Strike Bid Ask Strike Bid Ask # # # # Expected Price($)

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1 1 Exercises on Stock Options The price of XYZ stock is $201.09, and the bid/ask prices of call and put options on this stock which expire in two months are shown below (all in dollars). Call Options Put Options Strike Bid Ask Strike Bid Ask # # # # The bid price is the price at which you can sell the option and the ask price is the price at which you can buy the option. When you buy an option, the expected profitability of each option depends on your expected price of the stock between the settlement date and the expiration date. For each expected price of the stock given in the first row of the following table, write in the second row all options which are expected to be profitable. Assume there are no other transaction costs. Expected Price($) Options put #1 & #2 put #2 none call #2 call #1 & #2 Buying Options Call Option If you buy a call option at the ask price, you have two choices on the expiration date: either exercise the option or let it expire. - If you let the call option expire, your loss is the price of the option you paid for. - If you exercise the call option, you pay the strike price, receive a share of stock, and sell it in the market. If the market price is higher than the strike price (i.e., the call option is in the money), you gain, and If the market price is lower than the strike price (i.e., the call option is out of the money), you lose Therefore, you exercise the call option only if it is in the money (the market price>strike price). - When the call option is in the money, the net profit/loss is equal to (market price-strike price) - ask price. If the market price is $138, both call options are out of money. Therefore, you would buy neither call option if your predicted market price is $138.

2 2 If the market price is $150, call option #2 is out of the money and call option #1 is in the money. If you buy call option #1, you exercise the option and the net profit/loss=( )-61.50= Hence, you don't buy any call option. If the market price is $190, both call options are in the money, and you will exercise the option. The net profit/loss=( )-61.50= for #1 and net profit/loss=( )-21.30= for #2. You make money from stock transactions, but the gain is not enough to cover the cost of options. You buy neither call options. If the market price is $201.40, both call options are in the money, and you will exercise the option. The net profit/loss=( )-61.50=-0.1 for #1 and net profit/loss=( )-21.30=0.1 for #2. You make money from stock transactions, but the gain is not enough to cover the cost of options for #1, but it is enough for #2. Therefore, you buy #2, but not #1. If the market price is $202, both call options are in the money, and you will exercise the option. The net profit/loss=( )-61.50=0.5 for #1 and net profit/loss=( )-21.30=0.7 for #2. You make money from stock transactions, and the gain from them is large enough to cover the cost of options for both call options. Therefore, you buy both call options. Put Option If you buy a put option at the ask price, you have two choices on the expiration date: either exercise the option or let it expire. - If you let the option expire, your loss is the price of the option you paid for. - If you exercise the put option, you buy a share of stock at the market price, deliver it to the put writer, and receive the strike price. If the market price is lower than the strike price (i.e., the put option is in the money), you gain, and If the market price is higher than the strike price (i.e., the put option is out of the money), you lose Therefore, you exercise the put option only if it is in the money (the market price<strike price). - When the put option is in the money, the net profit/loss is equal to (strike price-market price) - ask price. If the market price is $138, both put options are in the money, and you will exercise the option. The net profit/loss=( )-0.05=1.95 for #1 and net profit/loss=( )-0.22=41.78 for #2. You make money from stock transactions, and the gain from them is large enough to cover the cost of options for both put options. Therefore, you buy both put options.

3 3 If the market price is $150, put option #1 is out of the money and put option #2 is in the money. If you buy put option #2, you exercise the option and the net profit/loss=( )-0.22= Hence, you don't buy put option #1 and buy put option #2. If the market price is $190, or or 202, both put options are out of the money, and you would buy neither put option if your predicted market price is $190 or higher.

4 4 Writing (selling) Uncovered Options Call Option If you sell a call option at the bid price, you face two cases on the expiration date: the buyer of your option either exercises the option or lets it expire. The buyer will exercise the call option only if it is in the money. - If the buyer lets the option expire (i.e., the call option is out of the money), your profit is the bid price of the option you sold at. - If the buyer exercises the call option (i.e., the call option is in the money), you buy a share of stock in the market, deliver it to the buyer, and receive the strike price. Your net profit is equal to bid price+(strike price-market price) Example: Suppose you sold call option #2 on the settlement date, and received the bid price $ Suppose the market price is $190 on the expiration date. The buyer of your call option will exercise the option. To fulfill the contract, you purchase a share in the market at $190, deliver it to the buyer and receive the strike price $180. Your profit is ( )= Other cases can be computed in a similar way. Put Option If you sell a put option at the bid price, you face two cases on the expiration date: the buyer of your option either exercises the option or lets it expire. The buyer will exercise the put option only if it is in the money (i.e., if the strike price is higher than the market price). - If the buyer of your put option lets the option expire (i.e., the put option is out of the money), your profit is the bid price of the option you sold at. - If the buyer of your put option exercises the option (i.e., the put option is in the money), you must pay the strike price, receive a share of stock and sell it at the market price. Your net profit is equal to bid price+(strike price-market price) Example: Suppose you sold put option #1 on the settlement date, and receive the bid price Suppose the market price is $138. The buyer can purchase a share of stock at $138, and sells it to you at the strike price $140. You have to pay $140 to the buyer, receive a share of stock and sell it in the market at $138. Therefore, your profit is =-1.99, a loss. Therefore, if your expected market price if $138, you would not sell put option #1.

