Trade in Groups

Most options traders are aware that volatility has an impact on their positions, but often the underlying reason is clouded by concepts like vega, when it is much easier to understand at a higher level.

In the last two months, the average absolute daily change in the S&P 500 has been 3.7%. This means that annualized volatility is running at a 74% rate. Shorter term averages put volatility at even more extreme levels; a ten day average shows the peak annualized volatility in October exceeded 97%. Even in the quietest periods (relatively speaking), volatility exceeded anything ever seen since the start of a VIX dataset going back to 1990.

Put another way, the largest intra-day percentage range in the S&P 500 was on October 13th, when there was a 13.5% difference between the day’s high and day’s low. This closely rivals the yearly high-to-low percentage change in the S&P from 2007 (15.55%), 2006 (17.4%), and 2004 (14.8%), and exceeds the trading range of the S&P for the whole of 2005 (12.3%).

So how does this relate to options? With such a high degree of volatility, it is very easy to quickly get underwater on a stock purchase, and a smart options strategy can help manage risk. Consider the following chart, generated using a model based on Geometric Brownian Motion – an applied physics concept that models short-term stock prices based on random shocks applied to a drift. With a volatility of 15%, similar to what was seen in financial markets in previous years, almost all the expected stock price outcomes at the 25th day (about equal to a one month option) fall within a 5% range of the starting value of $10/share.

If this is being applied to a standard $10 strike price, at-the-money option on 100 shares, the average value at expiration is roughly $19.80, assigning zero value to situations where the stock closes below $10 at expiration and assuming exercise if the stock closes above $10.

This is well and good, but the predicted range of extremes for the underlying stock generally fell between $8.60 and $11.75/share over several runs. Once upon a time, those ranges might have been large for one month, but when compared to the volatility being seen today it’s noise.

Now consider what happens when volatility is increased to 70%: the GBM model is no longer tightly clustered around a central point, but wildly dispersed to reflect the uncertainty. The range for this model run is somewhere between $6.50 and $12.50/share, with extreme values ranging from $5 to $20/share.

The expected options value for the contract this time is approximately $85.70 – more than four times as high, as suggested by the increase in volatility. In the low volatility example, the highest value for any options contract was just under $200; in the high volatility example end values exceeding $1000 were possible.

What does all this mean? Fancy physics models aside, it shows why options are so valuable to have at a time like this –  volatility means that owning the underlying could result in a steep loss, and an options contract allows one to profit from huge upside moves while simply walking away with a smaller principal loss should the underlying stock decline.

Of course, although call options were focused on here, puts are similar in principle – and together, strategic options use is a way to add value to your portfolio through a combination of risk management and intelligent speculation.