211 lines
26 KiB
Plaintext
211 lines
26 KiB
Plaintext
CHAPTER 8
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Dividends and Option Pricing
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Much of this book studies how to break down and trade certain components of option prices. This chapter examines the role of dividends in the pricing structure. There is no greek symbol that measures an option’s sensitivity to changes in the dividend. And in most cases, dividends are not “traded” by means of options in the same way that volatility, interest, and other option price influences are. Dividends do, though, affect option prices, and therefore a trader’s P&(L), so they deserve attention.
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There are some instances where dividends provide ample opportunity to the option trader, and there some instances where a change in dividend policy can have desirable, or undesirable, effects on the bottom line. Despite the fact that dividends do not technically involve greeks, they need to be monitored in much the same way as do delta, gamma, theta, vega, and rho.
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Dividend Basics
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Let’s start at the beginning. When a company decides to pay a dividend, there are four important dates the trader must be aware of:
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1. Declaration date
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2. Ex-dividend date
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3. Record date
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4. Payable date
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The first date chronologically is the declaration date. This date is when the company formally declares the dividend. It’s when the company lets its shareholders know when and in what amount it will pay the dividend. Active traders, however, may buy and sell the same stock over and over again. How does the corporation know exactly who collects the dividend when it is opening up its coffers?
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Dividends are paid to shareholders of record who are on the company’s books as owning the stock at the opening of business on another important date: the record date. Anyone long the stock at this moment is entitled to the dividend. Anyone with a short stock position on the opening bell on the record date is required to make payment in the amount of the dividend. Because the process of stock settlement takes time, the important date is actually not the record date. For all intents and purposes, the key date is two days before the record date. This is called the ex-dividend date, or the ex-date.
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Traders who have earned a dividend by holding a stock in their account on the morning of the ex-date have one more important date they need to know—the date they get paid. The date that the dividend is actually paid is called the payable date. The payable date can be a few weeks after the ex-date.
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Let’s walk through an example. ABC Corporation announces on March 21 (the declaration date) that it will pay a 25-cent dividend to shareholders of record on April 3 (the record date), payable on April 23 (the payable date). This means market participants wishing to receive the dividend must own the stock on the open on April 1 (the ex-date). In practice, they must buy the stock before the closing bell rings on March 31 in order to have it for the open the next day.
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This presents a potential quandary. If a trader only needs to have the stock on the open on the ex-date, why not buy the stock just before the close on the day before the ex-date, in this case March 31, and sell it the next morning after the open? Could this be an opportunity for riskless profit?
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Unfortunately, no. There are a couple of problems with that strategy. First, as far as the riskless part is concerned, stock prices can and often do change overnight. Yesterday’s close and today’s open can sometimes be significantly different. When they are, it is referred to as a gap open. Whenever a stock is held (long or short), there is risk. The second problem with this strategy to earn riskless profit is with the profit part. On the ex-date, the opening stock price reflects the dividend. Say ABC is trading at $50 at the close on March 31. If the market for the stock opens unchanged the next morning—that is, a zero net change on the day on—ABC will be trading at $49.75 ($50 minus the $0.25 dividend). Alas, the quest for riskless profit continues.
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Dividends and Option Pricing
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The preceding discussion demonstrated how dividends affect stock traders. There’s one problem: we’re option traders! Option holders or writers do not receive or pay dividends, but that doesn’t mean dividends aren’t relevant to the pricing of these securities. Observe the behavior of a conversion or a reversal before and after an ex-dividend date. Assuming the stock opens unchanged on the ex-date, the relationship of the price of the synthetic stock to the actual stock price will change. Let’s look at an example to explore why.
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At the close on the day before the ex-date of a stock paying a $0.25 dividend, a trader has an at-the-money (ATM) conversion. The stock is trading right at $50 per share. The 50 puts are worth 2.34, and the 50 calls are worth 2.48. Before the ex-date, the trader is
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Long 100 shares at $50
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Long one 50 put at 2.34
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Short one 50 call at 2.48
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Here, the trader is long the stock at $50 and short stock synthetically at $50.14—50 + (2.48 − 2.34). The trader is synthetically short $0.14 over the price at which he is long the stock.
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Assume that the next morning the stock opens unchanged. Since this is the ex-date, that means the stock opens at $49.75—$0.25 lower than the previous day’s close. The theoretical values of the options will change very little. The options will be something like 2.32 for the put and 2.46 for the call.
