The risk free interest rate today (date 0) is 10% EAR. Mark offers to sell you a 2-year risk free zero coupon bond with face value $100 for $80. Before you can take action, Mark realizes he is making a mistake and the price of the bond is now its fair value. You buy the bond at the fair value, expecting to hold the bond for 2 years.

1 year later (on date 1), the interest rate is 20% EAR.

a) What is the fair value of the bond?

b) What should its price be?

Suppose there was no arbitrage (price = fair value) and you sold the bond at date 1.

c) What HPR did you make?

Suppose instead that on date 1, the interest was 5% EAR.

d) What is the fair value of the bond?

e) What should its price be?

Suppose there was no arbitrage (price = fair value) and you sold the bond at date 1.

f) What HPR did you make?

g) Suppose instead you hold the bond for 2 years. What is the AHPR (annualized HPR) did you make? Is the bond truly risk free?