Consider a one year forward contract on 100 shares of stock when the stock price is $50. We assume that the risk-free interest rate continuously compounded is 7% per annum for all maturities. We also assume that dividends of $1.50 per share are expected after three months, six months, and nine months. What should be the equilibrium forward price now? What arbitrage opportunity is possible if the forward price for a contract is $54 (Case 1) or $44 (Case 2)? Show your works for both cases. I=$1.50e^(-0.07(3/12))+$1.50e^(-0.07(6/12))+$1.50e^(-0.07(9/12))=$4.35

F_0^*=(S_0-I)e^rT=($50-$4.35)e^(0.0710/12)=$48.96

Arbitrage Case 1: F_0=$54>F_0^*=$48.96

Today: long spot & short forward

Before & at maturity:

Arbitrage Case 2: F_0=$44

Today: long spot & short forward Before & at maturity: