Back in November 2008, I wrote an article about what appeared to be a substantial disconnect in the way that options of individual stocks were being priced. This was due to the very high level of fear in the market. This anomaly was most easily exploited by selling options. In June of 2009, I wrote an article looking at how well this strategy had worked out. In this article, I look at the very different options opportunities that exist today. The anomalies that existed in late 2008 have largely disappeared, but there are a range of other opportunities that look substantial. In describing the market opportunities in options, this article introduces some more sophisticated concepts in options valuation and trading.

Today, VIX stands at around 28. The implied volatility of long-dated options on SPY (December 2010 and December 2011) is 27%-28%. VIX measures the implied volatility of options expiring soon. What this means is that the options market is suggesting that volatility is stabilizing at a value of around 27%-28%. This level of volatility is almost twice the long-term average for the S&P 500 (which is around 15%) but is far lower than levels of late 2008.

The value of implied volatility we are citing here is for the at-the-money options, meaning that the strike price of the options is very close to where the market is trading right now. As the strike price moves out from the current price, the implied volatility typically increases—an effect known as the volatility smile. Today, we have the opposite situation—implied volatility is decreasing slightly for options as the strike price increases or decreases relative to the current market level. As of this writing, SPY is trading at around $90. Options with strikes at $90 have implied volatility at 28% for options expiring in December 2010. Options with strikes at $100 have implied volatility of 26%, and options with strikes at $110 have implied volatility at 25%. This effect is worth understanding. When implied volatility increases for strike prices that are substantially different from the current price of SPY, this means that the proportional cost of protecting against extreme market moves is high. In other words, the volatility smile means that the market is placing elevated odds on extreme moves or simply that the sellers of these options require additional risk premium for bearing these risks. Today’s conditions, by contrast, mean that the options market believes that large moves, up or down, are relatively less likely than smaller moves.

In summary, then, we have high implied volatility for SPY compared to historical levels, but a slightly inverted volatility smile so the relative odds of very large moves is expected to less than normal—the options prices imply that there is little risk of ‘fat tails’ relative to the fairly high implied volatility.

When I compare the implied volatilities on a series of options to the volatility projected by Quantext Portfolio Planner (QPP), having adjusted QPP’s baseline volatility for the S&P 500 to match the long-date options at 27%, the results are surprisingly consistent:

*click to enlarge*

The table above includes a series of individual stocks and some core ETFs and I have chosen the listed options with the longest period until expiration. The enormous disagreement we saw between QPP and the options market has largely disappeared. I find no consistent relationship between Beta, total volatility, or implied volatility that explains the differences between QPP’s volatilities and the implied volatilities. It is important to remember that these results exhibit this consistency once we assume that the future volatility of the S&P 500 is 27% to match the implied volatility on SPY, and this is very high compared to the long-term historical average of volatility on the S&P 500 (which is around 15%). On the other hand, given the state of our economy, I can imagine that market volatility could remain elevated for quite a while.

The implied volatilities on a series of stocks in the table above are lower than QPP’s projections today, but they were far higher than QPP’s projections in November 2008. The situation has gone from options on these stocks looking over-priced to under-priced, albeit not by a large margin. Options on EBAY, EFA, TIP, EEM, and KO are under-priced relative to options on the S&P 500. Options on a range of defensive stocks such as DUK, SO, JNJ, and PG will tend to be over-priced. It is interesting to note that implied volatility on TIP is below the expected level and implied volatility on AGG is above the expected level. This tells us that the market is discounting the risk of inflation relative to the risk of ongoing deflation—this does not come as a huge surprise.

It is important to understand that options prices and the calculations of implied volatilities assume that stocks and indexes follow a random walk with **zero expected return ** (this is a central assumption of the Black-Scholes model). QPP assumes that risky assets have expected returns greater than zero. This means that over time QPP’s expected value of call options will tend to have higher value than the prices at which these options are trading (the put options will be of less value). This effect is an enormous anomaly in the way that options trade. The prices of options make sense on the basis of pricing models that assume zero average return for the underlying instruments. In other words, using one of these models, the prices of the options are consistent with the assumption of zero return. You can use a Black-Scholes calculator or other zero average return models and price puts and calls and the prices are highly consistent with varying strike prices and time to expiration. On the other hand, investors would be irrational to invest in the underlying indexes and securities if they had zero expected return. There are a variety of ways to calculate the expected return on assets, but the equity risk premium is a well established notion. QPP reconciles this contradiction by using Black-Scholes calculators (with zero average return) and then allow prices of the underlying to follow Monte Carlo simulations with a positive expected return. This causes the median value of call options to drift upwards over time (and the median value of put options to drift downwards over time). This effect means that call options that are under-priced on the basis of implied volatility are actually even more under-priced when we consider a positive expected return.

It is also important for investors to understand the relationship between dividend yield and options prices. Dividends paid to investors reduce the upside potential for price appreciation. The owner of an un-exercised call option does not receive dividends. This means that higher dividends reduce the value of options. The larger the fraction of total returns than come in the form of dividends, the lower the mis-pricing in options that results from assuming that prices follow a random walk.

Let’s consider an example. The Jan 2011 $56 call option on IWM is trading at $5.51, with about a $0.30 bid-ask spread and expires on Jan 21, 2011 as of this writing. IWM is trading at about $51 and pays annual dividends of about $0.80, for a dividend yield of about 1.6%. Quantext Portfolio Planner calculates the value of this call options at $5.88, having matched the volatility of the SPY options at 27%. The QPP and market values are remarkably close. What these calculations assume, however, is that the expected future price gain of IWM is zero. Over time, however, QPP expects the return on IWM to be 9.6% per year. This means that the call options on IWM will tend to be under-priced to the tune of 8% per year in return (9.6% expected return – 1.6% in dividend yield). Puts will be over-priced.

