Alpha Representation For Active Portfolio Management and High Frequency Trading In Seemingly Efficient Markets

摘要

We introduce a trade strategy representation theorem for performancemeasurement and portable alpha in high frequency trading, by embedding a robusttrading algorithm that describe portfolio manager market timing behavior, in acanonical multifactor asset pricing model. First, we present a spectral testfor market timing based on behavioral transformation of the hedge factorsdesign matrix. Second, we find that the typical trade strategy process is alocal martingale with a background driving Brownian bridge that mimicsportfolio manager price reversal strategies. Third, we show that equilibriumasset pricing models like the CAPM exists on a set with P-measure zero. So thatexcess returns, i.e. positive alpha, relative to a benchmark index is robust tono arbitrage pricing in turbulent capital markets. Fourth, the path propertiesof alpha are such that it is positive between suitably chosen stopping timesfor trading. Fifth, we demonstrate how, and why, econometric tests of portfolioperformance tend to under report positive alpha.