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Oct

7

Options University’s Options 101 - Part 45

Filed Under Options 101 

Let’s take a look at a real example. Below are actual option quotes on September eBay calls with 32 days to expiration. The last trade on the stock is $79.21:
 
Strike
Bid
Ask
$70
9.90
10.10
$75
5.90
6.10
$80
2.90
3.00
 
If you were holding the $70 call and exercised early, you’d receive stock worth $79.21 by paying $70, which nets a gain of $9.21. However, if you just sold the call, you’d get the bid of $9.90, which is certainly better than $9.21 and it keeps you from holding the downside risk of the stock. If you were holding the $75 call, you’d gain $4.21 by exercising early but $5.90 by selling to close. As an extreme example, if you were holding the $80 call and exercised, you get stock worth $70.21 by paying $80, which leaves you in for a loss of 79 cents. Selling the $80 call to close, though, would bring in $2.90. It doesn’t matter how you cut it; it does not pay to exercise a call early. Early exercise only causes you to lose the time premium and take additional risk by holding the stock.
 
If that’s not enough to convince you, there is yet a third reason for not exercising a call early: You are giving up the time value of money. If you exercise 10 $50 calls that have three months remaining on them, you will pay $50,000 today in order to gain that stock. If, instead, you wait until expiration, you’ll hold on to that $50,000 for an additional three months on which you’ll earn interest. In either case, your purchase price does not change, so there is no rush to pay for it early.
 
 
Mathematical Examples
So far, we have covered three rationales for not exercising early:
1)      Increase your risk
2)      Discard the time value in the option
3)      Lose interest by paying for the stock early
 
While these are pragmatic arguments, there are some people who like to see the math behind the arguments. While mathematical proofs are convincing, they are often difficult to follow. But for those who are mathematically inclined, we’ll show you a mathematical proof for not exercising early.
 
Start by considering two traders. One holds the stock while the other holds a call option plus some cash. How much cash does he hold? He holds just enough so that, after the interest has been paid on that cash balance, he will have exactly the amount of the strike price. For example, if interest rates are 5% and the trader is holding a one-year $50 call, then he would need to hold $47.62 in cash. In one year, he will have $47.62 + 5% interest = $50 in cash. He could then take this $50 and buy the stock by exercising his call option. This amount of cash is the present value of the $50 strike. While the trader must pay $50 to exercise the call in the future, that payment is worth only $47.62 today if interest rates are five percent. If, instead, he were holding a three month, $50 call he would need $49.38 in cash since that amount would grow to $50 in three months at five percent interest. The two important points to understand are:
 
1) The cash held by the trader will always equal the exercise price at expiration.
2) The amount of cash necessary to hold is always less than the exercise price.
 
Keeping these points in mind, the two portfolios are as follows:
 
Trader #1: Stock
Trader #2: Call option + present value of the exercise price in cash
 
Now, at expiration, the value of the first trader’s position is always the value of the stock, which we can write as Trader #1 = S. No matter what happens to the stock’s price, Trader #1 is always worth S at expiration.
 
What about Trader #2? At expiration, this trader will be holding a call option plus cash that has grown to the exercise price, or +E. This trader has a choice. If the stock’s price happens to be above the strike price, then the second trader will exercise the call and will pay the exercise price, -E. His portfolio with then be worth S – E + E = S. In other words, no matter how high the stock’s price might be trading, Trader #2 can always gain the stock by simply paying the exercise price. That is, Trader #2 can always match the performance of Trader #1 for high stock prices.
 
However, prior to expiration, Trader #2 has cash that is worth Pv (E). This means that if he exercises early, his portfolio is worth (S-E) + Pv (E), which is less than S. (Remember, the Pv (E) is less than E so S-E + Pv (E) must result in a number less than S.) So if the second trader exercises early, he underperforms Trader #1. This means the second trader is better off not exercising until expiration.
 
Also notice what happens to the second trader by keeping the present value of the cash as long as possible. If the stock should fall below the strike, the second trader loses the value of the call but always has the cash. In the worst case, the stock could become nearly worthless, but the second trader will always walk away with the full exercise price in cash. We can’t say the same for the first trader. He will have lost everything.
 
We could also view the early exercise error in another light. Let’s say the second trader exercises early and does not have the cash in the account. He would need to borrow the exercise price and will owe the future value of the exercise price (E + interest). He buys the stock on borrowed funds, which means his portfolio is immediately worth S – future value of E after the exercise. However, this value is always less than the value of the call, since an in-the-money call must be worth at least S – E at any time. Remember, the future value of E is a bigger number than just E. Therefore S – future value of E must be a smaller value than S – E. Our goal is to make our positions worth more money, not less. By exercising early, the trader decreases the value of the call.
 
Hopefully you’re convinced that it is not to your advantage to exercise a call early. But it is still one of the biggest mistakes in option trading. While working for an active trading team for a large firm, I received a call from a client who had an account value of $124,000 at the close of trading and $120,000 the very next morning. All of his stocks were basically unchanged and certainly not down enough to create a $4,000 shortfall. He wondered what happened to the money. I found out that he exercised 10 call options the day before. When I looked up the previous day’s quotes, I found those options had four points of time premium in them. By exercising the 10 calls early, he literally threw away the $4,000. There is no way to get that money back. It’s gone for good.
 
 
Exercising a Call to Collect a Dividend
The previous section showed that exercising a call option early for the sole reason of gaining the stock is never to your advantage. However, exercising a call to collect a dividend is a viable strategy despite the fact that it is designed to offset a loss and not for a financial gain. To understand why, consider a simple example where the option is trading at parity (intrinsic value). Assume that the stock is trading for $50 and pays a $1 dividend. You own a $40 call that is trading at parity for $10. The day the dividend is paid, the stock price drops to $49 and the call option immediately becomes worth the $9 intrinsic value, which causes a $1 loss in value for you.
 
If you exercise the call, you will receive stock worth $50 and pay $40, so you will gain $10 of unrealized value. When the dividend is paid, your stock position becomes worth $49 but you also collect the $1 dividend, which still provides $10 of value for you ($9 unrealized plus a $1 dividend). So if you do not exercise your option, your value falls from $10 to $9. If you exercise the option, you maintain the $10 value. If you wish to collect a dividend to offset a loss, then only do it if the value of the dividend exceeds the time value of the call you are sacrificing.
 
Despite the advantage of collecting a dividend, you must consider whether offsetting a small loss is worth holding the downside risk of the stock.
 
 
Do not exercise a call option early except to capture a dividend. Even in this case, be sure the size of the dividend is worth letting go of your downside protection!
 
 

To be continued……

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