Wednesday, April 18, 2012

Accuracy Of Market Estimates of Volatility

In a couple of recent posts viz, Is It Better To Buy Or Sell Options? and Buy/Sell Musings & Volatility, I've been looking at the trader's bias of being a either a buyer or seller of options, or at least being nett short or long gamma.

The conclusion I have reached, for whatever that is worth, is that the decision generically boils down to volatility. That is to say that the trader must examine the volatility priced into the option, AKA implied volatility, and decide whether the price is at, over, or under the odds; or in option parlance, whether the option is fair value, over, or undervalued.

Some writers suggest a comparison to historical volatility, but I wrote in Buy/Sell Musings & Volatility that I thought that was naive and an inappropriate way of determining relative value. Implied volatility looks forward; it is the collective markets guestimate of the volatility it thinks will be realized in the future, in other words the market's view of correct value for that option. It is not definitive, cannot be definitive, because we don't know what will happen in the future.

Historical volatility is definitive however because it measures actual prices traded in the market place over a set of past data of the analyst's choosing. This can be any period, but most commonly over the preceding 20 or 30 days of data. For the purposes of this article I am going to use 20 day historical volatility as this represents the approximate number of trading days in one month.

The VIX is an index of near term implied volatility on S&P 500 options and is quoted according to a formula, to smooth out implications of impending expiry etc. Details and method of calculation are available from the CBOE at this LINK. Essentially it is recording implied volatility one month henceforth.

As I have stressed up til now, it looks at past data, whereas implied volatility looks forward and what happens in the next 20 trading days may be vastly different to what happened on the last 20 trading days, volatility wise. It does have it's uses however. It allows the analyst to examine the 'normal' range of actual volatility for an underlying instrument, how it's cycles, what has been its upper and lower boundaries under various market conditions etc.

Historic volatility has a further use. We can use it to measure how accurately the market forecast one month volatility by looking at the actual volatility realized in on month's time, via the historical volatility calculation.

Let's have a look at the S&P500 using VIX as proxy for implied volatility available at a given date and realized volatility one month later.

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As we can see in the above graphic, on the 1st of Feb the market overestimated volatility substantially, therefore we can say that on that date and with the benefit of hindsight, we would have been better to have been a seller of options, all other considerations aside.

Manipulating the historical volatility plot backwards by one month makes it easier to analyze by lining up the implied volatility with the volatility realized in one month later.

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In the data that we can see in this graphic, the market collectively forecast volatility correctly, finally, in about the third week of March. So we can say, again with the benefit of hindsight, that S&P500 options at that point were fair value, though it is only today, one month later, that we can say that.

The displaced historical volatility plot gives us the opportunity to view the implied volatility at any point in the past and also in toto, to see how well the market forecasts volatility over the long term. The graphic below shows, on SPX options at least, that the market tends to over estimate forward volatility chronically.

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That is it overestimates future volatility until it doesn't. Sellers at market tops get taken to the woodshed.

This evokes the 'picking up pennies in front of a steamroller' cliche for put sellers and synthetic equivalents (buy/write traders) and bull put traders. Put buyers who successfully pick tops score a big time try/touchdown/<or goal scoring nomenclature appropriate for your country> with the vega bomb that blew up in the seller's face. (With apologies for mixing metaphors there)

As intimated in the preceding paragraph, of course being short or long options is not the only consideration. Delta, gamma and theta also cohort the make the trade; or wreck it as the case may be. In markets swoons put buyers will be celebrating with festive dinners, Dom Perignon and Cuban cigars while quite obviously call buyers will be drowning their sorrows with rough red, despite being on the correct side of the buy/sell divide.

The overriding point here however is that market estimations of volatility aren't very accurate and I believe an edge can be obtained by being a better forecaster of volatility and I believe such analysis can help traders make better option trading decisions and not be stuck in a permanent buy or sell paradigm.

1 comment:

  1. The given information is very relevant to all the viewers who relates with trading and those who invest capital in share market.