Convergence of Expected Returns through Arbitrage: Beta Is Indifferent to Equity Valuation

Abstract

The CAPM is commonly used for an introduction of the equity cost in practice to calculate the corporate value, which is composed by the risk-free rate, equity market return and each respective beta. However, there is a fundamental complication between the risk, cost and return for the equity valuation. In the fixed income investment, the excess risk is basically derived from the default probability, which corresponds to the excess cost and return onto the risk-free rate. On the other hand, the volatility is one of the compositions of equity cost, which is indifferent to the equity return. Theoretically, the return should match to the cost, which is not the case for the equity cost, as it represents the equity risk, not actually the cost. This confusion has to dissipate with arbitrage at the market where the short selling is institutionalized or the index future is easily available. When there is a difference of expected returns, it should be monetized through the arbitrage, which recurs to dissipate all the differences; i.e. the expected returns must be converged to the single rate and we can ignore the beta as a component of the equity cost. The arbitrage results in valuation differences in the end, such as P/E difference for each stock, though there should be short-term windows for the expected return deviation when the stock prices drop unexpectedly with some corporate events to provide return opportunities until narrowing down the gap of expected returns. The future information is always imperfect and the cost cannot indicate the future return in the equity market, therefore the converged expected return is the best effort at the spot through the market mechanism. There is no convergence across asset classes, mainly due to their low correlation, and the long-short strategy beyond the classes does not represent arbitrage, but a risky trade.