# Greeks Coming and Going

Last week we looked at the Greeks related to a covered call position. Theta was the star of that show, and if all went according to plan, the rest wouldn’t matter. “According to plan” meant that the underlying would move up or go sideways, but would not be above the call strike price at expiration.

Let’s look at another case, where all the Greeks play much more significant roles. This time we’ll consider a straddle, which is a long put and a long call at the same strike price, usually the at-the-money strike. This is a position we might think about if we believed that a stock was going to move a lot, but we had no opinion as to which way that movement would be. This might be our price outlook, for example, if the release of earnings was expected. Some stocks frequently provide earnings “surprises” that move the stock one way or the other. Another case might be an expected announcement about drug trial results for a biotech company.

Would the straddle be a good idea? The answer, as always in options or any other kind of trading is – it depends.

We need the trade to pay us back more than we pay for it. At first glance, we might think that a straddle would be a waste of time. Since call prices move in the same direction as the underlying, and put prices move in the opposite direction, do the two just cancel each other out? Is a straddle similar to betting on both black and red on the roulette wheel?

Not exactly. Imagine that we make two $10 bets on our imaginary roulette wheel, and that each could lose only our $10, but might win any amount. We’d be risking a total of $20, but we might get back $22, or $220, or $2200. That sounds more interesting, and worth looking into further.

In some ways, this is similar to our straddle, if we paid $10 each for the put and the call. If the stock price moves up a great deal, the call will make money; in fact a theoretically unlimited amount. The put would lose money in that case, but it can only cost us at most the $10 we paid for it. Same thing in reverse if the stock moves down (almost – the stock can’t go below zero, so our put’s profit is not completely unlimited). If either option makes enough money to pay back more than our whole $20 investment, then we’ll make money. If we held both options until expiration, then the stock would have to move at least $20, either way.

Is there any chance of making money with a move of less than $20? Yes, there is, if it happens soon enough.

As I’m writing this, the stock of Amazon has January ATM options with values near $10 each. With the stock at $243.77, the Greeks for the nearest option strike, the $245, have these values:

Call – Delta +.50 Gamma .02 Theta -.10 Vega .37 IV 27% Option Price $ 9.20

Put – Delta -.50 Gamma .02 Theta -.09 Vega .37 IV 27% Option Price $10.75

Total- Delta 0 Gamma .04 Theta -.19 Vega .74 IV 27% Option Price $19.95

First, think about Delta and Gamma. Both our put and our call are nearly at the money, with Deltas at plus/minus .50. If the underlying price moved up by $1, then the call’s value would increase by $.50, and the put’s would decrease by $.50. No help so far. But remember that as the underlying price changes, the Deltas of both options change. Gamma measures how much. The gamma of the put and the call at the same strike will always be the same positive number.

After that first upward $1 move, the Delta of the call is now +.50 (the original Delta) plus .02 (the Gamma), for a new value of +.52. Meanwhile, the put’s Delta has changed to -.50 plus .02, for a new Delta value of -.48. So for the *second* $1 move up, the call will gain $.52 while the put will lose only $.48. Now we’re getting somewhere. If the price continues to move up, the call’s Delta gets to be a larger and larger positive number, so every additional dollar move up makes more money than the one before. Meanwhile, the put’s Delta gets to be less and less negative, so that it loses less and less with each additional upward move.

Excellent! The winning side wins faster and faster, while the losing side loses more and more slowly. This is also true, in reverse, for a downward move. The put wins faster and faster while the call loses more and more slowly. Now it looks like this trade is a sure winner. If price movement in either direction makes it a win, how can it lose?

Two ways. First, while we’re waiting for price to move, both options are losing money due to the passage of time. Theta measures this. With a Theta value of -.10, the call is losing $.10 per day (per share). The put, with a Theta of -.09, is losing $.09 per day. Not only that, Theta gets to be a larger negative number as time passes. This week it’s losing us a total of $.19 per day out of our $20. Next week it will cost more than that, maybe $.25 per day. Eventually, both options will lose all of their time value. If the price of AMZN is at $245 at expiration, both options will expire worthless, losing the whole $20. It’s literally a race against time. Price movement (either way) helps us, *if it happens*. Time’s passing hurts us, and there is no “if” about it.

Secondly, look at Vega. It measures how much each option’s price will change if implied volatility changes. Each option starts with a Vega of .37. If implied volatility increases by one percentage point, (from 27% to 28%, each option will gain 37 cents, so we make a total of $.74. If IV drops by a point, we lose $.74. In fact, a straddle is an example of a trade that we might use strictly to take advantage of an expected big increase in Implied Volatility. In that case, we might buy the straddle if IV was exceptionally low, in hopes that IV would increase (go back toward its normal range) before too much time decay offset it. In fact, straddles are likely to work only if IV gives us a big helping hand. With two long ATM options, we are losing time value quickly. The race will likely be won only if IV moves up. In this case, AMZN’s IV has ranged from 22% to 58% over the last year. At a current value of 27%, it’s low but not ultra-low.

So, we would want to take this position only if we believe either that AMZN will move by more than $20 in the next 51 days ; or that IV will increase dramatically long before expiration, so that we can sell our options while they still have a large amount of time value. The $20 price move is not very likely. Even though the average monthly range is higher at $31, there is strong supply only about $10 above. The increase in IV is not a slam dunk either, since we’re not close enough to the bottom of the range on IV. In the end, it was worth a look, but we’ll have to pass. Does that mean the examination was a waste of time? Absolutely not. Avoiding bad trades is just as important as making good ones. Knowing the effects of the Greeks can help us to do just that.

For comments or questions on this article, you can contact me at rallen@tradingacademy.com.