Chapter 20 Problem 10 A stock currently sells for %77.50. Call options on the stock have an exercise price of $75 and sell for $7.75, and put options have an exercise price of $75and sell for $4. These options will expire in three months. The three-month U.S. Treasury bill annualized yield is 5 percent. There are no transaction costs and no restrictions against using the proceeds from the short sale of any security. a. A synthetic Treasury bill can be constructed by investing in a combination of the securities identified. (1) Identify the three transactions needed to construct a synthetic Treasury bill. (2) Calculate the synthetic Treasury bill’s annualized yield. b. An arbitrage strategy can be constructed with 75 actual and 100 synthetic Treasury bills, producting a face amount of $750,000. (1) State the arbitrage strategy. (2) Calculate the immediate incoming net cash flow. c. Determine the net cash flow of the arbitrage strategy at the six-month expiration date if the stock price at expiration date if the stock price at expiration is $80. (Ignore any cash flows stemming from the original arbitrage profit.)
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