The Value of Convexity: A Theoretical and Empirical Investigation

Quantitative Finance, Volume 18, 2018 - Issue 1

We explore from a theoretical and an empirical perspective the value of convexity in the US Treasury market. We present a quasi-model-agnostic approach that is rooted in the existence of some affine model capable of recovering with good accuracy the market yield curve and covariance matrix. As we show, at least one such model exists, and this is all we require for our results to hold. We show that, as a consequence, the theoretical ‘value of convexity’ purely depends on observable features of the yield curve, and on statistically determinable yield volatilities. We then address the question of whether the theoretical convexity is indeed correctly reflected in the shape of the yield curve. We present empirical results about the predictive power of a strategy based on the discrepancies between the theoretical and the predicted value of convexity. By looking at 30 years of data, we find that neither the strategy of being systematically long or short convexity (and immunized against ‘level’ and ‘slope’ risk) would have been profitable. However, a conditional strategy that looks at the difference between the ‘implied’ and the statistically estimated value of convexity would have identified extended periods during which the proposed approach would have delivered attractive Sharpe Ratios.

Keywords: Asset pricing, Interest rate modelling, Interest rate derivatives, Interest rates, Convexity, Affine models, Term structure models