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Frustration for Option Buyers
By Lawrence G. McMillan

This article was originally published in The Option Strategist Newsletter Volume 9, No. 9 on May 11, 2000. 

More than a few customers have mentioned a “problem” that is quite universal, I’m sure. The following comment pretty much summarizes the situation: “I get so frustrated buying an option and having the stock move $4 or more and the option doesn't hardly move at all.” In this article, we’ll take a look at why this is happening and give some suggestions as to what you might be able to do about it.

First of all, if one buys an option that is “too far” out-of-the-money, it’s not going to move much when the underlying stock moves. However, the problem cited above occurs with at-the-money options, too. The items that are relevant to understanding what is going on are 1) the delta of the option, 2) the width of the bid-asked spread of the option, and 3) the implied volatility of the option.

Simplistically, the delta of an option indicates how much the option will change in price if the underlying stock changes by one point. In reality, though, delta is related to all of the factors that affect an option’s price – stock price, implied volatility, time, etc. Hence a change in one or more of these other factors will affect the option’s delta, too. One cannot assume that the original delta will always give an accurate description of what will happen to the option’s price. The “problem” described at the beginning of this article is not going to be addressed solely by calculating delta alone. However, calculating the delta of an option is a good place to start in order to determine what will happen to it as the market evolves during the holding period of the option. An option calculator will show one what the theoretical delta is. Usually, with this information, one can piece together what is happening.

Also, the width of the bid-asked spread in the option is important too. If the bid-asked spread is very wide, then one will need the stock to move far enough to cover the bid-asked spread before he can even think about making money.

Example: with XYZ at 115, you quote the July 130 call and find the following market:

Bid: 8
Asked: 9

The spread between the bid and offer is a full point. Furthermore, suppose that your option calculator indicates that the delta of this call is 0.46 – about a half point.

This stock is going to have to rise 2-1/4 points before you are even. That is, if the stock rises by 2-1/4 points, and the delta of the option is truly 0.46, then the option should rise by about one full point on that move:
2.25 x 0.46 = 1.04

In real life, however, all this means is that the bid and offer will have risen about a full point. So the option would then be bid at about 9 – exactly what you paid for it.

Hence, the delta is useful in determining just how far the stock has to move before you can begin to make money.

Implied volatility is also important. If the options are “expensive” when you buy them, and then implied volatility declines while you own them, they will not go up in price as much as you thought, as the stock rises. In such a case, the rise in the price of the option would be less than delta had estimated it would be. Delta is related to time, volatility, and stock movement. So delta is not "gospel" nor is it static, but it is certainly better than flying blind.

An option calculator (ours included – which sells for $100) gives you the implied volatility, plus the other "greeks" so that you can estimate what would happen to an option and perhaps give you a better understanding of what's going on. We also have free implied volatility history on our web site, www.optionstrategist.com, so that you can get some perspective on whether the implied volatility of the option is either expensive or cheap.

You can anticipate how these things, taken together, might affect your option purchase. Your analysis should go something like this:

Example: once again, using the prices shown in the previous example: XYZ stock is at 115. You are considering the purchase of an XYZ June 130 call for 9.
Our calculator (or whatever calculator you’re using) shows you the following information about that call:

Delta: 0.46 (i.e., it will move less than a half point for each point that the stock moves)

Theta: 0.20 (i.e., the option will lose 20 cents per day – of the 9.00 current price – to time value. So this is not a big deal, at least not initially).

Vega: 0.16 (this is 16 cents – the amount by which the option price will change if implied volatility changes. The call price will fall if implied volatility decreases. It may not seem like much, but this is VERY important, especially if the option is “expensive”).

Implied Volatility: 95%. (I would use the midpoint of the bid and asked – 8.50 – in determining implied volatility). On the surface you don't know whether that's expensive or not, but suppose you go to the free area on our web site and find that – at the most recent reading – the implied volatility of 95% is in the 90th percentile of implied volatility. The 90th percentile is very expensive. So now you know that if you buy this option, there's a chance that you're overpaying for volatility.

With this set of variables having been determined, you could experience something like this: suppose that within a day or two, the stock rises four points to 119, but the call you bought is only bid at 8-1/4! That is, even after the stock moved four points higher, you still have a loss! Quickly, you run the current figures through your option calculator and find that the current implied volatility is now 85% ( using the average of the bid and asked, 8.75, as the option price upon which the implied volatility is based).

