Understanding the Mathematics of Personal Finance

# OPTIONS

Many types of “futures” products are available for the aggressive investor. I’m going to explain just one of them: options. A stock option gives the purchaser the right, but not the obligation, to buy (a “call”) or to sell (a “put”) a certain number of shares of a given stock for a preset price at any time up until the expiration date of the option.

That was a mouthful. Let me break it down, using the option to buy, or call, for an example. Widgetarama stock is selling at \$28 (per sharei ) and I believe it will increase significantly in price over the next 90 days. I find that I can buy calls on Widgetarama stock for \$4.00 with a strike price of \$26 and an expiration date of 90 days from now. Exactly what am I buying? I am buying a contract that says that any time during the next 90 days, I can buy Widgetarama for \$26, regardless of the actual selling price of Widgetarama on that date. The strike price is my guaranteed purchase price for the Widgetarama stock. The contract will specify how many shares I can buy. Actually, buying the stock at the strike price is called exercising my option. If I don’t exercise my option before the expiration date, the option expires and I can toss it away. I don’t get any money back.

Table 13.3 shows several examples of what might happen. I’m ignoring present value considerations so that we don’t get buried in numbers. I do not intend to hold on to my shares of Widgetarama if I exercise the option; I’ll sell the shares imme­diately and realize my profit.

3 “Per share” is assumed when a stock or option price is quoted unless something else is specifically stated.

Stock price Profit Profit Annualized percent profit when

(\$) (\$) (%) exercised after (%)

 30 days 60 days 90 days 29.00 -1.00 - 25.00 29.50 1.75 - 12.50 30.00 0.00 0.00 0 0 0 30.50 0.50 12.50 150 75 50 31.00 1.00 25.00 300 150 100 31.50 1.50 37.50 450 225 150 32.00 2.00 50.00 600 300 200

When I exercise my option, I’m paying \$26 for a share of the stock. I’ve already paid \$4 for the option. This means that the stock price has to be more than \$30 for me to make a profit, or for the option to be “above water.” If the stock price never climbs above \$30 during the 90-day period, or I fail to exercise the option for whatever reason during this period, I lose money. This is a very important point. If I had bought shares of the Widgetarama stock and the stock price wandered around, up or down a few percent, the value of my investment would have wandered around this same few percent—I would have made or lost a few percent of my investment. If the option is never exercised, I’ve irretrievably lost my investment in the option. For stock prices between \$26 and \$30, I salvage part of my investment because the difference between my total cost and the price of the stock is still a loss, but it’s less than \$4.

This is a risky game to play. Why would I be doing it in the first place?

The answer to this question is in the table. I’m only showing results after 30, 60, and 90 days in the table. Suppose the stock price climbs to \$31 sometime during the 90-day period. If I can buy a share of Widgetarama for \$26 plus my \$4 for the option and turn around and sell this share immediately, my profit is \$30 - \$26 - \$4 = \$ 1, which is 25% of my (\$4) investment. I’m neglecting a small “operating cost” here: To buy the stock for \$26, I had to first raise the money. Since I’ll be selling the stock the same day, this is a very short-term loan. Even at credit card rates, a 1-day loan isn’t that expensive. If I traded options regularly, I’d have a line of credit established and waiting for my needs. Also, there are commission costs any time a security is bought or sold.

If I had to wait 60 days for the stock price to reach \$31, then my \$4 has been tied up approximately one-sixth of a year, and my annualized profit is 6(25%) = 150%. At this time, my original investment and my profit are in my pocket and I can play the game again.

This is clearly an example of high-risk versus high-reward investing. If the stock price doesn’t reach a high enough value during the lifetime of the option, I lose money, possibly everything. If the stock price climbs enough, I get a very high rate of return on my investment.

Table 13.4 Sample Actual Puts and Calls Listing

 Strike April 2009 Oct 2009 Call Put Call Put Ask (\$) Volume Ask (\$) Volume Ask (\$) Volume Ask (\$) Volume 40 48.60 0 0.05 0 45 43.60 0 0.05 0 50 38.60 0 0.05 10 39.20 0 1.20 0 55 33.60 0 0.15 10 34.70 0 1.75 30 60 28.70 0 0.20 16 30.30 0 2.45 30 65 23.80 10 0.35 121 26.20 0 3.40 10 70 19.10 10 0.55 156 22.30 0 4.50 10 75 14.50 2 1.05 558 18.70 0 5.90 10 80 10.30 64 1.80 4,027 15.40 0 7.60 0 85 6.60 465 3.20 297 12.50 0 9.70 2 90 3.70 923 5.30 2,075 9.90 0 12.10 11 95 1.80 2,959 8.40 740 7.60 24 14.80 0 100 0.75 236 12.40 0 5.80 7 18.00 43 105 0.30 660 16.90 50 4.50 2 21.50 0 110 0.15 404 21.80 30 3.10 73 25.30 0 115 0.10 6 26.70 5 2.10 0 29.40 0 120 0.10 0 31.70 0 1.45 0 33.70 0 125 0.05 0 36.80 0 0.95 0 38.20 0 130 0.05 0 41.80 0 0.60 158 42.90 0

