The Effect of Bond Convexity in Abnormal Volatility

Abstract

According to earlier empirical studies, convexity in the U.S. treasury market is arbitrage-free priced. This paper study whether the arbitrage-free pricing of convexity held even in the financial crisis and the volatile period that followed.

A fixed-income investor must consider interest rate exposure since it is the factor affecting the value of the security the most. This direct relationship can be shown in the negative correlation between interest rates and price; if rates decline prices increase. The shape of this price-yield relationship is more or less convex for individual bonds. Theory suggests that this convex property is desirable for investors experiencing yield shifts in the market. However, no return enhancing aspect of convexity has been found in empirical studies before, which proposes convexity to be arbitrage-free priced. By analyzing U.S. treasury bonds in the volatile interest rate period of 2007-2012, we extend earlier research of convexity’s impact on bond returns.

Our regression results show no significant effects of convexity generating excess returns. The tests are based on yearly data from 2007-2012 and monthly data from 2008-2009, respectively. Results for entire periods show no positive significant results, neither for the yearly or monthly datasets. When analyzed period-by-period significant effects of convexity are found, but with just as many results showing negative effects on returns as positive. Implications of these results are that convexity is priced by the market, sometimes even over-priced, and higher convexity is thereby not consistent with excess returns for longer periods. Hence, our findings strengthen earlier research and conclude that convexity does not generate excess returns, even in the most volatile periods.