Option Strategies

Dr. Tversky purchased 3,000 shares of AMZN (Amazon) in 2005, based on the recommendation of his colleague, Dr. Boombatz. The investment cost him $99,330 (about $33.10 per share). Amazon's stock has neither split nor paid dividends since 2005. In mid-June 2017, Dr. Tversky became anxious about this equity position and wanted to sell it for $968 per share, which was the approximate intra-day trading range on the day he wanted to lock in his profits. Selling AMZN at the June 2017 price would net Dr. Tversky a capital gain of $2,804,700, on a sell transaction of $2,904,000. Of course, he would then be faced with paying state and federal income tax on his capital gains. Dr. Tversky is planning to move to Florida next year. Florida is a state which has no income tax on capital gains. He now lives in Massachusetts, where his approximate income tax rate on the gains would be 6%. He would like to avoid paying nearly $170,000 in taxes to MA this year, but would also like to lock in his gains. Assume that the risk-free rate of return is 3.0%

a. Assume AMZN has a nearly constant volatility (i.e. σ) of 28% and a market value of $968 per share. Estimate of the cost a 1-year put option on a share of AMZN, assuming a strike price of X=$960.

b. Estimate of the cost of 1-year call option a share of AMZN, assuming a strike price of X=$980.

c. What options strategy could you use that would enable Dr. Tversky to avoid $170,000 in MA taxes while locking in his gains?

d. How much would it cost, up-front, to establish the strategy you described in part (c). Assume that the option prices you calculated in parts (a) and (b) reasonably reflect market prices. It is possible that the collar will not incur costs, depending on the valuation of the options used to engineer the collar.

e. Ignoring taxes and assuming the options strategy you describe in part (c) is utilized, what would be Dr. Tversky's net gain on this position if the stock trades at $1,000 next June?

f. Ignoring taxes, what would be Dr. Tversky's net gain if the stock trades at $925 next June and he liquidates his position at that time?

g. What will be approximate gain or loss on the options strategy if the stock price increases by $1 immediately after establishing it? [Hint: You can use the aggregate option delta to approximate this.]