Question

Patrick bought a stock index fund today at $400 per unit. To protect this investment against loss, he also bought an at-the-money European put option on this fund for $20, with exercise price $400 and 3-month time to expiration. His wife, Marie, argues that Patrick’s purchase of that put option is unwise since another 3-month put with exercise price of $390 costs cheaper at $15. She suggests to buy this cheaper put instead.

a. Analyze the strategies of Patrick & Marie by showing the profit profiles of their strategies for various values of the stock index fund in 3 months. Draw diagram(s) as appropriate.
b. Use the results from part (a) to compare and identify, under different situations, which strategy should do better.

Answer 1

Patrick's at-the-money put option begins to gain if the stock index drops below $380 due to its $20 premium and $400 exercise price. Marie's put option requires the stock to fall below $375 to begin gaining, factoring in her $15 premium and $390 exercise price. Which strategy is better depends on the exact drop in the stock index fund's value.

Step-by-step explanation:

The student's question involves analyzing the strategies of buying two different European put options as a form of investment protection, and determining which strategy provides better coverage under various stock index fund values.

To compare Patrick's and Marie's strategies, one must consider the potential profit profiles for each. Patrick's put option, which is at-the-money, has a premium cost of $20 and an exercise price of $400. This means Patrick's breakeven point would be when the stock index is at $380 (exercise price minus the premium). If the stock index falls below this point, Patrick will begin to realize gains from the put option.

Marie suggests purchasing a cheaper put option with an exercise price of $390 and a premium of $15. Her breakeven point would be $375. While her upfront cost is lower, the stock index fund must fall further before she starts gaining from the hedge.

Drawing profit profiles would show two lines with different slopes beginning at their respective breakeven points. Patrick's line would be less deep because the protection kicks in sooner, whereas Marie's line would start further left as the index needs to fall more significantly before her option becomes profitable.

There is no universal answer to which strategy is better, as it depends on the performance of the stock index fund. If the fund falls slightly below $400, Patrick's strategy would outperform Marie's, since he starts to gain at a higher stock value. However, if the stock value plummets well below both exercise prices, the difference in outcomes between the strategies would be the difference in premiums paid.