A common metric used to measure a bond's price volatility is called duration.
Duration is a relatively simple concept but very difficult to manually calculate. Many bond pricing services provide duration information. The duration measure will predict how much a bond's price should change given a 1% point change in interest rates. Thus, a bond with a duration of 8, will decrease 8% in price if yields rise by 1%. For example, if interest rates rise from 6% to 7%, an investor holding a 6% bond priced at 100 will see the price of that bond drop by 8% to 92. So the duration measure is an important consideration to investors assembling a portfolio of bonds, since often times these bonds are not held to maturity, either due to portfolio re-balancing or active strategic management of the portfolio.
To understand duration and its implications, one must understand the price-yield curve, which basically states that as yields fall, bond prices rise and vice versa. However, at low yields, prices rise at an increasing rate as yields fall and at higher yields prices fall at a decreasing rate as yields rise. This price behavior creates a familiar looking convex shaped curve called the price/yield curve. See illustration below.
So, the duration formula estimates a bond's movement along the price-yield curve. However, the duration formula is only a linear approximation of movement along the curve. It follows that for large swings in interest rates, the duration formula will consistently underestimate the amount of price movement associated with a large increase in rates. Conversely, duration overestimates the price decline associated with a large upward move in interest rates. How do bond investors account for the discrepancy? A measure called convexity accounts for the additional price movements associated with changes in interest rates.
The convexity formula is the second derivative of the price-yield line and therefore accounts for the curvature of the line. So as duration measures the change in prices accompanied by changes in interest rates, the convexity formula measures the rate of change of duration as interest rates change, fully accounting for the dynamic relationship between prices and rates.
So what does all this mean to bond investors? A few simple rules of thumb will help clear things up.
1) With all other things held constant, the lower the coupon rate, the greater the bond's duration (i.e. more cash flows later in the life of the bond), thus the greater the sensitivity to changes in rates.
2) With all other things held constant, the longer a bond's maturity, the greater the duration measure, and thus greater price volatility. This is intuitive since a longer stream of cash flows would be more sensitive to changes in rates since most of a bond's yield to maturity is composed of the reinvested coupon payments.
3) With respect to convexity, the lower the coupon rate, the higher the convexity. Thus zero coupon bonds have greater convexity than coupon bonds of the same maturity, and greater price sensitivity. Since zeros pay no coupon, these issues are the most volatile as the future lump sum value is highly sensitive to changes in current interest rates through the bond discounting formula. Coupons provide a stream of cash flow, thereby lowering the duration and the price sensitivity of the bond.
So when investing in bonds, investors prefer issues with high convexity values, all other things held equal. Greater convexity accelerates price gains and slows price losses. Of course, bonds with higher convexity are priced higher than similar low convexity issues. Therefore, if investors expect increased rate volatility, high convexity bonds will increase in price over low convexity bonds.
The concept of convexity is also important in hedging. If hedging a portfolio of bonds, investors prefer instruments with less convexity than the target portfolio. This is because you are short the hedging instrument and will experience less volatile pricing in terms of adverse interest rate movements.
All of these factors, as well as many more complexities of more exotic fixed income instruments can be actively utilized by professional bond fund managers. In reality, unless individuals have substantial amounts of money to invest, bond funds are usually the best vehicle to consider.
