Diffusing explosive portfolio performance evaluation of high frequency traders

ABSTRACT Several analysts report explosive annualized Sharpe ratios (ASRs) for investment portfolio performance evaluation of high frequency traders (HFTers) ranging from 4.3 to 5000. This suggests that the profitability of high frequency trading (HFT) is much higher than that of other actively managed portfolios. In highly competitive financial markets where ASRs for experienced traders are often much less than 2, those numbers imply that the ASR for HFT is misspecified. Thus, HFT performance is incomparable to the performance of experienced traders, hedge funds and other actively managed portfolios. This paper addresses the misspecification problem by introducing an efficient Sharpe ratio (ESR) that diffuses explosive ASRs for HFT so that they are comparable to SRs for other actively managed funds. We derive a subordinate stochastic process for HFT strategy that jumps positively only when the trader executes a successful trade and otherwise stays flat. And we use that process to construct an SR deflator for ESR. We apply the ESR formula to a sample of risk and return data on HFT strategy, and find that the ESR for aggressive HFT is 1.15, medium HFT is 2.88, and passive HFT is 1.43. For the HFT industry as a whole the ESR is between 1.07 and 1.87. Those ESRs for HFT are equivalent to SRs reported for experienced traders, hedge funds multistrategy, convertible option arbitrage, and fund-of-fund strategies. Thus, contrary to reports, the profitability of HFT is in line with industry norms for active portfolio management.