What is volatility? Like the Supreme Court justice defining obscenity, many market participants say they know volatility when they see it.

Recently, they've gotten a close-up look, as the market rode a roller coaster in the first quarter.

On a basic level, volatility the actual change in the value of a bond or the market as a whole. But the word can also mean the propensity of a given bond to change value. In that sense, volatility is used to make investment decisions consistent with investment goals, and to price a myriad of securities that contain options, including callable bonds.

The first use is the more straightforward. A bond analyst can usually look at two bonds, or two types of bonds, and figure out which is likely to be more volatile - that is, which will change more under the same conditions.

In general, a shorter maturity bond will be less volatile than a longer term bond. Higher coupon bonds will tend to be less volatile than lower coupon or zero coupon bonds.

A widely used measure of the expected volatility of a bond under changing market conditions is modified duration. The measure indicates the percentage change in the value of a given bond if interest rates rise or fall 1%.

An investor looking for low risk and steady returns would shun volatile bonds. But another investor, willing to accept more risk, might seek out a volatile bond for its higher yield.

But volatility also directly affects the value of options, according to the Black-Scholes options pricing model developed by Fischer Black and Myron Scholes. And since all callable bonds have embedded options - giving the issuer the right to buy back the bond at a preset price on a future date - changes in volatility have a broad impact on prices.

The price of an option is calculated from five variables: the price of the underlying asset, the strike price of the option, the expiration date of the option, the rate of return on a risk-free investment such as a Treasury note, and the expected volatility of the price of the underlying asset.

The higher the volatility, the more likely that the price of the asset will reach and exceed the strike price. So if volatility rises, the option will be worth more. If volatility declines, the option will worth less, all other things being equal.

The value of a callable bond is the value of an identical noncallable bond minus the value of the option that the investor has granted to the issuer. As volatility increases, the value of the option will increase, which, in turn will decrease the value of the callable bond.

Of the five variables in the option pricing model, volatility is the only one that requires making a subjective judgment. While an investor knows with certainty how much the value of a bond changed in the past, future changes are unknown.

Measures such as modified duration, for example predict how volatile a bond will be given a certain change in interest rates. But since no one knows just how much rates will change in the future, modified duration does not provide an objective input for the pricing model.

So market participants look at historical volatility to approximate future volatility.

They also "reverse engineer" the value of options. Knowing the value of the other four variables and the price of an option, an investor can solve for the volatility. When calculated in this fashion, the measure is known as implied volatility, because, its value is implied from the price of the option.

Sometimes, an investor may feel that future volatility is likely to be significantly different from the experience of the recent past. Since most options are valued using some form of historical volatility, this hunch about the future provides investment oportunities.

If volatility has been high, but the investor believes it is likely to decline, options may be overvalued. A quick check of the implied volatility of the call option in a callable bond provides a benchmark of expected future volatility.

Again, high volatility would depress the value of callable bonds. Since the investor expects future volatility to decline, and be lower than the implied volatility priced into the market, the investor might buy callable bonds. If volatility does decline, all other things being equal, the options will decrease in value and the bonds will be worth more.

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