5 Covered Call to hedge against downside risk - You bought 1000 shares of stock ABC at $20 per share - You are concerned about the price decline. - If the price falls to $18, you lose $2 per share and $2,000 in total. - You sell 10 call options at strike price $21 at a price $0.5 per share, and receive $ If the price falls to $18, the call option expires (buyer of the call option does not exercise the option) and you get to keep $500. Therefore, your loss will be only $1, If price rises, however, your gain is also limited. For example, if price rises to $23, the holder of the call option exercises the option and you have to sell at the striking price $21. Note: When you sell a call option while you are long on a stock, it is called the covered call option. - cost of purchase 1000 shares=$20,000 - revenue from selling 10 lots of call option for 1000 shares = $500 stock price at the expiration date when you don t buy put option Profit/Loss when you sell call option $17 $3000 loss $2500 loss no $18 $2000 loss $1500 loss no $20 0 $500 profit no $22 $2000 profit $1500 profit yes $23 $3000 profit $1500 profit yes Exercise the option? yes or no 5 Covered put option to hedge against downside risk. - You bought 1000 shares of stock ABC at $20 per share - You are concerned about the price decline. - If the price falls to $17, you lose $3 per share and $3,000 in total. - You buy 10 put options at strike price $19 at a price $0.5 per share, and pay $ If the price falls to $17, you exercise the option, selling your 1,000 shares at the strike price $19. - Your loss is $2,000, $1 loss per share plus the put option cost. - cost of purchase 1000 shares=$20,000 - cost of buying 10 lots of put option for 1000 shares = $500

6 6 stock price at the expiration date when you don t buy put option Profit/Loss when you buy put option $17 $3000 loss $1500 loss yes $18 $2000 loss $1500 loss yes $20 0 $500 loss no $22 $2000 profit $1500 profit no $23 $3000 profit $2500 profit no Exercise the option? yes or no When the price is $17, it is profitable to exercise the put option because you can sell it at the strike price $19. You lose only $1/share, and incur the cost of buying the option, which is $500. The total loss is $1500. Call options to hedge short sale Short Sale: - Borrow shares of stock from a broker and sell them. - The proceed is kept in investor s account (cannot use it). - Margin requirement: Investor must put up 50% additional fund in the account, total 150% usually borrow the margin amount from the broker - If the price falls, buy shares in the market at a lower price and return to the broker. The difference in prices is the profit (need to pay fees to the broker and interest on the borrowed margin) - If the price rises before you close your account, you need to put up more margin to meet 150% of the total value of the stock Example: borrow 1,000 shares, short sell at $20 per share, and receive $20,000 You need to put up 50% additional fund and your account has $30,000 If price falls to $18, buy 1,000 shares, return them to the broker and close the account. Makes the profit of $2,000, minus some interest and fees on the margin account If price rises to $22, the current margin $30,000 is not sufficient It requires 150% of $22,000, i.e., $33,000. The broker issues a margin call of $3,000, which the investor must pay to the broker.

7 7 Buy call options to hedge short sale - Current price of stock ABC is $20, and you expect the price to fall to $18 You sell 1000 shares short at price $20 per share, receiving $20,000. When price falls to $18, you buy 1000 shares and give them back to the broker Your profit is $2,000 (need to pay fees to the broker and interest on the margin) - If the price rises to $22 instead, you lose $2, You can limit this risk by buying call options. - Suppose call option with strike price $21 is traded at price $0.5 per share. - You buy 10 call options (one call option is for 100 shares), paying $ If price rises to $22, you exercise the option, buying 1000 shares at $21 to return to the broker. You incur a loss of $1,000 plus option cost $500, totaling $1500 loss. This loss is smaller than the loss of $2000 in trading long. No option: Call option stock price at the expiration date when you don t buy call option Profit/Loss when you buy call option $17 $3000 profit $2500 profit no $18 $2000 profit $1500 profit no $20 0 $500 loss no $22 $2000 loss $1500 loss yes $23 $3000 loss $1500 loss yes Exercise the option? When the price is $17, you buy and return the stocks, realizing $3000 profit. When the price is $22, you buy and return the stocks, realizing $2000 loss. cost of options = $500. This is a sunk cost. When the price is $17, you buy and return the stocks. Profit is $2500=$3000-$500. Do not exercise the option When the price is $22, you exercise the option: buy at $21 and return the stocks. The loss is $1500=$1000+$ Note: the usual fees and interests that are involved in short sales are not considered. - The difference between short-sale+call option and covered call option is that the amount investment

8 8 of your fund. In the short sale case, it requires $10500 to cover the initial margin call and cost of call option. In the covered call option case, you have to invest $20,500 to purchase stock shares and the cost of call option