Suggested Answers to Discussion Questions

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Tiffany Adams
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1 Suggested Answers to Discussion Questions 1. Premium Time Premium Break Even Dec put103 Strike Dec call100strike (a) The stock price is currently at $ There is no gain on the shares, but thankfully no loss either. Also a call with a $55 striking price would expire out of the money, allowing you to earn $370 ($3.70 striking price times 100 shares). (b) The total gain would come from the stock price increase and call premium retention. Stock price increase: ($55.00 $52.51) 100 shares = $249 Call premium received: $ shares = $370 Total Income $619 (c) The premium on the option would offset the loss experienced on the stock. There is still a gain because the price decline was less than the call premium. Stock price decrease: ($49.00 $52.51) 100 shares = $351 Call premium received: $ shares = 370 Total Income $ Answers will vary according to student choices. Solutions to Problems 1. Fundamental value ($19 $18) 100 $100 Time premium Option price Fundamental value $250 $100 $ Fundamental value ($45 $36) 100 $900 Time premium $1,050 $900 $ A call option purchased for $600 with a $60 strike price can later be sold (or exercised) when the underlying stock has a $75 price; given this, it will generate the following:

2 Profit Value at expiration Purchase price [($75 $60) 100] $600 $1,500 $600 $900 [($75 $60) 100] $600 HPR $600 $ % $600 Annualized rate of return 150% ( ) 300% 7. You would lose the cost of the puts, which would expire worthless $1,000 $1.20 $1, Protecting profits with a put hedge: Original purchase price of the stock $48.50 Current market price of the stock Market price of the three-month put 2.50 (a) Stock price drops to $60 three months later Value of the put: $75 $60 $ shares of stock ($60 $48.50) $6,900 Value of 6 puts (6 100 $15) $9,000 Cost of 6 puts (6 100 $2.50) 1,500 Total profit $14,400 With the stock trading at $75, Myles has already made a profit of $15,900. His intent is to protect this profit with a put hedge. If the stock price drops to $60 per share, his profit will go down to $14,400, as shown above. His profit decreases by the cost of the put, or $1,500. (b) Stock price rises to $90 in three months: Value of the put: $0 600 shares of stock ($90 $48.50) $24,900 Value of 6 puts (6 100 $0) 0 Cost of 6 puts (6 100 $2.50) 1,500 Total profit $23,400 If the stock price goes up to $90, Myles would make additional capital gains on the stock. Net of the cost of the put, he made $23,400 on the entire transaction. He made an additional profit of $7,500 by holding the stock ($23,400 15,900) when the stock price rose from $75.00 to $ (c) The major advantage of a put hedge is that it allows investors to enjoy the upward profit potential while at the same time protecting the profits already made on the long transaction. In the worst case, the put hedge would only result in the loss of the cost of the put.

3 (d) In-the-money options are more expensive and, as a hedging device, they are riskier than at-the-money options (those with strike prices exactly equal to the current market price of the underlying stock). In this case, the cost of $600 puts would be $6,300 ($600 $10.50). In the worst case, the investor would lose $6,300, compared to only $1,500 with an at-themoney option. Even though out-of-the-money options are inexpensive, using those options to create a put hedge will leave part of the profits unprotected. For example, using the put with a strike price of $70 would cost only $600 (600 $1). But if the stock price drops to $70, Myles would lose $5 per share in unprotected capital gains. His profit on the out-of-the-money put hedge would be: 600 shares of stock ($70 $48.50) $12,900 Value of 6 puts (6 100 $0) 0 Cost of 6 puts (6 100 $1.00) 600 Total profit $12,300 Myles s profit dropped from $15,900 to $12,300, for a net loss of $3,600 on the put hedge. This loss is due to $3,000 of unprotected capital gains and the $600 cost of the put. 11. Covered call writing: Current market price of the stock $61.50 Current market price of the call 5.75 Initial investment: $ $30,750 (a) If the stock price rises to $65 per share, the call options expire worthless: Value of the call: $0 Quarterly dividends received $400 Proceeds from sale of call 2,875 Capital gains on stock [($65 $61.50) 500] 1,750 Total profit $5,025 Holding period return: Total profit HPR Initial Investment $5, % $30,750 (b) For any price above $65, the loss on the call option will be exactly offset by the additional capital gains made on the long position in the stock, leaving the profit of $5,025 unchanged. The HPR also remains the same, 16.34%. (c) The covered call position offers limited protection against a drop in stock price. The capital loss on the stock can be protected to the extent of the option premium received, namely $2,875. In this case, the investor is protected against losses until the stock price drops to $55.75, the breakeven price. If the stock drops below this price, the investor would have to bear the additional losses. Thus, the upward potential of this covered call is limited to $5,025 while the potential losses are only partly covered.

4 13. (a) LONG STRADDLE Cost of one July 112 Call Option $ $265 Cost of 100 July 112 Call Options $ $26,500 Cost of one July 112 Put Option $ $165 Cost of 100 Dec 93 Put Options $ $ Cost of the LONG Straddle $26,500 $16,500 $43,000 If the Market Falls by 750 Points: Profit from 100 Call Options $0 Profit from 100 Put Options $75,000 Gross Profit from the straddle (ignoring transaction costs) $75,000 Cost of Straddle $43,000 Net Profit (Loss) $32,000 If the Market Goes Up by 750 Points: Profit from 100 Call Option $75,000 Profit from 100 Put Options $0 Gross Profit from the straddle (ignoring transaction costs) $75,000 Cost of Straddle = $43,000 Net Profit (Loss) = $32,000 If the Market Stays at 11,200 Points: Profit from 100 Call Option $0 Profit from 100 Put Options $0 Gross Profit from the straddle (ignoring transaction costs) $0 Cost of Straddle = $43,000 Profit (Loss) = ($43,000) (b) SHORT STRADDLE (You are the writer) Profit of one July 112 Call Option $ $265 Profit of 100 July 112 Call Options $ $26,500 Profit of one July 112 Put Option $ $165 Profit of 100 Dec 93 Put Options $ $16,500 Profit from the SHORT Straddle $26,500 $16,500 $43,000 If the Market Falls by 750 Points: Loss from 100 Call Options $0 Loss from 100 Put Options $75,000 Total Loss from the straddle $75,000 Sale of Straddle = 43,000 Net Profit (Loss) = ($32,000) If the Market Goes Up 750 Points:

5 Loss from 100 Call Options $75,000 Loss from 100 Put Options 0 Total Loss from the straddle $75,000 Sale of Straddle = 43,000 Net Profit (Loss) = ($32,000) If the Market Stays at 11,200 Points: Gain from 100 Call Options $26,500 Gain from 100 Put Options $16,500 Total Gain from the straddle $43,000 (c) Option straddles are extremely risky investment strategies; hence an investor using this strategy must completely understand the risk involved in the above. For larger movements in the market, the short straddle will start losing money and the long straddle will start gaining money. (The instructors may use this example to illustrate that options are a zero-sum game. If an option writer makes money, the option buyer would lose money and vice versa).

Currency Option Combinations

APPENDIX5B Currency Option Combinations 160 In addition to the basic call and put options just discussed, a variety of currency option combinations are available to the currency speculator and hedger.