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Volatility Potential

Is implied volatility an asset class, and if so, how can it fit into a portfolio?

Philip Guziec, 06/16/2008

In the Winter 2008 issue of Morningstar Advisor, we discussed the suitability of equity and index options for individual investor portfolios. We concluded there are many ways equity and index options could be suitable for balancing risk and cash flows, but we also mentioned that options prices as measured by implied volatility have some very unique characteristics. The characteristics of implied volatility are so unique, in fact, that some have taken to calling implied volatility an asset class. In this article, we'll discuss the unique characteristics of volatility, how to view the world in terms of implied versus realized volatility, and how implied volatility could fit into investors' portfolios.

Characteristics of Volatility
Implied volatility is simply the value plugged into an options pricing model, commonly the Black-Scholes-Merton model, to force the model to spit out the market price for the option. The actual dollar value of an option varies with a number of known variables, including strike price, duration, underlying stock price, and interest rate. Implied volatility is the only unknown variable used to determine option prices and, as such, is the measure commonly used to discuss prices of options. To develop a better intuition about implied volatility, it is helpful to return to our favorite options graphic, the probability distribution of the price of a stock.

The price of a stock is equal to the expected value of the distribution of potential prices at the expiration date for the option. As a simple example of expected value, a stock that has a 50% chance of being worth $51 and a 50% chance of being worth $49 has an expected value of $50 and a probability distribution of only two outcomes. As we increase the number of potential outcomes and probabilities, we approach a smoother probability distribution. You can think of the expected value of a stock price distribution as the point where you could place a knife edge under the distribution, and the distribution would balance perfectly. Implied volatility for an option is a measure of the width of the expected stock price distribution relative to that balance point. As we can see in figure A, with the same stock price, the distribution of potential outcomes can be wider or narrower.

Figure A: With the same expected value, probability distributions can be wider or narrower.
Click here to view the image.

Options allow us to split the probability distribution into upside and downside at a strike price, and we think of options as allowing us to buy or sell the upside or downside on an investment relative to some price, called the strike, along this distribution. If we were to sell exposure to the downside (puts) relative to the stock price and buy exposure to the upside (calls) relative to the stock price, we'd be putting the probability distribution back together, and our investment would generate the same payoff as the stock. Because this characteristic holds true regardless of the width of the probability distribution, implied volatility is theoretically completely distinct from stock price. Going back to our simple example to reinforce this concept, let's say we have two stocks with $50 value. One stock is our simple example above, which has a 50/50 chance of being $51 or $49. The second has a 50% chance of being worth zero, and a 50% chance of being worth $100. The two examples have the same expected value but the width of the probability distributions is entirely different.

To understand how implied volatility translates to option prices, let's split the distribution into its upside and downside and evaluate the options graphically in figure B.

Figure B: Options allow us to split the stock price distribution into upside and downside exposure.
Click here to view the image.

The value of each option is determined by the expected value of the upside and downside pieces of a probability distribution, rather than by the expected value of the stock. If we now balance the upside of the distribution on a knife edge, the distance between the balance point and the strike price is the expected value for the upside, and therefore the option value. If we compare the wide distribution with the narrow one, we can see in figure C how the wider distribution generates a balance point further from the strike price, so the two options have different values with the same stock price.

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