The risk free interest rate today (date 0) is 10% EAR. If you invest $1 now at t

Question

The risk free interest rate today (date 0) is 10% EAR. If you invest $1 now at that interest rate, you will receive 1+.1 in one year, and (1+.1)2 = 1.21 after two years.

a) Mark offers to sell you a 2-year risk free zero coupon bond with face value $100 for $80. This bond will pay $100 in 2 years. Is there an arbitrage opportunity? Describe how to take advantage of the arbitrage opportunity. What will you "buy" and what will you "sell"?

b) Mark realizes that he is making a mistake and changes the price at which he is willing to sell the bond. The price is now its fair value (no arbitrage opportunity any more). You buy the bond at fair value, expecting to hold the bond for 2 years.

Explanation / Answer

QAThere is an arbitrage opportunity for this I will borrow $80 at 10% EAR and will buy bond for $80 after two years I will sell the bond for $100 after this I will pay back my borrowed amount $80*(1+10%)^2 = 96.8 and I left with the profit of $100-96.8 = $3.2

QB fair price of the bond in case of no arbitrage = 100/1+10%)^2 = 82.644

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