Volatility and Its Measures

This chapter introduces the concepts underlying the interest in duration and convexity. It covers volatility, why it is important, and how we measure it.

When you finish this chapter, you should understand the importance of volatility, the characteristics of volatility, and the three ways we measure it.


Volatility is the relative tendency of a bond price to change when the yield changes. Some bonds can clearly change more than others for a particular change of yield. For example, if a 30-year 6% bond moves from a 6% yield (a price of 100) to a 6.25% yield, the price will decline by 3.37% to a price of 96.63. A T-bill maturing in 1 week, on the other hand, will decline from a price of 99.883 to 99.878, a decline of about .005%. The 30-year bond is much more volatile than the T-bill maturing in 1 week.


Volatility can measure one kind of bond risk, or portfolio risk. By measuring risk, we can determine the risk of a bond or of a portfolio. This also means that risk is not something to be avoided; indeed, one cannot avoid risk completely in any investment. But the portfolio manager who can measure portfolio risk can also manage the portfolio's risk. The portfolio manager selects investments so as to maintain a predetermined level of risk in the portfolio.

Volatility has become much more important in bond portfolio management than it was years ago. Partly this is due to increased analytical knowledge about bond management, but also it is because bond prices are more volatile than they were years ago. This has given volatility a much greater importance than it previously had, and this volatility has also resulted in numerous articles in the press. Nowadays, bonds may fluctuate more in one day than in a whole year many years ago.

For example, on the day this discussion were written, the United States Treasury announced that is was suspending the issuance of 30-year bonds. As a result, the 30-year bond rose more than 5 points, the largest rise in 13 years. The bond rose more than 2 points the following day, but gave up most of that additional gain on the next trading day.

No one really knows the reason for the increase in bond market volatility during the past few decades. Inflation, increased bond trading, increased bond investment, and the increasing use of bond-related derivatives may all play a part. But bonds do seem much more volatile than they were a few decades ago. This volatility shows no sign of going away, so it seems to be a permanent fixture of the bond market.

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