Sharpe Ratio for strategies with different rebalancing period

Strategies published in journal papers like SMB, HML, UMD have annualized sharpe ratios around 0.5. These long-short portfolios are formed with monthly rebalance. People who backtest some daily rebalancing strategies usually claim annualized sharpe ratio that is above imaginable like above 3. How is this frequency of trading affect this? From what I can recall, if returns are iid, one can simply multiply your sample average daily return over sample daily standard deviation of your return by $\sqrt{365}$ to get the annualized shape. Mean grows as horizon increases at a speed of T, and std grows at speed of sqrt T. That is where this number come from.

Is it fair to compare strategies with different rebalancing period by sharpe ratio? How come a strategy that is backtested to perform this well exist, assuming there is some rationale behind it not just pure data mining?

2 Answers

It is true that strategies with higher trading frequencies have Sharpe ratios that appear implausibly high by the standards of Fama-French factors. The strong law of large numbers really helps them, as they realize profits repeatedly while not increasing the standard deviation very quickly.

The real barriers to entry for them are the costs that traditionally don't make it into Sharpe calculations. FPGA programmers don't work for free!

I tend to think of this as something like a law firm, where there's not necessarily any capital to speak of so the return on capital is "nearly infinite". It doesn't mean that, as a business, the enterprise is infinitely profitable.

One very basic reason why one can't compare Sharpe ratios with different rebalancing (trading?) timeframes is in the way they calculate SR: the numerator is proportional to $N$ while denominator is proportional to $\sqrt(N)$. By increasing the frequency over which returns are averaged and annual volatility is calculated one inflates SR by a factor of $\sqrt(N)$. This is a well known trick in the industry so full disclosure is necessary for comparability.