As an extreme case, we can look at stocks that pay no dividends at all. Consider EBAY, for example, trading at about $17 per share. The January 2011 $20 call option on EBAY is trading at about $2.30. QPP projects that this option should be trading at $3.10, before accounting for a non-zero expected return, simply because the projected volatility is higher than the current implied volatility (see table above). QPP projects that the expected return is 14%. Thus, the call option at $2.30 is substantially under-priced (and the put options tend to be over-priced).

Let’s consider another example: Duke (NYSE:DUK). DUK is trading at about $14 per share and has a dividend yield of about 6.7%. QPP projects that the average rate of return for DUK is 6.6% per year. The Jan 2011 $15 call option is trading at around $1. QPP’s baseline calculation generally agrees, although QPP projects slightly lower future volatility for DUK than the implied volatility (see table above). Further, the dividend yield on DUK almost perfectly matches our projection for expected return, so the expected price appreciation is zero. This means that the value of the call options based upon the assumption of a random walk in return (as you will find on ivolatility.com or with a Black-Scholes calculator) is probably a pretty good approximation—assuming that we agree on the implied volatility, and this is often not the case.

It does not take too long to find equities for which the implied volatilities look very odd. Google is currently trading at about $424. The Jan 2011 $440 call options currently have an implied volatility of 33% and have an ask price of $67. This means that the options market is telling us that a Google (NASDAQ:GOOG) has the same upside potential as MSFT (see table above). QPP projects the future volatility of GOOG at 55% (once we have calibrated QPP’s baseline volatility for SPY to match long-dated options, as in all calculations above). QPP puts the baseline value of this option at $112, even before we add the positive expected return for GOOG. This means that call options are substantially under-priced for GOOG. Google would be an example of the kind of stock on which one would want to be long call options.

An interesting strategy for exploiting this pricing anomaly is to sell covered calls on high yield stocks (like DUK) and buy calls on low-dividend high-volatility stocks (like EBAY). This approach provides income in the form of dividends on the stocks on which the covered calls are sold plus the income received from the sale of the option. To exploit this strategy, we would seek stocks with relatively low volatility and high dividend yields relative to expected return on which to sell covered calls and stocks with high volatility and zero dividends on which to buy call options.

There is also an additional factor that adds value to the strategy of selling calls on low volatility / high yield stocks and buying calls on high volatility / high yield stocks: autocorrelation in returns. Autocorrelation in returns is the correlation between returns in successive months. The random walk model that is the basis of Black-Scholes assumes that autocorrelation in returns is zero, but this is often not the case. In particular, the trailing three-year autocorrelation in monthly returns on the S&P 500 is currently high and positive, on the order of 40%. This substantial positive autocorrelation is present for a range of asset classes and individual stocks. Autocorrelation is important because positive autocorrelation will increase the value of options beyond the values provided by a model that assumes a random walk. The current trailing three-year autocorrelation on EBAY is 29% and on GOOG is 22%. The current trailing three-year autocorrelation on DUK is 2%. We are looking at autocorrelation in total returns. To be rigorous, we would prefer to look at autocorrelation in price returns (no dividend adjustment), and this comes out to be about -10%. In other words, the options on DUK are actually worth less than the market is indicating and the GOOG and EBAY options are worth more—and this is an additional incremental factor beyond those listed above. Autocorrelation changes in time, and this is not a powerful indicator—but it is pointing in the right direction.

To summarize, I have discussed three factors that can be used to find current opportunities in options:

- Look for inconsistencies in implied volatility between the market and individual stocks or sectors

- Look for inconsistencies in the way that options prices are impacted by non-zero expected returns

- Look for inconsistencies in the relationships between options prices and autocorrelations of returns

I see substantial potential for investors who are savvy enough to parse through the enormous amount of information that options markets provide—and not just for the active trader. In 2001, Zvi Bodie proposed that investors saving for retirement would be well served by purchasing TIPS with 90% of their portfolios and then buying call options on equities to maintain exposure to the upside potential in equities. My analysis suggests that an interesting variant on this approach that is to buy high-yield moderate volatility stocks, sell covered calls on these stocks and purchase call options on high volatility stocks that pay no dividends to maintain exposure to the potential for a rally in equities. Quantext Portfolio Planner is projecting that call options on a range of high volatility stocks are under-priced at current market conditions and that call options on a range of solid dividend-yielding stocks are fairly priced or slightly over-priced. In this environment, building a solid income portfolio, selling calls on holdings, and buying calls on the high volatility stocks makes some sense (depending upon your risk tolerance). This type of strategy requires care and detailed analysis of the specific options and instruments, of course.

Beyond the statistics, I see potential in this type of strategy because I do not foresee a rapid economic recovery. The income provided by high-quality, moderate-volatility stocks such as utilities looks good in this environment: I am not betting on price appreciation in the overall market. Selling covered calls provides additional income. Meanwhile, being long calls on high-volatility, zero-dividend stocks provides a share of the upside if we do see price gains but limits losses in the event of a swoon in prices.

*Note:** QPP was run with all default settings, except for the calibration of volatility on the S&P 500 to long date options on SPY, with three years of data through 5/31/2009 as input.*

*Disclosure:** At the time of this writing, the author is long DUK, SO, MSFT, AA, EBAY, TIP, and JNJ. The author is short long-dated calls on JNJ and SO.*