Moving Beyond the Fear
Calling implied volatility a fear gauge is only telling half of the story.
Investing Specialists
The implied volatility of the stock market is typically described as the "market fear gauge." But calling implied volatility a fear gauge is only telling half of the story. Whether volatility is measured using the Chicago Board of Options Exchange VIX or the Morningstar Volatility Index MVI, volatility is not simply a gauge of fear but also a gauge of opportunity.
Although it is true that implied volatility typically spikes when market prices fall, implied volatility is actually a measure of uncertainty about the future, including both the fear about the downside and the opportunity to the upside. Gaining an intuitive grasp of this concept is essential to understanding what the option market is telling you about the market's perceptions of the future.
A Tale of Two Tickers
As a simplified example, let's think about two stocks, tickers ABC and XYZ. Let's say both are trading at $50 with 50 strike one-year options available, but they have differing ranges of possible future value. What are the options worth on each of these companies?
ABC
- 50%/50% chance of either $45 or $55
- Call option is worth 50% * ($55-$50) = $2.50
- Plugging $2.50 into the Black-Scholes-Merton Model:
Implied volatility = 10%
XYZ
- 50%/50% chance of either $25 or $75
- Call option is worth 50% * ($75-$50) = $12.50
- Plugging $12.50 into the Black-Scholes-Merton Model:
Implied volatility = 60%
Since XYZ is expected to swing to either $25 or $75 by the end of the year, it is clearly more uncertain than boring old ABC, which is only expected to swing between $45 and $55. The implied volatility of the options on XYZ is 60% not because there is more fear about the future of XYZ, but because there is more uncertainty about the future! The added downside is paired with added upside.
Getting the Picture
To me, uncertainty is much more intuitive when displayed graphically. A graphical display can translate implied volatility to real world numbers that I can understand and compare to stock or index prices--which are much more intuitive than an implied volatility number used in isolation.
Below is a graphical illustration of the future probabilities for company ABC discussed above, or a "probability distribution" for the outcomes of company ABC.
Clearly, stocks don't behave this way in the real world, with simple upside and downside outcomes. However, we can extend the principle and add outcomes and probabilities as shown below:
In the second probability distribution, most of the outcomes are clustered closely around the current price, so there is less uncertainty about the future, therefore lower implied volatility. Valuing a 50 strike one year call option using our simple option pricing math from above:
[(52.50 � 50) * 0.4] + [(55-50) * 0.1] = $1.50.
Calculating the implied volatility for the call option produces a number of 7.5%, down dramatically from the 60% volatility of the first calls because the outcomes are clustered more closely to the current stock price. As we add more and more prices and probabilities, we approach a continuous probability distribution that better represents the typical distribution of stock prices over time as shown below:
The current stock price is the balance point of this distribution, or the "expected value" of the distribution. Implied volatility is just a way of measuring the width of this distribution. The distribution shape shown here is called log-normal, and it is the distribution shape assumed by the Black-Scholes model that is used to price options and to calculate implied volatility.
Just to hammer the point home, implied volatility is the measure of the width of the probability distribution around the stock price, or the uncertainty around the stock price, as show below. The higher the uncertainty as measured by implied volatility, the wider and flatter the probability distribution.
The above graphic shows a spike in the VIX or MVI, assuming the market price doesn't change. Uncertainty about the future has risen and both fear to the downside and opportunity to the upside have increased. Conversely, a drop in implied volatility or uncertainty would be represented by a probability distribution getting narrower and higher.
In the real world, this is actually how implied volatility works. News that causes fear about the future relative to what was already expected also causes an increase in implied volatility until that fear is resolved. Similarly, news that may imply opportunity also causes an increase in implied volatility.
Up, Down, Or Sideways, Just Tell Me What You're Thinking
Let's take a simple real world example. Uncertainty typically rises ahead of Federal Reserve interest rate announcements because interest rates impact economic activity, which impacts earnings and stock prices of companies listed on the stock exchange. While there are exceptions, generally lower interest rates are considered bullish, and higher rates are bearish.
Let's say the Fed is expected to hold rates steady at the next announcement, but there is a chance that it will either raise or lower rates by 25 basis points. Implied volatility will generally rise ahead of the announcement. After the announcement, if the Fed holds rates steady, as expected, the market won't move, but implied volatility will fall because the uncertainty about what the Fed will do is lower.
However, if the Fed lowers rates in a surprise move, the market will rise because the outcome is more bullish than expected, and implied volatility for the market will fall, because there is less uncertainty.
Finally, if the Fed surprises and raises rates, the market will fall and implied volatility will still fall because there is less uncertainty.
The point is, knowing there is an upcoming source of uncertainty about the future raises implied volatility, and eliminating that source of uncertainty lowers implied volatility, regardless of the bullish, neutral, or bearish implications of the outcome.
Why the Fear Gauge?
So why does implied volatility seem to spike when the market falls? There are a few factors at work. Usually, market declines come on surprise negative news, and on unexpected news events--and the uncertainty remains until the issue is resolved completely. Negative news that has a quick impact, like our Fed example, is not usually the driver of major declines in market prices. Think of it this way: When economic conditions are good, stable, and improving, nobody is asking when the next recession will happen, but when economic conditions are terrible, everybody is wondering when the recession will end. The end of the recession is a more likely and more imminent source of uncertainty than the end of the boom.
Another reason is that investors demand compensation for risk, so as news arrives that makes the world more uncertain, implied volatility increases. Because investors require more return from their investments when risk increases, prices today need to be lower, all else being equal, to generate the required return. Therefore, increasing uncertainty causes stocks to fall, not the other way around.
Yet another reason is that volatility begets volatility. Just as the temperature today is a better estimate of the temperature tomorrow than the average temperature over the last year, the volatility today is a good predictor of volatility tomorrow, at least in the short term. Downward movements tend to be sharper than upward movements, increasing current volatility, which increases the prediction of future volatility.
Finally, there is the common "buying insurance" argument. As the theory goes, when the market falls, investors flock to puts to buy insurance. The thing to keep in mind when evaluating this argument is that put-call no-arbitrage principles increase implied volatility as well as increasing upside uncertainty, so "opportunity" becomes more expensive at the same time that "insurance" becomes more expensive.
So, when thinking about the uncertainty gauge, remember that fear may come with opportunity.
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