%$ in the first $6$ months and to $8\mathrm{.}25\%$ in the final $6$ months.

b$)$ Compare the holding period return calculated in part a$)$ to the yield to maturity of this bond and explain why there may be a difference between the two.

c$)$ What is the current yield of this bond? Answer explaining the difference between the current yield and yield to maturity.

d$)$ If this bond is a BB$-$rated corporate bond, and if there is a government bond comparable to it in terms of coupon and maturity, which one would you expect to exhibit greater price volatility? Explain.