A Proof of the Outperformance of Beta Arbitrage Strategies

By modeling asset returns via Brownian processes, we construct dynamic portfolios whose weights, relative to the market portfolio, are inflated (respectively, deflated) depending on high (respectively, low) levels of ex-ante beta for the corresponding assets. We establish under mild conditions that these portfolios are dominated by the market portfolio in finite time almost surely. Our result proves the out-performance potential of beta arbitrage strategies, which tilt portfolios towards low-beta holdings and away from high-beta holdings. Such strategies have recently been the subject of considerable interest in the financial community