# Straddles and Strangles Part 1

This is essentially a re-post of an entry from the (now dead) FactorWave blog. It is relevant again because it is the first part of what will be a series on strike and strategy selection.

One of the things that make options great is that there are many ways to express an opinion. But this is also one of the things that make options tricky. Just because there are many ways to express an opinion doesn't mean they will all be equally good. Some will be a lot worse than others.

As always, simulations help. I sold a one year ATM straddle at 40% implied volatility and then simulated 10,000 paths of the stock where the realized volatility was 30%. The drift and interest rates were both zero. Assuming that the initial stock price was $100, this position would have a margin call of $2,000. The distribution of returns (profit/margin) is shown in Figure One.

Figure One: The returns of the short straddle.

The dollar value of the straddle was $3,704. So the maximum return is 3,704/2,000=1.58. The fair value of the straddle (evaluated using a volatility of 30%) was $2,385, the the average return should have been (3,704-2,385)/2000=0.39. The simulation confirms both of these figures. But the results are also significantly negatively skewed (-1.8). The worst return was negative 5.3 and the worst decile was a loss of 0.63.

Now we run the same simulation for a short 90/110 strangle (corresponding to shorting the 32 delta put and the 48 delta call). This position has a margin requirement of $1,000.

Figure Two: The returns of the short strangle.

The dollar value of the strangle was $2,269. So the maximum return is 2,269/1,000=2.69. The fair value of the strangle (evaluated using a volatility of 30%) was $1,515, the the average return should have been (2,269-1,515)/1000=0.75. As before, the simulation confirms both of these figures. But the results are also more negatively skewed than for the straddle(-2.1). The worst return was negative 16.0 and the worst decile was a loss of 1.4. But even if you don't look at the numbers, a quick glance at the histograms tells us a lot. The strangle hits its maximum profit more often than the straddle (26% of the time versus essentially 0%), but, because the total premium we took in is lower than with the straddle, the losses can be much greater.

There are a lot of studies that show that selling options is a profitable trade. So when we enter short volatility positions we should focus on controlling our risk, because if we can keep plugging along the profits should eventually take care of themselves. So instead of just comparing the straddle and strangle in the case where we have been correct in our forecast (selling an implied volatility of 40% when realized volatility was 30%), we now look at the results where we are completely wrong. Specifically, realized volatility was 70% and there is also a 20% drift. The straddle returns for this scenario are shown in Figure Three.

Figure Three: The returns of the short straddle when our forecast was poor.

Now our average return was -1.59, but skew was - 3.0 and the worst result was -86.7. The worst decile was -5.1. Not a good result. But we were wrong so we can really expect great results.

But now look at the returns of the strangle in Figure Four.

Figure Four: The returns of the short strangle when our forecast was poor.

The average return was -3.0, and the skew was - 4.2 with the worst result as -141. The worst decile was -10. All of these were worse than the corresponding straddle returns.

So here is my initial conclusion. The straddle has a payoff that is less sensitive to either extreme moves or to making a poor forecast. It won't return as much as the strangle when things go well, nor will it practically ever make its theoretical maximum, but it also won't go as badly wrong as a strangle can. The straddle might appear to be the more risky position but it really isn't.

Finally lets look at where the strangle hides its most vicious risk. The strangle can seem less risky because we will generally start off far from both strikes, and so at a price where we are set to make the maximum return if we stay there until expiration. As humans, it is hard for us not to anchor to this price and see it as being a likely outcome for the expiration price. Further, we can fool ourselves even more by choosing to sell strikes that are a

*long way from the current price*and make the illusion of safety very powerful. Figure five shows the returns when we sell the 50/150 strangle.
Figure Five: The returns of the short 50/150 strangle when our forecast was poor.

Again, on average we lose money. Again this isn't surprising because our volatility forecast was poor. But what is interesting is that we make money 61% of the time. When we sold a straddle under this scenario we only made money 36% of the time. The strangle's win percentage is a very powerful piece of feedback that can trick us into doing trades like this even when they have negative expectation. This is what many people who sell options "for income" go wrong. There is no magic in selling strangles, even if they are struck a long way out of the money. If you don't have an edge in volatility you will lose eventually.

The straddle has a better correspondence between correctness of forecast and profits. Hence you will be far less likely to fool yourself into thinking you have a volatility edge than you would with a strangle.

(By the way, the same arguments would lead me to favor butterflies over condors)