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Lies, Damned Lies and Equity Skew

​​While skew measures can occasionally offer valuable information on the flows within equity derivatives, they can also be highly misleading.

Equity skew, which at its most basic purports to measure the difference in the value of stock options with different strike prices, is one of the most used (and abused) sentiment measures in the equity options market. While skew measures can occasionally offer valuable information on the flows within equity derivatives, they can also be highly misleading.

There are a number of reasons why. One, you can look at and interpret skew many ways, and two, much equity skew analysis does not yield actionable investment information. I sometimes think of skew as the “ultimate talking point,” wonderful for making you sound smart but not particularly useful when it comes to day-to-day capital management decisions.

We suggest a more straightforward approach to looking at options, focusing on premiums, market directionality and intent. The price at which you can sell or buy an option at any given time, your view on the likely direction of the security price, or the market in general, or what you hope to achieve – an effective hedge or inexpensive exposure to a future market move – are all more important considerations than what traditional measures of equity skew suggest, in our view.

There are at least three material reasons why the profit and loss (P&L) of a “skew trade,” a position based on volatility curve shape, can greatly differ from an initial analysis suggesting that the skew was too steep or flat: rolling strikes inherent in the measure, changing vega of traded options and path dependency. These reasons apply to any volatility trade but they are exacerbated with skew trades, which typically take opposing options positions on the same underlying but different strike prices.

Why the confusion? First, few can agree on precisely how to measure skew.

Should we look only at the raw difference between the implied volatilities of out-of-the-money puts and calls? Or do we need to normalize this difference for the volatility level? Normalizing is meant to adjust for the overall volatility level. A five-volatility-point skew, for example, means different things in a low-volatility environment than in a high one. 

Which strikes should we choose? When comparing skew over time, should we look at a constant “moneyness” (a constant percent distance from the spot or forward price of the underlying), comparable deltas (25-delta puts versus 25-delta calls) or fixed strike prices?

These calculation differences matter. In Figures 1 and 2, is SPX (S&P 500 Index) three-month skew steep or flat by historical standards? (In the options market, we refer to high skew as “steep” and low skew as “flat.”) High skew means excessive demand for out-of-the-money puts relative to calls; flat skew means less demand for puts (or greater demand for calls).



Skew, based on the volatility differences between specific options (green lines), is extremely steep, and has been increasing steadily. But that’s misleading because the sample options chosen (a 17 July 2015 put with a strike price of 2000 and a call with a strike price of 2200) were very different animals in the past.

Looking only at the green lines is analogous to tracking the yield of a specific bond over many years because the relative strike and maturity are changing dramatically as time passes. For instance, when a 10-year Treasury note is first issued it trades differently than it does as it approaches maturity and trades more like a Treasury bill. So most practitioners would urge you to discard the green lines when looking at skew over long periods.

But which of the remaining four lines should we focus on? The gold line in Figure 1, measuring the difference between three-month 25-delta puts and calls, suggests that SPX skew is midrange, especially when including 2011’s high numbers. But the blue line, measuring the volatility difference of three-month 95% puts and 105% calls (both 5% out-of-the-money), suggests elevated skew.

To normalize, we divide these differences by either the at-the-money or 50-delta implied volatility (Figure 2). Both “moneyness” and “delta” suggest elevated skew, but moneyness (blue line) is close to a four-year high.

Second, even if we could agree which measure is best, the link between the P&L of trades based on any of these analyses and the analysis itself is tenuous.

Consider a trade in which we sell “rich” puts and buy “cheap” calls. The first order risk of this trade is directional or “delta.” So regardless of how the skew behaves after trade initiation the trade profits will be driven primarily by whether the market goes up or down.

For example, the skew can “flatten,” but the trade of selling the skew may not make money. Because the skew in the gold and blue lines represents the volatility of different strikes and maturities every day, it can move simply because the calculations are based on new options. A trade, on the other hand, involves specific options.

And the skew – measured by the difference between the volatility of specific options – almost always steepens as out-of-the-money options approach maturity.

But do not confuse steepening of skew over time with a recommendation to always buy the skew and wait until it steepens. Owning the high-volatility put and being short the low-volatility call while waiting for the (very likely) steepening is not free. A vega-neutral position – meaning the options’ sensitivity to parallel shifts in the volatility surface is close to zero – will have negative time decay as you own the high-volatility strike and are short the low-volatility strike. Also, the vega of traded options changes over time.

And, most important, the stock’s actual volatility (and where it occurs relative to the strike) matters a lot when delta-hedging, a strategy to immunize the first-order directional risk of an options position with trades in the underlying.

Figure 3 illustrates the estimated P&L of a delta-hedged options trade compared with the actual P&L. This means that it looks at the difference between the implied volatility at which we traded the option compared with the underlying’s actual volatility and then compares this difference with the actual P&L of a delta-hedged option. Implied volatility is, essentially, the market’s prediction of the underlying’s future volatility, whereas the actual volatility is based on how much the underlying moved.

Each blue diamond represents a combination of actual P&L and estimated P&L generated from a simulated path of potential underlying prices. Comparing the actual outcome with the estimated outcome, it’s as if one rolled a die and compared the outcome with a prediction and then plotted the results.The blue diamond circled in red was generated from a simulated trade that we estimated would have generated 1.7 volatility points of P&L but instead resulted in 5.7. Our estimation of 1.7 was based on the difference between the implied volatility embedded in the option price and realized (or actual) volatility on the underlying’s path. This difference, let’s call it a windfall gain of 4 points, is an example of what we in derivatives markets call “path dependency” – a technical term for luck (good, in this case).

But the windfall’s magnitude is pretty big. True, we chose one of the largest outliers to make a point, but it does illustrate how much the P&L of a delta-hedged options position can vary based on when (relative to maturity) and where (relative to the strike price) the actual volatility of the underlying occurs.

If all of the above measures lack practical application, then how should we look at skew? Like most things in finance, it pays to keep it simple. Focus on premiums – they don’t lie. Consider the matrix of option premiums for the S&P 500 (Figure 4).


The 91-day 5% out-of-the-money put costs 131 basis points (bps), whereas the 91-day 5% out-of-the-money call costs only 30 bps, enabling an investor to sell one put and purchase 4.4 calls for no net premium outlay. Is selling puts and buying calls a “skew trade?” That’s the wrong question. Better to ask whether it’s a good trade. I think it is.

The bearish arguments on U.S. equities typically revolve around full valuations and imminent interest rate hikes, valid concerns for a bullish position in equities. But a 4-to-1 ratio between put and call premiums? That seems excessive given that equities have arguably been rich for some time and the highly uncertain timing of the Fed’s first interest rate hike.

The other important question is how much directional bias to have when implementing a skew trade. I think it’s critical. If we firmly believed that the market is headed lower, then why sell puts and buy calls, even at these levels? But for inexpensive exposure to a U.S. equity market rally, then the “risk reversal” (selling puts and buying calls) makes a lot of sense.

As premium is more intuitive than implied volatility, the Credit Suisse Fear Barometer is not a bad measure of skew. It calculates the moneyness of a three-month put that has the same premium as a three-month 10% out-of-the-money call. 

So the recent reading of 35 means that a three-month 10% out-of-the-money call has the same premium as a 35% out-of-the-money put (Figure 5). Think about that. For the same premium (a few basis points in this case), you can either bet that market rises 10% in a short period or drops more than 35%. Neither outcome is likely, but the moneyness differences seem large for equal premiums, in our view.


Yes, SPX skew is steep by historical standards. If you believe there’s more upside to equities, take advantage of it.

The Author

Jason Goldberg

Portfolio Manager, Equity Derivatives

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