Bonds are an important component of many investment portfolios. The value of a bond is based on the interest earned over the bond's maturity period and the final payout at maturity. Bond prices change with changes in market interest rates. When interest rates rise above the bond's coupon rate (i.e., the annual interest payment to the bondholder), the bond becomes less attractive, its value decreases, and vice versa. Bond duration and convexity influence these prices.
A bond's duration approximates how long it takes for investors to recover their initial investment. Macaulay and modified duration are key measures of bond price sensitivity to interest changes. Macaulay duration measures the average time it takes to receive cash flows from a bond, weighted by present value and bond price. It is useful for portfolio managers who use an immunization strategy to protect their portfolio's value against interest rate changes. On the other hand, modified duration is an extension of the Macaulay duration and measures a bond's price sensitivity to interest rate changes.
Duration is important for fixed-income investors as it affects returns. Bonds with longer durations tend to perform well when interest rates fall, but their value declines as interest rates rise. Investors need to understand the duration of their bond investments, whether individual bonds or bond funds, to prepare for the potential benefits and risks of holding long-duration fixed-income securities.
Convexity is another important metric that affects bond prices. It measures how sensitive a bond's duration is to changes in its yield. As yield changes, duration also changes. Convexity helps assess the potential price changes of bonds that experience significant fluctuations in interest rates. It helps correct the linear duration assumption and accurately measures bond price changes. To calculate a bond's convexity, one must consider the bond's current market price, the Macaulay duration, and the bond's current yield to maturity.
A bond with positive convexity (when duration increases as yield decreases) will experience larger price surges when yields fall than price declines when yields rise. This can benefit investors since they offer more potential for capital appreciation when interest rates move in their favor. Conversely, a bond with negative convexity will exhibit the reverse pattern, with duration increasing as yields rise, which may work against the investor's best interest. Generally, the greater the bond's convexity, the less sensitive it is to changes in its yield to maturity.
Bond investors use modified duration and convexity to measure the risk of interest rate changes on bond prices. Modified duration predicts how bond prices will change with small interest rate shifts, while convexity measures how bond prices will change with larger shifts. Additionally, convexity helps measure the effect of interest rate changes on the bond portfolio's value.
When investing in bonds, duration is a key metric for short-term holdings since it projects the potential impact of small changes in interest rates. However, for medium-term bond holdings exposed to the risk of large interest rate changes, convexity is more important since it measures a bond's price sensitivity to interest rate changes. This helps to inform investment strategy and plan positions around interest rate forecasts.
