BOSTON (TheStreet) -- Stocks have rebounded after bottoming a year ago, but weary investors are still putting more money into bonds. Unfortunately, many of them lack the tools to pick the right issues.Last week, we discussed how investors could use duration to gauge a bond's sensitivity to interest rates. Duration can help investors determine the price change for a bond when there's a small parallel shift in the yield curve. However, a measure based on duration isn't exact because the price-to-yield curve isn't a straight line. Here's where "convexity" can help. Duration and convexity can help investors pick bonds that match their interest rate assumptions. Investors who are trying to anticipate rising interest rates should seek bonds with short duration and high convexity. Convexity measures the curve of the price-to-yield line. A more curved line will make a bond's price move less when interest rates change. Using these metrics requires some low-level calculus. Duration is the first derivative of the price-to-yield curve, meaning that it's the rate of change for a given point. Convexity is the second derivative of the same point, meaning that it is the rate of change of the rate of change. The graph below shows the duration and convexity of a 10-year Treasury note. The duration is a straight line touching the price-to-yield curve at the current price. The duration estimates the bond's price accurately when the changes in interest rates are small. When the charges are large, duration becomes a less reliable price gauge. Convexity adjusts for the curvature of the price-to-yield curve to generate an accurate price.
After the price changes are calculated, the following formula will give the bond's convexity: (Price for a negative 100-basis-point yield change + Price for a positive 100-basis-point yield change - 2 x Current Price) / (2 x 0.01^2 x Current Price) Bonds with similar durations can have different convexities. Procter & Gamble ( PG), Berkshire Hathaway ( BRK.B) and Pfizer ( PFE) have bonds with AA- ratings that mature in eight years with similar coupon payments, but the convexity for Berkshire and Pfizer is 26.3, while Procter & Gamble's bond has a duration of 24.1. This suggests that Pfizer and Berkshire Hathaway will see their prices change less for a given change in the yield curve than will Procter & Gamble. Risk-averse investors should buy the bonds with higher convexity, while those who expect interest rates to fall should consider Proctor & Gamble bonds because they stand to appreciate more if rates decrease. The difference can be far more drastic than that. General Electric ( GE) and Wal-Mart ( WMT) offer long-term bonds with AA ratings, but the Wal-Mart bonds have convexity of 32 while the GE bonds have convexity of 24. Investors interested in bonds should use duration and convexity to build a portfolio that matches their risk tolerance. These concepts are more complicated than typical stock metrics, but they may prove invaluable if you're trying to anticipate the direction of interest rates. -- Reported by David MacDougall in Boston.