The Calls tab of the Ch13Stocks. xls spreadsheet lets you create tables such as Table 13.4. In the spreadsheet, Nr of Days is the number of days remaining before the option expires when you buy the option. In Table 13.4, I rounded 90 days to four times a year. The spreadsheet actually divides the number of days by 365, so the results look a bit different from the table results.

Option trading can get much more involved than simply buying calls. Let’s look at some other option-trading opportunities.

You can sell calls. This means that you sell somebody a contract to buy a number of shares of a certain stock from you at a specified price and before a specified date—if he or she wants to. The call seller is the other party in the call-buying example above. When you sell a call, you receive a fixed amount of money. This money is yours to keep, whether or not the option is exercised. If the stock never gets above the strike price or the buyer never exercises the option for whatever reason, you walk away with this money. If the stock price goes up and the buyer exercises the option, you have to deliver the stock.

The potential risks and opportunities of buying and selling calls mirror each other. When you buy a call, you can never lose more than the price you paid for the call, but you can lose it all. If the stock price goes up enough, you get tremendous “leverage” and can make a lot of money. When you sell a call, you can never earn more than the price you received for the call. If the stock price goes up enough, your buyer can make a lot of money, which comes out of your pocket.

You can sell covered calls. Suppose you have some shares of Widgetarama that you bought a while ago. It’s selling for \$25 a share today; whether this is more or less than you paid doesn’t matter right now. You sell somebody an option to buy these shares at a strike price of \$27 for \$5. If the option expires, that is, it is never exercised, you just earned \$5. If the stock price goes up above \$27, the option will get exercised and you must hand over your stock.

If the stock price never climbs above \$27 before the option expires, you got your \$5 for selling the option and you still own your stock. Even if the stock price falls below \$5, you haven’t lost money because of the \$5 you were paid for the option. With a covered call, the stock price can go down by the amount you sold the call and you still make money (by selling the stock). If the stock price goes down even further, you will lose some money, but only the difference between the change in stock price and the amount you sold the call for. If the stock price goes up to the level where the option is exercised and you have to deliver the stock, you’ve still made money. What you’ve given up is the opportunity to make even more money because you’re delivering the stock at a fixed price regardless of the market price of the stock.

You can buy and/or sell puts. A put is similar to a call except that with a put, you’re buying or selling somebody the right to sell you a stock at a specified price.

By cleverly buying puts and calls at different strike prices, you can arrange things so that you make money if the stock either goes up or goes down by at least a certain amount.

Notice that there is no entry in the spreadsheet for the price of the stock when you buy an option. That’s because this price doesn’t affect any of the ensuing cal­culations. This does not mean, however, that this price is not an important number in your purchasing decision.

Table 13.4 is excerpted from the puts and calls listing for IBM stock on March 19, 2009 at midday. Notice how busy this table is—there are a lot of choices that can be made here. In Table 13.4. I’m only showing the April and October (2009) listings. The stock price at the time these listings were generated was 88.39.

First, look at the put and call asking prices for either the April or the October options. Note that the call price goes down as the strike price goes up, whereas the put price goes up as the strike price goes up. This is because the direction that the stock has to move for the option buyer to make money is opposite for puts and for calls.

Next, look at the volumes column. For both puts and calls in the April options, the curves are more or less “bell curves.” Since these listings are from March 11, 2009, option buyers are developing pretty strong opinions about where they believe this stock will be selling at the end of April. In the October listings, however, the volume is fairly low and prices are all over the place. On March 11, the overall stock market is very volatile and people aren’t sure about the future of the recession; they

 Figure 13.9 Profits and losses from the IBM option example.

are being conservative and there is no consensus about the stock market 7 months from now.

Figure 13.9 shows the trade-off between risk and potential reward, specifically what the future holds for the April \$85, \$95, and \$105 IBM calls strike prices as a function of what the stock price is when the option is exercised (and the stock is sold). If you buy the \$85 strike price option, you can lose as much as \$6.60 (your option purchase price) if the stock price goes down enough. If you buy the \$105 option, you can lose as much as \$0.30, a far lower risk than losing \$6.60. On the other hand, if the stock price goes up, you start making money sooner with the \$85 option, and at all times (when you’re making money), you make more money than you do with the \$105 option.

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