Question

Mr. Strong is a portfolio manager of an investment bank. He is planning to sell 100,000 shares of Apple stock for his wealthy client, Mr. Weak. The current stock price of Apple is $40.  Mr. Weak would like to defer selling the stock until March next year because he is optimistic about the future prospect of Apple. However, Mr. Weak is also worried about the price risk involved in keeping his shares until March. At current price, Mr. Weak would receive $4,000,000 for the stock. If the value of his stock holdings falls below $3,000,000 in March next year, Mr. Strong would not be able to buy his dream house. Mr. Strong is evaluating two hedging strategies for Mr. Weak:

a. Strategy A is to write March call options (i.e. short call) on Apple shares with strike price $45. These call options are currently selling for $3 each.

b. Strategy B is to buy March put options (i.e. long put) on Apple shares with strike price $35. These put options are also selling for $3 each.

Evaluate these two strategies with respect to the need of Mr. Weak to buy his dream house. Explain which strategy Mr. Strong should recommend.           

Answer 1

a) Selling call options with a strike price of $45 for $3 each would result in the following situations in March next year

1. if Price of stock > $45, the option will be exercised and the total payoff to Mr, Weak per share would be $45 from selling the share and $3 from selling the option i..e $48 per share

2. if Price of stock < $45, then the call option will not be exercised , so Mr. Weak would anyway get $3 per share., and the total payoff  will be Stock price +$3 per share. However, if price of the stock falls much below $30 also, the total payoff to Mr. Weak would be $3 plus the market price of the share

Hence, if Market price falls below $27 , the payoff per share will be less than $30, so total payoff will be less than $3 million and owning the dream house will not be realised.

So, in this case, maximum payoff is $48 but it can go below $30 per share and the dream may not be realised

b) If put option is bought with a strike price of $35 for $3 each would result in the following situations in March next year

1. If Price of stock < $35, the option will be exercised and the total payoff to Mr, Weak per share would be $35 from selling the share less $3 from selling the option i..e $32 per share

2. if Price of stock > $35, then the put option purchased will not be exercised and it will become worthless, so the total payoff  will be Stock price - $3 per share. So, in all such cases, the payoff will be more than $32

So, in this case, minimum payoff per share is $32 and it can go above $32 and in all the cases, so minimum total payoff is $3.2 million and above, so the dream house can always be purchased

So, buying the put option (Strategy B) is recommended as it will fulfill the buying of dream house