Joe Finance has just purchased a stock index fund, currently selling at $2,400 per share.

To protect against losses, Joe also purchased an at-the-money European put option on the fund for $120, with exercise price $2,400, and 3-month time to expiration. Sally Calm, Joe’s financial adviser, points out that Joe is spending a lot of money on the put. She notes that 3-month puts with strike prices of $2,340 cost only $90, and suggests that Joe use the cheaper put.

a. Analyze Joe’s and Sally’s strategies by drawing the profit diagrams for the stock-plus-put positions for various values of the stock fund in three months.

b. When does Sally’s strategy do better? When does it do worse?

c. Which strategy entails greater systematic risk?