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After the ex-date, the trader is
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Long 100 shares at $49.75
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Long one 50 put at 2.32
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Short one 50 call at 2.46
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Each option is two cents lower. Why? The change in the option prices is due to theta. In this case, it’s $0.02 for each option. The synthetic stock is still short from an effective price of $50.14. With the stock at $49.75, the synthetic short price is now $0.39 over the stock. Incidentally, $0.39 is $0.25 more than the $0.14 difference before the ex-date.
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Did the trader who held the conversion overnight from before the ex-date to after it make or lose money? Neither. Before the ex-date, he had an asset worth $50 per share (the stock) and he shorted the asset synthetically at $50.14. After the ex-date, he still has assets totaling $50 per share—the stock at $49.75 plus the 0.25 dividend—and he is still synthetically short the stock at $50.14. Before the ex-date, the $0.14 difference between the synthetic and the stock is interest minus the dividend. After the ex-date, the $0.39 difference is all interest.
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Dividends and Early Exercise
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As the ex-date approaches, in-the-money (ITM) calls on equity options can often be found trading at parity, regardless of the dividend amount and regardless of how far off expiration is. This seems counterintuitive. What about interest? What about dividends? Normally, these come into play in option valuation.
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But option models designed for American options take the possibility of early exercise into account. It is possible to exercise American-style calls and exchange them for the underlying stock. This would give traders, now stockholders, the right to the dividend—a right for which they would not be eligible as call holders. Because of the impending dividend, the call becomes an exercise just before the ex-date. For this reason, the call can trade for parity before the ex-date.
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Let’s look at an example of a reversal on a $70 stock that pays a $0.40 dividend. The options in this reversal have 24 days until expiration, which makes the interest on the 60 strike roughly $0.20, given a 5 percent interest rate. The day before the ex-date, a trader has the following position at the stated prices:
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Short 100 shares at $70
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Long one 60 call at 10.00
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Short one 60 put at 0.05
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To understand how American calls work just before the ex-date, it is helpful first to consider what happens if the trader holds the position until the ex-date. Making the assumption that the stock is unchanged on the ex-dividend date, it will open at $69.60, lower by the amount of the dividend—in this case, $0.40. The put, being so far out-of-the-money (OTM) as to have a negligible delta, will remain unchanged. But what about the call? With no dividend left in the stock, the put call-parity states
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In this case,
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Before the ex-date, the model valued the call at parity. Now it values the same call at $0.25 over parity (9.85 − [69.60 − 60]). Another way to look at this is that the time value of the call is now made up of the interest plus the put premium. Either way, that’s a gain of $0.25 on the call. That sounds good, but because the trader is short stock, if he hasn’t exercised, he will owe the $0.40 dividend—a net loss of $0.15. The new position will be
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Short 100 shares at $69.60
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Owe $0.40 dividend
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Long one 60 call at 9.85
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Short one 60 put at 0.05
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At the end of the trading day before the ex-date, this trader must exercise the call to capture the dividend. By doing so, he closes two legs of the trade—the call and the stock. The $10 call premium is forfeited, the stock that is short at $70 is bought at $60 (from the call exercise) for a $10 profit. The transaction leads to neither a profit nor a loss. The purpose of exercising is to avoid the $0.15 loss ($0.25 gain in call time value minus the $0.40 loss in dividends owed).
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The other way the trader could achieve the same ends is to sell the long call and buy in the short stock. This is tactically undesirable because the trader may have to sell the bid in the call and buy the offer in the stock. Furthermore, when legging a trade in this manner, there is the risk of slippage. If the call is sold first, the stock can move before the trader has a chance to buy it at the necessary price. It is generally better and less risky to exercise the call rather than leg out of the trade.
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In this transaction, the trader begins with a fairly flat position (short stock/long synthetic stock) and ends with a short put that is significantly out-of-the-money. For all intents and purposes, exercising the call in this trade is like synthetically selling the put. But at what price? In this case, it’s $0.15. This again is the cost benefit of saving $0.40 by avoiding the dividend obligation versus the $0.25 gain in call time value. Exercising the call is effectively like selling the put at 0.15 in this example. If the dividend is lower or the interest is higher, it may not be worth it to the trader to exercise the call to capture the dividend. How do traders know if their calls should be exercised?
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The traders must do the math before each ex-dividend date in option classes they trade. The traders have to determine if the benefit from exercising—or the price at which the synthetic put is essentially being sold—is more or less than the price at which they can sell the put. The math used here is adopted from put-call parity:
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This shows the case where the traders can effectively synthetically sell the put (by exercising) for more than the current put value. Tactically, it’s appropriate to use the bid price for the put in this calculation since that is the price at which the put can be sold.
