Beta-Arbitrage Strategies: when do they work, and why ?

Contrary to what traditional asset pricing would imply, a strategy that bets against beta, i.e. long in low beta stocks and short in high beta stocks, tends to out-perform the market. This puzzling empirical fact can be explained through the concept of relative arbitrage. Considering a market in which diversity is maintained, i.e. no single stock can dominate the entire market, we show that beta-arbitrage strategies out-perform the market portfolio with unit probability in finite time. We use the theoretical decomposition of beta-arbitrage excess return to provide empirical support to our explanation on equity country indices, equity sectors and individual stocks. Finally we show how to construct optimal beta-arbitrage strategies that maximize the expected return relative to a given benchmark