Fixed Income Mathematics
Offering explanations, exercises, and examples without demanding sophisticated mathematics, this self-teaching book will serve as a gateway to financial mathematics and to increased competence in business analysis.
TABLE OF CONTENTS Fixed Income Mathematics
Chapter 14: 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.
WHAT IS VOLATILITY?
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.
WHY DO WE CARE ABOUT VOLATILITY?
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...
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