A stock is currently trading at $50.A one-year at-the-money put costs $10.The stock price at the end of one year can be equally likely to be one of the following three values: {20,50,80}.What is the expected one-year return of a protective put portfolio?

Question

Quizplus · Accepted Answer

The protective put portfolio involves buying the stock and the put. The initial cost is $50 (stock) + $10 (put) = $60. At the end of the year, the portfolio values are $50, $50, and $60 for stock prices $20, $50, and $80 respectively. The expected value is (1/3)($50) + (1/3)($50) + (1/3)($60) = $53.33. The return is ($53.33 - $60)/$60 = -11.11%, but since the question asks for the expected return, which is 0% as the protective put ensures no loss beyond the premium paid.

A Stock Is Currently Trading at $50 −16.67%- 16.67 \%−16.67% B) 0%0 \%0%

A Stock Is Currently Trading at $50 $- 16.67 \%$ B) $0 \%$