Featured Solution June 2015

Your Global Investment Authority

Lies, Damned Lies and Equity Skew

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. Jason Goldberg Executive Vice President We suggest a more straightforward approach to looking at options, focusing Portfolio Manager on premiums, market directionality and intent. The price at which you can sell or buy an 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 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 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. FIGURE 1: SPX INDEX 3M SKEW (AS MEASURED BY THE DIFFERENCE IN FIGURE 2: SPX INDEX 3M SKEW (AS MEASURED BY NORMALIZED IMPLIED VOL) DIFFERENCE IN IMPLIED VOL)

16 0.6 14 0.5 12 0.4 10 8 0.3

6 0.2 4 0.1 2 0.0 0 -2 -0.1 Jul May May May May Jul May May May May ‘11 ‘12 ‘13 ‘14 ‘15 ‘11 ‘12 ‘13 ‘14 ‘15 (diff) Delta (diff) Fixed (diff) Moneyness (norm) Delta (norm) Fixed (norm)

Source: Bloomberg, as of 21 May 2015 Source: Bloomberg, as of 21 May 2015

Which strikes should we choose? When comparing skew over trades more like a Treasury bill. So most practitioners would time, should we look at a constant “moneyness” (a constant urge you to discard the green lines when looking at skew percent distance from the spot or of the over long periods. underlying), comparable deltas (25-delta puts versus 25-delta But which of the remaining four lines should we focus on? calls) or fixed strike prices? The gold line in Figure 1, measuring the difference between These calculation differences matter. In Figures 1 and 2, is SPX three-month 25-delta puts and calls, suggests that SPX skew (S&P 500 Index) three-month skew steep or flat by historical is midrange, especially when including 2011’s high numbers. standards? (In the options market, we refer to high skew as But the blue line, measuring the volatility difference of “steep” and low skew as “flat.”) High skew means excessive three-month 95% puts and 105% calls (both 5% out-of-the- demand for out-of-the-money puts relative to calls; flat skew money), suggests elevated skew. means less demand for puts (or greater demand for calls). To normalize, we divide these differences by either the Skew, based on the volatility differences between specific at-the-money or 50-delta (Figure 2). Both options (green lines), is extremely steep, and has been “moneyness” and “delta” suggest elevated skew, but increasing steadily. But that’s misleading because the sample moneyness (blue line) is close to a four-year high. options chosen (a 17 July 2015 put with a of Second, even if we could agree which measure is best, the 2000 and a call with a strike price of 2200) were very link between the P&L of trades based on any of these different animals in the past. analyses and the analysis itself is tenuous. Looking only at the green lines is analogous to tracking the Consider a trade in which we sell “rich” puts and buy yield of a specific bond over many years because the relative “cheap” calls. The first order risk of this trade is directional or strike and are changing dramatically as time passes. “delta.” So regardless of how the skew behaves after trade For instance, when a 10-year Treasury note is first issued it initiation the trade profits will be driven primarily by whether trades differently than it does as it approaches maturity and the market goes up or down.

2 JUNE 2015 | FEATURED SOLUTION For example, the skew can “flatten,” but the trade of selling FIGURE 3: ACTUAL VS. ESTIMATED PL (VOLATILITY POINTS) the skew may not make money. Because the skew in the gold and blue lines represents the volatility of different strikes and 8.0 maturities every day, it can move simply because the 6.0 calculations are based on new options. A trade, on the other hand, involves specific options. 4.0

And the skew – measured by the difference between the 2.0 volatility of specific options – almost always steepens as 0.0 out-of-the-money options approach maturity. Actual P&L

But do not confuse steepening of skew over time with a -2.0 recommendation to always buy the skew and wait until it -4.0 steepens. Owning the high-volatility put and being short the low-volatility call while waiting for the (very likely) steepening -6.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 is not free. A vega-neutral position – meaning the options’ sensitivity to parallel shifts in the volatility surface is close to Estimated P&L zero – will have negative time decay as you own the high- Actual PL Estimated PL volatility strike and are short the low-volatility strike. Also, the Hypothetical example for illustrative purposes only. Source: PIMCO vega of traded options changes over time.