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In this case, the traders would be inclined to not exercise. It would be theoretically more beneficial to sell the put if the trader is so inclined.
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Here, the traders, from a valuation perspective, are indifferent as to whether or not to exercise. The question then is simply: do they want to sell the put at this price?
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Professionals and big retail traders who are long (ITM) calls—whether as part of a reversal, part of another type of spread, or because they are long the calls outright—must do this math the day before each ex-dividend date to maximize profits and minimize losses. Not exercising, or forgetting to exercise, can be a costly mistake. Traders who are short ITM dividend-paying calls, however, can reap the benefits of those sleeping on the job. It works both ways.
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Traders who are long stock and short calls at parity before the ex-date may stand to benefit if some of the calls do not get assigned. Any shares of long stock remaining on the ex-date will result in the traders receiving dividends. If the dividends that will be received are greater in value than the interest that will subsequently be paid on the long stock, the traders may stand reap an arbitrage profit because of long call holders’ forgetting to exercise.
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Dividend Plays
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The day before an ex-dividend date in a stock, option volume can be unusually high. Tens of thousands of contracts sometimes trade in names that usually have average daily volumes of only a couple thousand. This spike in volume often has nothing to do with the market’s opinion on direction after the dividend. The heavy trading has to do with the revaluation of the relationship of exercisable options to the underlying expected to occur on the ex-dividend date.
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Traders that are long ITM calls and short ITM calls at another strike just before an ex-dividend date have a potential liability and a potential benefit. The potential liability is that they can forget to exercise. This is a liability over which the traders have complete control. The potential benefit is that some of the short calls may not get assigned. If traders on the other side of the short calls (the longs) forget to exercise, the traders that are short the call make out by not having to pay the dividend on short stock.
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Professionals and big retail traders who have very low transaction costs will sometimes trade ITM call spreads during the afternoon before an ex-dividend date. This consists of buying one call and selling another call with a different strike price. Both calls in the dividend-play strategy are ITM and have corresponding puts with little or no value (to be sure, the put value is less than the dividend minus the interest). The traders trade the spreads, fairly indifferent as to whether they buy or sell the spreads, in hope of skating—or not getting assigned—on some of their short calls. The more they don’t get assigned the better.
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This usually occurs in options that have high open interest, meaning there are a lot of outstanding contracts already. The more contracts in existence, the better the possibility of someone forgetting to exercise. The greatest volume also tends to occur in the front month.
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Strange Deltas
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Because American calls become an exercise possibility when the ex-date is imminent, the deltas can sometimes look odd. When the calls are trading at parity, they have a 1.00 delta. They are a substitute for the stock. They, in fact, will be stock if and when they are exercised just before the ex-date. But if the puts still have some residual time value, they may also have a small delta, of 0.05 or perhaps more.
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In this unique scenario, the delta of the synthetic can be greater than +1.00 or less than −1.00. It is not uncommon to see the absolute values of the call and put deltas add up to 1.07 or 1.08. When the dividend comes out of the options model on the ex-date, synthetics go back to normal. The delta of the synthetic again approaches 1.00. Because of the out-of-whack deltas, delta-neutral traders need to take extra caution in their analytics when ex-dates are near. A little common sense should override what the computer spits out.
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Inputting Dividend Data into the Pricing Model
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Often dividend payments are regular and predictable. With many companies, the dividend remains constant quarter after quarter. Some corporations have a track record of incrementally increasing their dividends every year. Some companies pay dividends in a very irregular fashion, by paying special dividends that are often announced as a surprise to investors. In a truly capitalist society, there are no restrictions and no rules on when, whether, or how corporations pay dividends to their shareholders. Unpredictability of dividends, though, can create problems in options valuation.
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When a company has a constant, reasonably predictable dividend, there is not a lot of guesswork. Take Exelon Corp. (EXC). From November 2008 to the time of this writing, Exelon has paid a regular quarterly dividend of $0.525. During that period, a trader has needed simply to enter 0.525 into the pricing calculator for all expected future dividends to generate the theoretical value. Based on recent past performance, the trader could feel confident that the computed analytics were reasonably accurate. If the trader believed the company would continue its current dividend policy, there would be little options-related dividend risk—unless things changed.
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When there is uncertainty about when future dividends will be paid in what amounts, the level of dividend-related risk begins to increase. The more uncertainty, the more risk. Let’s examine an interesting case study: General Electric (GE).
