Question

Joe Finance has just purchased a stock-index fund, currently selling at \(1,200 per share. To protect against losses, Joe plans to purchase an at-the-money European put option on the fund for \)60, with exercise price \(1,200, and three-month time to expiration. Sally Calm, Joe’s financial adviser, points out that Joe is spending a lot of money on the put. She notes that three-month puts with strike prices of \)1,170 cost only $45, 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?

Short answer

a. As below

b.When stock price is high, Sally does better, and does worse, when stock price is low.

c. Sally’s strategy has greater risk.

Step-by-step solution

Calculation of Joe’s and Sally’s strategies

Joe’s strategy

			Final Payoff
Position	Initial outlay	ST < 1800	ST > 1800
Stock index	1800	ST	ST
Long put (X=1800)	90	1800 - ST	0
Total	1890	1800	ST
Profit = Payoff - 1890		-90	ST-1870

Sally’s strategy

			Final Payoff
Position	Initial outlay	ST < 1750	ST > 1750
Stock index	1800	ST	ST
Long put (X=1750)	700	1750 - ST	0
Total	1890	1750	ST
Profit = Payoff - 1750		-120	ST-1870

Graphical representation of Joe’s and Sally’s strategies

Explanation of Sall’s stock doing great-worse

When stock price is high, Sally does better, and does worse, when stock price is low.

Explanation of greater systematic risk

Since profits are more sensitive to the value of the stock exchange, Sally’s strategy has greater risk.