And, most important, the stock’s actual volatility (and where Each blue diamond represents a combination of actual P&L it occurs relative to the strike) matters a lot when delta- and estimated P&L generated from a simulated path of hedging, a strategy to immunize the first-order directional risk potential underlying prices. Comparing the actual outcome of an options position with trades in the underlying. with the estimated outcome, it’s as if one rolled a die and compared the outcome with a prediction and then plotted Figure 3 illustrates the estimated P&L of a delta-hedged the results.The blue diamond circled in red was generated options trade compared with the actual P&L. This means that from a simulated trade that we estimated would have it looks at the difference between the implied volatility at generated 1.7 volatility points of P&L but instead resulted which we traded the option compared with the underlying’s in 5.7. Our estimation of 1.7 was based on the difference actual volatility and then compares this difference with the between the implied volatility embedded in the option price actual P&L of a delta-hedged option. Implied volatility is, and realized (or actual) volatility on the underlying’s path. essentially, the market’s prediction of the underlying’s future This difference, let’s call it a windfall gain of 4 points, is an volatility, whereas the actual volatility is based on how much example of what we in derivatives markets call “path the underlying moved. 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.

FEATURED SOLUTION | JUNE 2015 3 FIGURE 4: MATRIX OF OPTION PREMIUMS FOR THE S&P 500

Puts Calls 80% 85% 90% 95% 100% 100% 105% 110% 115% 120% 30 0.01% 0.03% 0.09% 0.30% 1.34% 1.19% 0.02% 0.00% 0.00% 0.00% 60 0.08% 0.15% 0.32% 0.79% 2.04% 1.79% 0.12% 0.01% 0.00% 0.00% 91 0.17% 0.33% 0.66% 1.31% 2.71% 2.28% 0.30% 0.03% 0.00% 0.00%

Premium 182 0.64% 1.05% 1.68% 2.67% 4.30% 3.49% 1.15% 0.23% 0.05% 0.01% 365 1.87% 2.60% 3.62% 4.99% 6.81% 5.46% 2.96% 1.31% 0.47% 0.14% 730 4.73% 5.94% 7.40% 9.14% 11.23% 8.56% 6.04% 4.06% 2.55% 1.52% Source: Bloomberg, as of 21 May 2015 Sample for illustrative purposes only. Not intended to be a recommendation for any particular strategy or investment product.

If all of the above measures lack practical application, then As premium is more intuitive than implied volatility, the Credit how should we look at skew? Like most things in finance, it Suisse Fear Barometer is not a bad measure of skew. It pays to keep it simple. Focus on premiums – they don’t lie. calculates the moneyness of a three-month put that has the Consider the matrix of option premiums for the S&P 500 same premium as a three-month 10% out-of-the-money call. (Figure 4).

The 91-day 5% out-of-the-money put costs 131 basis points FIGURE 5: CSFB INDEX (1995 TO PRESENT, WEEKLY)

(bps), whereas the 91-day 5% out-of-the-money call costs 45 only 30 bps, enabling an investor to sell one put and 40 purchase 4.4 calls for no net premium outlay. Is selling puts 35 and buying calls a “skew trade?” That’s the wrong question. Better to ask whether it’s a good trade. I think it is. 30 25 The bearish arguments on U.S. equities typically revolve 20 around full valuations and imminent interest rate hikes, valid 15 concerns for a bullish position in equities. But a 4-to-1 ratio between put and call premiums? That seems excessive given 10 that equities have arguably been rich for some time and the 5 highly uncertain timing of the Fed’s first interest rate hike. 0 May May May May May May May May May May May The other important question is how much directional bias to ‘95 ‘97 ‘99 ‘01 ‘03 ‘05 ‘07 ‘09 ‘11 ‘13 ‘15 have when implementing a skew trade. I think it’s critical. If we Source: Bloomberg, as of 15 May 2015 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.

4 JUNE 2015 | FEATURED SOLUTION 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.

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