The APR 83/85 short call spread went to a full loss on expiration Friday. The loss amounted to $1.45 on the 2-point spread because of the initial credit of $0.55 that was received on March 20, 2009.

When this trade was taken, there was 28 days to expiration. At the time, SPY was trading just under $77. It closed on expiration Friday just over $87. That’s over 12% in about a month. I won’t bother annualizing that rate of return. Unfortunately for this trade, that is a rally it didn’t expect. Using the traditional methods of calculating probability of success, there was a 77% chance that SPY would not hit my short strike of 83 in the last 28 days. The chance that it would exceed $87 stood at 9%. Hmmmm. This is enough to make one ponder the validity of probability of success as a statistical measure. Or maybe we’re just experiencing some very volatile times. Let’s investigate.

The VIX, which measures volatility in the S&P 500, would be the place to look for what happened to volatility during our 28 days. Remember, SPY is an ETF for the S&P 500, so VIX is valid measure of its volatility. VIX closed around $46 on March 20 and closed at around $34 on expiration Friday. That’s a decrease of over 26%. Nope, we cannot attribute this unusually large move to an environment of increase volatility.

We can let it go and attribute it to bad luck. After all, we limited the risk on this trade and knew going into it what the loss could amount to. We took a trade that had a high probability of success with an additional edge of positive theta (time decay).

At the heart of calculating the probability of success is a Gaussian distribution of price around a moving target of standard deviation. In the option world, standard deviation is volatility. The theory behind option writing, or selling option spreads, is that the market is efficient at distributing information to all its participants and that price action follows a random walk. In efficient markets, it’s not possible for a trader to gain an edge and actually profit in the long term. So why even pursue selling options? The reason is theta. The edge premium sellers have is time decay. Maintain a positive theta position and you’ll gather profits over the long term.

It’s no great feat to persuasively argue against efficient market theory and against a random walk theory (prices have no memory). I’ll leave that for another time. Right now I’ve got a bone to pick with probabilities based on market volatility. Every option premium seller will acknowledge the Black Swan. Essentially, a statistically improbable event that should almost never happen, but happens all the time in markets. I read that there were 12 greater-than 4 sigma moves last year, including a fair share of 5 sigma and 6 sigma moves. A sigma is a standard deviation. The classic Gaussian bell curve puts the probability of a 3 sigma move at the very tips of the bell curve and ascribes its probability to less than 1%. The quick fix for that in trading is to describe markets as having fat tails. And the way the option world takes care of this pesky problem is to point to all the non-zero bid options way, way out-of-the-money. When trading the options in the middle of the bell curve, you get no credit for fat tails. So whether you use delta of the option or a fancier calculation to determine the probability of success, you need to understand going into the trade that your chances are dependent on the arrival of Black Swans.

A quick note on how this trade was closed.

Since I was short the 83 call, it was assigned to me. In other words, the holder of the option wasn’t stupid enough to not cash-in on a winning ticket. For a brief moment I was short SPY at the price of $83 a share. But that was a brief moment as my long 85 call essentially canceled out the short stock position by being exercised. My broker automatically exercises long in-the-money options so there was nothing I needed to do. Except gaze in horror at the week’s rally.

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