ANALYTICAL TOOLBOX: Strategy Follow-UpVolatility Mean Reversion

Study Review

In Options Returns and the Cross-Sectional Predictability of Implied Volatility, by Amit Goyal of Emory Universitys Goizueta Business School and Alessio Saretto of Purdue Universitys Krannert School, the authors examine volatility trends for SPX component stocks along with strategy assessments to capitalize on these trends. Using the index components rather than the index itself is a somewhat unique approach and was determined to be a better means for predicting future volatilities.

One of the main findings of the study was that a stock with an implied volatility [IV] below its 12-month moving average value tended to have a higher IV the next month. On the other side of the volatility picture, stocks with IVs higher than its 12 month moving average tended to have a lower IV the next month. These results were based upon 10-year of data (120 monthly data sets) and used decile groupings to identify the component stocks with the highest relative IV and those with the lowest relative IV. 字串1

The study identified a group of 50 relatively high IV stocks along with a group of 50 relatively low IV stocks each month on the trading day prior to expiration. On the Tuesday following this scan, long straddles were entered for the relatively low IV stocks since mean reversion implies a boost in premium from rising IV levels. To capitalize on decreasing IV levels using the relatively high IV stocks, short straddles were established for this group. While rational, this represents 200 individual option trades and significant margin for 100 short option positions.

Although spread mid-points were used for transactions, the study also separately examined increased transaction costs to more accurately model actual costs. Even when thinly traded options (with greater spreads) were evaluated using higher transaction cost methods, the results remained impressive. An average monthly return of 15% declined to 5.3%. A significant decline, but the approach still justifies further investigation.

Modified Approach

The modified approach makes three modifications. First, it reduces the number of trades to allow for smaller allocations. Rather than breaking the 500 component stocks into 10 x 50 stock groupings, 50 x 10 stock groupings are used, with long straddles created for the 10 relatively low IV stocks. It should be noted that this group excludes deal stocksthose with IVs that have recently decreased significantly due to pending corporate actions such as private equity takeovers or spin-offs.

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The second significant modification makes use of a comparison of current IV versus median IV over one year rather than mean IV for the year. The advantage of using a median value is that it minimizes the impact of outlier values on the results. A very brief period of unusual, high volatility will skew mean results for the entire period, while having much smaller impact on median results.

The final modification was in expiration month selection. Rather than using near month options, the approach tested options for: 字串7

1. The following month and 
2. January expirations, which represented 90 to approximately 365 days.

This was done to minimize the impact of accelerated time decay within 30 days and within 45 days, respectively. The study portfolio included an equal number of short options which benefit from time decay.

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Method & Results

On a monthly basis on the last trading day prior to option expiration (usually a Friday) the S&P 500 stocks were ranked by IV using a comparison of current IV levels to 12-month median IV levels (7-149 days) using a percent difference calculation [(Current IV Median IV) / Median IV]. After removing stocks with pending corporate actions, the 10 stocks furthest below the 12-month median IV were used in a long straddle paper-trading strategy.

On the second day following option expiration (usually a Tuesday), straddles that were at or near the money were purchased on the 10 ranked stocks. The contracts had varying days to expiration; there was approximately 60 days for the next month group and anywhere from 90 to 365 days for the January group. The contracts were sold immediately prior to the next option expiration. Closing data was used for all comparisons, buys and sells.

The Optionetics Platinum Skew Finder II was used to obtain current and 12-month median IV data for the S&P 500 component stocks each month. This data was downloaded to Microsoft Excel so a % difference form the median could be calculated for each stock. The data was then sorted by the % from Median and relevant corporate action stocks removed. Using Jul-06 data, the following was obtained:

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Table 1:  July 2006 Relatively Low IV Rankings
(Click here for larger view.)

The last column identifies the percent difference from the median, with NOVL being the relatively lowest at -39.5%. Since this stock trades for less than $10, another parameter was added to use only stocks trading above $10 per share. The first portion of Table 2 provides ranking data, while the second portion identifies trade entry data, including the closing price for the underlying stock; the strike price used; the symbol, premium and IV for the call and the put; commission ($20 per straddle) and finally, the net costs. Closing data is similar, but not included here due to space constraints.

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Table 2: July 2006 Relatively Low IV Straddle Trades
(Click here for larger view.)

The results were not favorable, but consistent. Although it almost makes for an argument to reverse the strategy, more work must be completed to better understand the reason for losses. IV declined in most cases and it appears to be impacted by the bid ask spread. Commissions also represent a significant portion of the costs; however, the results were not good enough to test increasing contracts and achieving economies of scale. 字串7

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Table 3: Straddle Trade Results for Next Month Options
(Click here for larger view.)

The Net IV Change is an average value using the IV change for the calls and the IV change for the puts. In the event IV decreased 100% because the option premium went to 0 (too far out of the money) or represented intrinsic value only (too deep in the money), the average was excluded. As a result the average of Net IV changes are significantly less than the individual call or put IV changes.

Although the IV declines for all categories were smaller when using January expirations, the trade results were actually worse for this approach. Unfortunately there is not a good apples-to-apples comparison here for two reasons: 字串9

1. Not all next month options had January expirations and higher ranked stocks had to be added to the grouping, and 
2. Time to expiration varied.

Table 4: Straddle Trade Results for January Options
(Click here for larger view.) 字串4

Next Steps

The study results were impressive enough to merit further reviewparticularly since there were significant variations from the approach. Unfortunately, some modifications must be made given the prohibitive trading costs associated with the study. The following will be completed as a next step: review individual data sets to see if there are any trends can be identified that will filter the data in an unbiased manner. For instance, the results may be more favorable for options with smaller relative spreads (usually higher premiums), at certain IV levels or when a stock is in the relatively low IV grouping two consecutive months.

Next weeks article will take one last look at the existing trades and data to determine if retail traders can use a long straddle approach to capitalize on the study results even when different trading costs are incorporated. In addition, the most significant modificationusing a median value rather than mean valuewill be evaluated to determine if this change played a larger role than costs associated with slippage and commissions.

See Analytical Toolbox: Volatility Mean Reversion for more background.

To see the other articles by this author, please click here.

Clare White, CMT

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