Rajiv Sethi: Risk and Reward in High Frequency Trading: "These are interesting findings, but there is a serious problem with this interpretation of risk-adjusted performance. The authors are observing only a partial portfolio for each firm, and cannot therefore determine the firm's overall risk exposure. It is extremely likely that these firms are trading simultaneously in many markets, in which case their exposure to risk in one market may be amplified or offset by their exposures elsewhere. The Sharpe ratio is meaningful only when applied to a firm's entire portfolio, not to any of its individual components. For instance, it is possible to construct a low risk portfolio with a high Sharpe ratio that is composed of several high risk components, each of which has a low Sharpe ratio."
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