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For a long time, GE was a company that has had a history of increasing its dividends at fairly regular intervals. In fact, there was more than a 30-year stretch in which GE increased its dividend every year. During most of the first decade of the 2000s, increases in GE’s dividend payments were around one to six cents and tended to occur toward the end of December, after December expiration. The dividends were paid four times per year but not exactly quarterly. For several years, the ex-dates were in February, June, September, and December. Option traders trading GE options had a pretty easy time estimating their future dividend streams, and consequently evaded valuation problems that could result from using wrong dividend data. Traders would simply adjust the dividend data in the model to match their expectations for predictably increasing future dividends in order to achieve an accurate theoretical value. Let’s look back at GE to see how a trader might have done this.
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The following shows dividend-history data for GE.
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Ex-Date
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Dividend
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*
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12/27/02
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$0.19
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02/26/03
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$0.19
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06/26/03
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$0.19
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09/25/03
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$0.19
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12/29/03
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$0.20
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02/26/04
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$0.20
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06/24/04
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$0.20
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09/23/04
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$0.20
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12/22/04
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$0.22
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02/24/05
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$0.22
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06/23/05
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$0.22
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09/22/05
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$0.22
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12/22/05
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$0.25
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02/23/06
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$0.25
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06/22/06
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$0.25
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09/21/06
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$0.25
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12/21/06
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$0.28
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02/22/07
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$0.28
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06/21/07
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$0.28
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*
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These data are taken from the following Web page on GE’s web site:
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www.ge.com/investors/stock_info/dividend_history.html
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.
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At the end of 2006, GE raised its dividend from $0.25 to $0.28. A trader trading GE options at the beginning of 2007 would have logically anticipated the next increase to occur again in the following December unless there was reason to believe otherwise. Options expiring before this anticipated next dividend increase would have the $0.28 dividend priced into their values. Options expiring after December 2007 would have a higher dividend priced into them—possibly an additional three cents to 0.31 (which indeed it was). Calls would be adversely affected by this increase, and puts would be favorably affected. A typical trader would have anticipated those changes. The dividend data a trader pricing GE options would have entered into the model in January 2007 would have looked something like this.
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Ex-Date
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Dividend
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*
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02/22/07
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$0.28
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06/21/07
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$0.28
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09/20/07
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$0.28
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12/20/07
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$0.31
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02/21/08
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$0.31
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06/19/08
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$0.31
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09/18/08
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$0.31
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*
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These data are taken from the following Web page on GE’s web site:
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www.ge.com/investors/stock_info/dividend_history.html
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.
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The trader would have entered the anticipated future dividend amount in conjunction with the anticipated ex-dividend date. This trader projection goes out to February 2008, which would aid in valuing options expiring in 2007 as well as the 2008 LEAPS. Because the declaration dates had yet to occur, one could not know with certainty when the dividends would be announced or in what amount. Certainly, there would be some estimation involved for both the dates and the amount. But traders would probably get it pretty close—close enough.
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Then, something particularly interesting happened. Instead of raising the dividend going into December 2008 as would be a normal pattern, GE kept it the same. As shown, the 12/24/08 ex-dated dividend remained $0.31.
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Ex-Date
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Dividend
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*
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02/22/07
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$0.28
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06/21/07
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$0.28
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09/20/07
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$0.28
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12/20/07
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$0.31
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02/21/08
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$0.31
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06/19/08
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$0.31
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09/18/08
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$0.31
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12/24/08
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$0.31
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*
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These data are taken from the following Web page on GE’s web site:
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www.ge.com/investors/stock_info/dividend_history.html
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.
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The dividend stayed at $0.31 until the June 2009 dividend, which held another jolt for traders pricing options. Around this time, GE’s stock price had taken a beating. It fell from around $42 a share in the fall of 2007 ultimately to about $6 in March 2009. GE had its first dividend cut in more than three decades. The dividend with the ex-date of 06/18/09 was $0.10.
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12/24/08
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$0.31
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02/19/09
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$0.31
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06/18/09
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$0.10
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09/17/09
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$0.10
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12/23/09
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$0.10
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02/25/10
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$0.10
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06/17/10
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$0.10
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09/16/10
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$0.12
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12/22/10
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$0.14
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02/24/11
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$0.14
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06/16/11
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$0.15
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09/15/11
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$0.15
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Though the company gave warnings in advance, the drastic dividend change had a significant impact on option prices. Call prices were helped by the dividend cut (or anticipated dividend cut) and put prices were hurt.
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The break in the pattern didn’t stop there. The dividend policy remained $0.10 for five quarters until it rose to $0.12 in September 2010, then to $0.14 in December 2010, then to $0.15 in June 2011. These irregular changes in the historically predictable dividend policy made it tougher for traders to attain accurate valuations. If the incremental changes were bigger, the problem would have been even greater.
