Alpha Representation for Active Portfolio Management and High Frequency Trading in Seemingly Efficient Markets

We introduce a trade strategy representation theorem for performance measurement and portable alpha in high frequency trading, by embedding a robust trading algorithm that describe portfolio manager market timing behavior, in a canonical multifactor asset pricing model. First, we present a spectral test for market timing based on behavioral transformation of the hedge factors design matrix. Second, we find that the typical trade strategy process is a local martingale with a background driving Brownian bridge that mimics portfolio manager price reversal strategies. Third, we show that equilibrium asset pricing models like the CAPM exists on a set with P-measure zero. So that excess returns, i.e. positive alpha, relative to a benchmark index is robust to no arbitrage pricing in turbulent capital markets. Fourth, the path properties of alpha are such that it is positive between suitably chosen stopping times for trading. Fifth, we demonstrate how, and why, econometric tests of portfolio performance tend to under report positive alpha