What happened? Well, the stock went up four points, so the delta of 0.46 indicates that the option should have risen 1.84 points (4 x 0.46 = 1.84) when that happened. However, the now-current implied volatility has fallen to 85%. (i.e., after the stock moved up, the options got cheaper, in general). Since implied volatility fell 10 points (from 95% to 85%), and since each one point drop in implied volatility costs you 16 cents, the 10-point drop costs you 1.60. Hence your option should have only gained a quarter of a point: the gain indicated by "delta" was offset by the loss indicated by the drop in implied volatility.

The following figures summarize the situation:

Gain due to delta: 4 x 0.46 = 1.84
Loss due to vega: –10 x 0.16 = –1.60
Estimated theoretical gain: 0.24 points (sum of above 2)
Bid-asked spread: –1.00 points
Estimated “real-world” loss: –0.76 (sum of above 2)

That is, we can estimate the “theoretical gain” by using delta and vega. However, that estimated theoretical gain (24 cents, in this case) must be reduced by the width of the bid-asked spread in order to estimate the gain we would expect to incur in the real world. In this case, 24 cents less one full point (the bid-asked spread) leaves us with an estimated “real-world” loss of 76 cents.

I doubt if an owner of this call would feel too good about this happening to him, but it shows you that you can figure out what happened if you use an option calculator. It’s always better to have knowledge than to just be guessing about things. The knowledge gained from this example should help this customer avoid the same disappointing results in the future.

How can you combat this? 1) don't buy options that have such historically high implied volatility; and 2) don't buy out-of-the-money options (an in-the-money option has a higher delta and less sensitivity to changes in implied volatility). Thus, if you had bought the June 110 call, say, and the same things happened (i.e., the stock rose four points while implied volatility fell by 10 points), you would probably still have had a small profit to show for your troubles.

Let’s see how an option calculator would estimate those values:

Example: As before, XYZ is trading at 115, but now one observes that the June 110 calls have the following market:
Bid: 15-3/4
Asked: 17-1/4

Note that this bid-asked spread is wider. That is typically the case for more expensive options. The average of the bid and asked, 16.50, is also a 95% implied volatility. So this option has the same volatility characteristics as the June 125 call in the previous examples. This option has a vega of 0.14; it is slightly less sensitive to changes in implied volatility than is the June 125 call. Finally, the delta of this call is 0.62 – indicating that it will track the stock price more closely than an out-of-the-money option would.

Assume that this call is bought for 17-1/4, and that the stock then experiences the same upward move as in the above example – it rises to 119. Furthermore, keeping the other assumption the same, suppose that implied volatility has fallen to 85%. In that case, the option would have a “mid-point” of about 18. That would mean it would probably be bid at 17-1/4 or perhaps 17-1/2. So, even though the initial bid-asked spread was wider than that of the June 125 call, this call buyer at least broke even when the stock rose 4 points. Again, one can use the greeks to help him estimate how much the option should have changed:

Gain due to delta: 4 x 0.62 = 2.48
Loss due to vega: –10 x 0.14 = –1.40
Estimated theoretical gain: 1.48 points (sum of above 2)
Bid-asked spread: –1.50 points
Estimated “real-world” loss: –0.02 (sum of above 2)

So even choosing the “proper” option doesn’t solve all problems. One must address how wide the bid-asked spread is. What caused the major problem with the calls in these examples is that implied volatility dropped rather sharply. That can often happen, and it is stark proof that buying overpriced options can cause problems. Does it mean that we can never buy overpriced options? Of course not, but one should be aware of what he is doing. If options that are in a high percentile of implied volatility are purchased, one must realize that his option purchase could underperform unless the options hold onto that high level of implied volatility.

In less extreme circumstances, similar problems occur for option buyers all the time. Perhaps it takes longer for the stock to move, so that theta begins to weigh against the call’s value as well. Then, even if implied volatility holds its levels, it might be difficult to make much money – even on what seems to be a sizeable move by the underlying stock.

In summary, it is important to use an option calculator before buying an option – so that one can observe the option’s delta, as well as its sensitivity to changes in implied volatility and to time decay. Furthermore, if need be, a “what-if” analysis should be run as well, to allow the buyer to see what to expect for various stock moves over various time periods. Armed with this information, it is still not certain that an option buyer will be profitable, but he will certainly have a good idea of how he expects his option to behave under various circumstances. Thus, knowledge is power, even if it isn’t always profit.

This article was originally published in The Option Strategist Newsletter Volume 9, No. 9 on May 11, 2000.