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Good and Bad Dates with Models
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Using an incorrect date for the ex-date in option pricing can lead to unfavorable results. If the ex-dividend date is not known because it has yet to be declared, it must be estimated and adjusted as need be after it is formally announced. Traders note past dividend history and estimate the expected dividend stream accordingly. Once the dividend is declared, the ex-date is known and can be entered properly into the pricing model. Not executing due diligence to find correct known ex-dates can lead to trouble. Using a bad date in the model can yield dubious theoretical values that can be misleading or worse—especially around the expiration.
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Say a call is trading at 2.30 the day before the ex-date of a $0.25 dividend, which happens to be thirty days before expiration. The next day, of course, the stock may have moved higher or lower. Assume for illustrative purposes, to compare apples to apples as it were, that the stock is trading at the same price—in this case, $76.
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If the trader is using the correct date in the model, the option value will adjust to take into account the effect of the dividend expiring, or reaching its ex-date, when the number of days to expiration left changes from 30 to 29. The call trading postdividend will be worth more relative to the same stock price. If the dividend date the trader is using in the model is wrong, say one day later than it should be, the dividend will still be an input of the theoretical value. The calculated value will be too low. It will be wrong.
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Exhibit 8.1
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compares the values of a 30-day call on the ex-date given the right and the wrong dividend.
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EXHIBIT 8.1
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Comparison of 30-day call values
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At the same stock price of $76 per share, the call is worth $0.13 more after the dividend is taken out of the valuation. Barring any changes in implied volatility (IV) or the interest rate, the market prices of the options should reflect this change. A trader using an ex-date in the model that is farther in the future than the actual ex-date will still have the dividend as part of the generated theoretical value. With the ex-date just one day later, the call would be worth 2.27. The difference in option value is due to the effect of theta—in this case, $0.03.
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With a bad date, the value of 2.27 would likely be significantly below market price, causing the market value of the option to look more expensive than it actually is. If the trader did not know the date was wrong, he would need to raise IV to make the theoretical value match the market. This option has a vega of 0.08, which translates into a difference of about two IV points for the theoretical values 2.43 and 2.27. The trader would perceive the call to be trading at an IV two points higher than the market indicates.
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Dividend Size
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It’s not just the date but also the size of the dividend that matters. When companies change the amount of the dividend, options prices follow in step. In 2004, when Microsoft (MSFT) paid a special dividend of $3 per share, there were unexpected winners and losers in the Microsoft options. Traders who were long calls or short puts were adversely affected by this change in dividend policy. Traders with short calls or long puts benefited. With long-term options, even less anomalous changes in the size of the dividend can have dramatic effects on options values.
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Let’s study an example of how an unexpected rise in the quarterly dividend of a stock affects a long call position. Extremely Yellow Zebra Corp. (XYZ) has been paying a quarterly dividend of $0.10. After a steady rise in stock price to $61 per share, XYZ declares a dividend payment of $0.50. It is expected that the company will continue to pay $0.50 per quarter. A trader, James, owns the 528-day 60-strike calls, which were trading at 9.80 before the dividend increase was announced.
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Exhibit 8.2
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compares the values of the long-term call using a $0.10 quarterly dividend and using a $0.50 quarterly dividend.
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EXHIBIT 8.2
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Effect of change in quarterly dividend on call value.
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This $0.40 dividend increase will have a big effect on James’s calls. With 528 days until expiration, there will be six dividends involved. Because James is long the calls, he loses 1.52 per option. If, however, he were short the calls, 1.52 would be his profit on each option.
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Put traders are affected as well. Another trader, Marty, is long the 60-strike XYZ puts. Before the dividend announcement, Marty was running his values with a $0.10 dividend, giving his puts a value of 5.42.
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Exhibit 8.3
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compares the values of the puts with a $0.10 quarterly dividend and with a $0.50 quarterly dividend.
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EXHIBIT 8.3
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Effect of change in quarterly dividend on put value.
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When the dividend increase is announced, Marty will benefit. His puts will rise because of the higher dividend by $0.66 (all other parameters held constant). His long-term puts with six quarters of future expected dividends will benefit more than short-term XYZ puts of the same strike would. Of course, if he were short the puts, he would lose this amount.
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The dividend inputs to a pricing model are best guesses until the dates and amounts are announced by the company. How does one find dividend information? Regularly monitoring the news and press releases on the companies one trades is a good way to stay up to date on dividend information, as well as other company news. Dividend announcements are widely disseminated by the major news services. Most companies also have an investor-relations phone number and section on their web sites where dividend information can be found. |