Question

The current price of stock in Company XYZ is $45 and no ex-dividend dates are to occur for the next three months. The risk-free rate is 4.00% per year. The standard deviation for the period in question is 0.4. You are a financial advisor and one of your best clients is Mr. John Smith who is a senior-level manager at a Fortune 500 company. A portion of Mr. Smith’s incentive compensation is paid in restricted stock in the company he works for which he cannot sell for a period of three years from the date of the award of the shares. Smith has been employed at the company for 35 years and he has been in a senior position for the last 20 years. Mr. Smith has a concentrated equity position in the company owning 1,000,000 shares. More than 80% of his wealth is in the company stock. Assume that due to contractual obligations, he cannot sell his stock over the next three months. Due to his concentrated position, he wants to hedge against the price of XYZ stock falling more than 20%. He can do this by buying put options with a strike price of $36.

1. Assume that Mr. Smith does not have the necessary amount of liquid assets (other than his stock which he cannot sell) to be able to purchase these put options so he will have to enter into an equity collar. At what strike price should he strike the corresponding call options?
2. If Mr. Smith decides that he can raise enough cash to put up $200,000 to pay for some of the puts, how will it affect the strike price on the call?
3. If instead of three months, the restriction on his stock is six months, how will this change the hedge? Solve for the appropriate put and call strikes.
4. Using your answers from a) above, assume that after one month, the stock price goes up to $70 and Mr. Smith wants to unwind his hedge. Describe how you would go about terminating this hedge. Determine what it would cost to terminate this hedge.
5. Again, using your answers from a) above, if after one month the stock price went down to $28 instead and Mr. Smith wanted to terminate this hedge, what would be the economic repercussions? Calculate this amount.
6. As Mr. Smith’s financial advisor, would you recommend this strategy to Mr. Smith? Why or why not?
7. List down the benefits and advantages of this strategy.

Answer 1

Okay, here are the solutions to the questions:

1. Since Mr. Smith cannot sell his stock for 3 months and wants to hedge against a drop of more than 20%, a put option with a strike price of $36 would be appropriate. To collar this with call options, we would want the call strike to be $54 ( $45 current price + 20% hedge).

So put strike = $36 and call strike = $54.

2. If Mr. Smith can put up $200,000 for the puts, he can buy more put options which will allow a lower put strike, e.g. $32.

So now put strike = $32 and call strike = $51.

3. If the restriction is for 6 months instead of 3 months, a longer dated put and call would be needed.

For a 6 month hedge, put strike could be $30 and call strike $50.

4. If the stock price goes up to $70 after a month, Mr. Smith can:

- Buy back the put options at a lower price since the strike is now out of the money. This will cost less than the original purchase price.

- Sell the call options which are now in the money. This can generate a profit.

The total cost to terminate the hedge would be the amount spent buying back the puts plus any loss from selling the calls in the money.

5. If the stock price drops to $28, Mr. Smith would:

- Lose the $200,000 put premium since the puts are now deep in the money.

- Potentially have to exercise the puts and sell the stock at $28, taking a $17 per share loss.

- Lose the value of the call options which would expire worthless.

The economic loss could be substantial in this scenario.

6. I would recommend this strategy to Mr. Smith with some cautions:

Pros: Provides downside protection for a concentrated position. Allows Mr. Smith to keep the stock long-term.

Cautions: The strategy is complex and expensive. There are opportunities for losses as shown above. Mr. Smith needs to monitor the position closely. The hedge may not provide full downside protection.

Overall, for a large concentrated position, a hedge could provide some comfort but needs to be done carefully with full understanding of the risks and costs. Close monitoring is required.

The benefits of the strategy are downside protection and the ability to keep a large long-term stake in the company. But there are also risks of losses and the costs of implementing and unwinding the hedge. Proper evaluation of these pros and cons is necessary before employing this strategy.