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Volatility Does Not Equal Risk

Real risk is not the danger of prices moving, but the danger of prices moving suddenly and permanently downward

Erik Kobayashi-Solomon 2 June, 2011 | 1:03PM

Read more from Morningstar's Managing Risk Week here.

In modern financial theory, volatility is taken to be equivalent to risk. However, I believe it is more helpful to think of volatility as simply "sudden price movement," since this phrase removes some of the emotional connotations implied by "risk" and is actually more accurate in terms of the underlying mathematics.

Case in point: When I was working as the risk manager for a hedge fund, a fund-of-funds came to interview my portfolio manager and to take statistics of our performance. Funds-of-funds usually try to figure out which hedge fund would be good to place customer assets by looking at funds' historical performance and trying to draw conclusions about future performance from that data.

About a week later, a manager at the fund-of-funds called my portfolio manager and said, "We like your performance, but the volatility of returns is pretty high, and we are looking for a fund with lower risk profiles." I spent less than five minutes with the performance data and after massaging it a bit, managed to significantly lower the risk of the fund on a pro-forma basis. I told my portfolio manager, who happily called the fund-of-funds back with a potential solution.

That solution involved pretending that each day our fund had truly exceptional performance, the fund-of-funds client would not receive that day's performance, but instead be credited with a daily return of 0%. My portfolio manager mentioned that he would be happy to keep that day's worth of the client's return. Simply by removing all of the very large upward moves in the fund's net asset value, we were able to keep a good portion of our returns, but drop our statistical volatility significantly!

The reason this solution worked to reduce "risk" in the mind of the fund-of-funds analyst was because the fund-of-funds was used to thinking of "large stock price movements" as if they were equivalent to "risk." This is despite the fact that, if you are long a stock, a large price movement to the upside is not risk, but return!

As investors who are long a stock or asset, rising prices are not something to worry about. Risk, from a practical investing sense, means not the danger of prices moving, but the danger of prices moving suddenly and permanently downward. However, in terms of modern financial theory, risk is taken to mean rapid price movements in either direction. (One reason for this strange definition of risk in the mind of financial theorists is linked to the underlying assumption that stock prices are random. A large move to the upside implies that a large move to the downside has an equal chance of occurring. In my cynical view, the other reason for this strange definition of risk is because the mathematics involved in measuring risk the way investors really do--i.e., the threat of a sudden and permanent downward price movement--is very difficult and not nearly as powerful and elegant as the much less useful method used.)

While this may seem like nothing more than a linguistic nuance, the practical implications of this difference when investing in options is very important and gives rise to many important option investing opportunities, which we will discuss more below.

Two Types of Volatility
Once you understand that volatility does not mean risk, the next thing to be clear about is the difference between the two "types" of volatility:

1. Statistical (or Historical) Volatility

2. Implied Volatility

Implied volatility is the number that goes into option pricing formulas, so it has the greatest direct influence on option prices. However, statistical volatility usually influences option pricing indirectly through investor psychology. Both measures are usually quoted on a per year basis.

Statistical volatility is a purely descriptive data point that is simply a measure of how large of a periodic (usually daily) price movement a stock has had over the previous year. Here is a graph of the statistical volatility of Procter & Gamble (PG) over the last year (orange line) along with the price history (blue line) on which the volatility calculations were made.

In this graph, we can see that P&G's stock price has increased by about 8% since May 2010 while its statistical volatility fell about 25% over this same period. In the year before we started calculating the statistical volatility (May 2009-May 2010) the stock price increased by around 28%. The beginning values for statistical volatility are higher than the later ones simply because the daily change in price during that first year were larger than those in the second.

The closing statistical volatility value of 13.35% means that if the stock fluctuated as much over the next year as it did on average over the last year, it would fluctuate in a band of 13.35% around the forward price of the stock through May 2012. (The forward price of a stock is simply the stock's price increased at the risk-free rate and decreased by any dividends.)

Statistical volatility is a simple, descriptive measure, but the assumptions underlying it form the basis of implied volatility, which is a predictive measure.

Let's take a look at a glaring weakness of statistical volatility in terms of saying something sensible about stock prices.

First a question: If you heard that a stock was priced at $100 and that its volatility over the next 60 days was going to be close to 0% per annum, at what price would you say the stock would be trading at the end of the 60-day period?

Would you be surprised if I said the stock would be trading at $160? Take a look at this chart:

Here, I made Asset 1 (the dark blue line) increase by $1 a day for 60 days. Since it started at $100 a share, the first day increase was 1%, and it was less each day. Its average annualized volatility over this short period averaged 0.16%--nearly zero! The reason that the volatility is so low is that the increase is slow and gradual (in fact, I could have made the volatility precisely zero by increasing the price by 1% per day).

The light blue line is Asset 2, which I also started out at $100 and which ended up at the same price as Asset 1 ($160), but which made a great many ups and downs between start and finish. Any idea what that statistical volatility came out to be? Around 350% per annum!

Note, though, that both of these assets started and finished at the same price. If you were an investor who checked your account once every 60 days and just saw the price changes, you would say these two assets were just the same. What this says is that the statistical volatility of a stock is not directly related to the stock's increase in price, only to the amount of daily variation in the stock's price.

Here is something else to blow your mind a bit:

This time, I decreased the price of Asset 1 by $1 each day. This meant that the first day's percentage decline was 1% and it increased after that. Even with this dog of an investment, which lost 60% of its value over 60 trading days, the average statistical volatility for this asset was only 0.63% (it was higher in this example because the daily percentage change grew over time rather than decreasing like in the first example).

Again, we see that volatility does not have to do with the stock increasing or decreasing, but only with the amount of wobbling it does from day to day. In fact, the higher volatility stock rose significantly over a short period of time, while the lower volatility stock consistently fell.

With both examples--the consistently increasing price and the consistently decreasing one--we can see the huge problem underlying the calculation of volatility: It is non-directional and in fact implicitly assumes that prices are as likely to move up as they are to move down.

Erik Kobayashi-Solomon is co-editor of the Morningstar OptionInvestor online newsletter and research service, and is co-author of the Morningstar Investor Training course on Option Investing. For more about Morningstar's fundamental approach to investing in options, please use the link below to download our free guide to option investing: http://option.morningstar.com/OptionReg/OptionFreeDL1.aspx

The information contained within is for educational and informational purposes ONLY. It is not intended nor should it be considered an invitation or inducement to buy or sell a security or securities noted within nor should it be viewed as a communication intended to persuade or incite you to buy or sell security or securities noted within. Any commentary provided is the opinion of the author and should not be considered a personalised recommendation. The information contained within should not be a person's sole basis for making an investment decision. Please contact your financial professional before making an investment decision.

About Author

Erik Kobayashi-Solomon  is a market strategist and co-editor of the Morningstar OptionInvestor newsletter.