In the last two articles I discussed Delta and Gamma, which measure change to an option’s price resulting from a change in the price of the underlying. As listed earlier, the other Greeks measure the option price change due to the passage of time (Theta), and due to changes in implied volatility (Vega). Rho, the littlest Greek, measures the effect of interest rate changes, and is only a minor player.
Delta, Gamma, Theta, Vega – how can we make use of these?
We can use them to estimate how effective a particular position will be at accomplishing what we want it to do. Let’s look at a popular strategy and see how each of the Greeks comes into play.
The first options strategy that many people are exposed to is the Covered Call. In this strategy, the investor (we’ll call him Al ) owns 100 shares of the QQQ ETF, which is currently at $63.80 per share. Al thinks QQQ will be pretty stagnant for a while, so he sells calls at the $65 strike price one month out. Those particular calls (the QQQ December 65 Calls) have these readings for the Greeks:
Delta: .33 Gamma: .14 Theta: -.02 Vega: .07
They are quoted at $.55 bid, $.56 ask. By selling them now, Al collects $55 for one call option contract ($.55 per share times 100 shares per contract). If, when the call expires, QQQ is at or below the strike price of $65, then the calls expire worthless. Al will then keep the stock and the option premium. If the stock is above the strike at expiration, the calls will be exercised by the call buyers. The stock will be “called away” from Al, who will then get paid $65 per share for it, whether the stock is at $65, $165 or $6500.
The reason the position is called a “covered” call is that Al’s obligation to deliver the stock, if need be, is covered, because he owns the stock. He can just give up stock he already owns, and will not have to buy it on the open market. If Al had sold the calls without owning the stock, then his obligation to deliver the stock would not be covered – his position would be uncovered, or naked. He might then end up having to buy the stock at a much higher price, taking a big loss.
A covered call position like this is used to generate income. That $55 in Al’s pocket represents a return of .86 of 1% ($55 divided by $6380) in 31 days, which is a 10% annualized rate of return ( .86 X 365 / 31 = 10.15). Not a world-shaking return for a trader, but pretty good for an investor. Especially considering that it happens with no movement by the stock. If there is movement upward, the return gets even better: if QQQ should happen to be at $65 when the call expires, then Al also has gotten $120 in appreciation (from $63.80 to $65.00) along with the $55 call premium. This is a total profit of $175 in a month on $6380, which is a 32% annualized rate of return. Note that this is the best that he can do. Even if the stock goes much higher, it won’t help Al. He has committed to selling it at $65 per share no matter how much higher it goes.
If instead of moving up, the price of QQQ moves down, Al is better off by the $55 call premium than he would have been had he not sold the call. In fact the only case where someone who owns the stock is not better off by selling calls, is when the stock moves up past the strike price, by more than the call premium. In that case, the stock owner would have been better off to get all the appreciation and keep the stock. That chance is what you take when you sell calls against a stock position.
Let’s look at those Greeks again for this case.
The Delta of .33 means that the calls are gaining value at the rate of 33 cents for the next dollar that QQQ ‘s price increases. Since Al is short the call, that is working against him, right? Instead of gaining a whole dollar if QQQ moves up by a dollar, he’s gaining a dollar per share on the stock and losing 33 cents on the call. That is true. He has sold something with a delta of .33, so he changed the delta of his position by minus .33 X 100 = -33. Combining that with the delta of his stock position of 100 shares at 1 delta per share, his delta is now 100 – 33 = 67.
But remember two things: 1) He already got paid $.55 per share and 2) The call is going to expire soon. Upon expiration, the price of all out-of-the-money calls is zero. This second point means that as long as the QQQ ends up at expiration at or below the $65 strike, the 65 call will be worthless at that time. It won’t matter what its price did in the meantime. This is a factor that we need to keep in mind in looking at any option position that includes options that are expected to expire worthless.
Separately, remember another one of the three interpretations of the delta – as the approximate probability that the option will expire in the money. In this case that’s .33 or 33%. Al has a two-out-of-three chance that the option will not expire in the money.
Let’s look at Gamma. Gamma measures the acceleration of the change in option price resulting from underlying price change. In this case its value is .14. That means that if QQQ moves by a dollar, the delta will change by .14 from its current value of .33. If QQQ moves up a dollar, delta becomes .33 + .14 = .47. So for second dollar increase, the option will increase in value by the new delta of .47. Likewise, if QQQ falls, the option’s delta will decrease to .33 – .14 = .19, and if it then falls by another dollar, the option’s price will drop by 19 cents (in addition to the 33 cents it dropped for the first dollar). As with Delta, in this case the effect of Gamma will become academic if the option expires out of the money.
That last sentence also applies to Vega. We are not going to have any option position when this one expires. There will be no time and no time value, so volatility, which can only affect time value, won’t matter. It is only a temporary factor during the life of the option.
The last Greek we’ll look at is Theta. This had a reading of -.02. This meant that the option was about to lose 2 cents of its value the very next day. That’s working for Al, since he was short the option. You could say that theta was what this position was all about. Al sold $.55 per share worth of time value, expecting the option to expire worthless. With every passing day, an increasing amount of that $.55 melts away, until there’s nothing left. As long as the option does expire worthless, all the movements measured by delta, gamma and vega will have been much sound and fury signifying nothing. In the end Al gets his $.55.
The fact that in the end delta, gamma and vega were not significant was only true here because the single option position expired. In most strategies, that is definitely not the case. Next time we’ll look at another one where all the greeks play a much bigger part.
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