Convexity arbitrage–the idea which does not work

Abstract

Algorithmic trading, so popular nowadays, uses many strategies that are algorithmizable and promise profitability. This research answers the question whether it is possible to successfully use a convexity arbitrage strategy in a bond portfolio in financial practice. It should provide a positive expected excess return and a small or zero potential loss. Convexity arbitrage has been described in academic literature before, but an assessment of its practical success is lacking. Arbitrage portfolio, which consists of two portfolios of bonds, is constructed theoretically and practically. These two portfolios have the same Macaulay Duration and price, but a different convexity at a certain yield to maturity point (YTM point). As the first portfolio is long, while shorting the second (with higher convexity), the result would therefore be a market-directional bet on parallel YTM shifts of the same size. Methodology: a mathematical definition of this arbitrage; the construction of the arbitrage portfolio; back-testing on USD and EUR zero-coupon yield curve. To construct the arbitrage portfolio could be unrealistic on markets with low liquidity. Moreover, the assumption of parallel YTM shifts of the same size is not fulfilled enough to ensure that the arbitrage is profitable. This research helps practitioners considering the implementation of this strategy in algorithmic trading to make an adequate assessment. Its findings show that the practical and profitable utilization of convexity arbitrage is unrealizable.