# How is the volatility of a bond measured?

The volatility of a bond price arises from the fluctuation of the interest rates. The volatility of a bond is given by duration and its yield to maturity (YTM). The formula for volatility is given below

$$Volatility = \frac{Duration}{1 + YTM}$$

## Price Volatility

Price volatility is represented by percentage bond price change divided by changes in interest rate which is given by $\frac{(𝜕𝑃⁄𝑃)}{𝜕𝑦}$, where is the period required for yield.

The degree of volatility is given by the absolute value of $\frac{(𝜕𝑃⁄𝑃)}{𝜕𝑦}$. So, a bond with $\frac{(𝜕𝑃⁄𝑃)}{𝜕𝑦}= −200$ is more volatile than one that had a $\frac{(𝜕𝑃⁄𝑃)}{𝜕𝑦}$ value of 100. The sign of the degree of volatility gives the direction of the interest rate change. It shows the price change with respect to interest rate changes. It can also be deciphered easily that for $\frac{(𝜕𝑃⁄𝑃)}{𝜕𝑦}$ < 0is applicable to bonds without embedded options.

Volatility is called Modified Duration, as mathematically it shows similarity to Macaulay Duration (or simply Duration). Both Macaulay and Modified Durations are expressed in years and they are calculated utilizing the price coupon rate and maturity of the bond.

Note − Volatility is also known as duration because it acts like Macaulay duration or simply the duration of a bond.

## Modified Duration and Investing

It is easy to find the modified duration of a debt fund in its monthly fact sheet. Usually, the issuers of bonds publish the facts related to bonds for the investors to keep them updated about the bond performance. Low modified duration bonds are good for low risk-taking investors. It is a general rule of investing that as the duration goes up the interest rates come down.

If the investor thinks that interest rates will come down in the future, then they should go for a higher modified duration. Investors with a higher risk appetite can go for bonds with a duration of more than 5 years. Investors with a moderate risk appetite should go for moderate interest-offering debt funds with the duration of 3 to 5 years.

Note − The ideas of modified duration can be used in investment. The duration should go up and down for higher risk-taking and lower risk-taking investors respectively.