Interpreting High Sharpe Ratios in Low-Frequency Equity Strategies

# How high of a Sharpe ratio is implausibly high for a low-frequency equity strategy?


# How high of a Sharpe ratio is implausibly high for a low-frequency equity strategy?












I am looking to convince someone that an annualized Sharpe Ratio of 7 is 'extremely high' for a low frequency (daily rebalancing, say) long-short technical strategy on U.S. equities. I was hoping for a published source (preferably a journal article or conference paper) that either

- Provides a scale for interpreting Sharpe (e.g. "> 1 is good, > 2 is excellent, ... "), based on observed Sharpe ratios of, say, active managers, or some such. (I can imagine this being rejected as "biased" or "underinformed")

- Preferrably, presents statistics on achieved Sharpe ratios of Hedge Funds and other active managers, perhaps by strategy class, with long-ish histories, even with some back-fill bias, that would allow one to estimate what quantile a given Sharpe ratio would fall at. (e.g. "the cutoff for top 1% of Convertible Arb. funds achieved Sharpe is 1.5" (I am making that up.))

edit: I reiterate that I have no doubts the number is bogus, but am trying to convince someone else, someone without much market experience, that this is way outside of normal.

## Answer by Matt Wolf (score 12)

https://quant.stackexchange.com/a/3881

Here are couple references. Especially the first link to Andy Lo's paper contains a list of Sharpe ratios of popular mutual and hedge funds:

The Statistics of Sharpe Ratios

Dow Jones Credit Suisse Hedge Fund Index

Generalized Sharpe Ratios and Portfolio Performance Evaluation

I would go with the first paper.

## Answer by Ryogi (score 11)

https://quant.stackexchange.com/a/3883

The answer your are looking for might be the story in "Benchmarking Measures of Investment Performance with Perfect-Foresight and Bankrupt Asset Allocation Strategies", by Grauer (Journal of Portfolio Management).

While this work main concerns are the differential ranking of various performance measures and with negative betas for market timing strategies, its analysis of perfect foresight allocation is relevant to the point you want to make.

The punch line is that even perfect foresight strategies that grow an investment more than trillion-fold over ~60 years have a sharpe ratio that is barely in excess of 1.

The table below describes summarily the low frequency strategies considered (I believe monthly, but it might be quarterly) and reports the wealth accumulated from 1934 to 1999 assuming an initial investment of 1 dollar.

Some selected performance measures for this strategies are in the next table:

The "Industry No Margin" perfect foresight strategy multiplies the initial investment by a factor of $\mathbf{1.4x10^{14}}$ over 65 years, yet it achieves a Sharp ratio of 1.14.

These observations don't settle the question, but they should instill enough doubts about any claim of a 7+ sharpe ratio for a low frequency strategies.

## Answer by vanguard2k (score 5)

https://quant.stackexchange.com/a/3882

I would even stick to the original paper by Sharpe (1966):

Mutual Fund Performance. The Journal of Business Vol. 39, No. 1, Part 2 pp.119--138

If you look at the numbers on Page 6 you can see that the funds sharpe ratios roughly are between $0$ and $1$.

Since the Sharpe ratio already adjusts for the risk-free rate, you cannot really argue about its change. And if you do, you have to take into account that markets have become more efficient since 1966 (computers) so one would suspect the Sharpe ratio to have a tendency to be lower.

If you know facts about the calculation methodology of the backtest (which timeseries are involved) you could also look for signs of bias (look-ahead?) or to re-calculate the strategy for yourself.

## Answer by arithmetic (score 4)

https://quant.stackexchange.com/a/4018

Pardon the lack of an actual link, and the formatting, but in footnote 6 of "Alpha is Volatility times IC times Score", Grinold, Richard C., Journal of Portfolio Management, Summer 1994 v20 n4 p9(8), Grinold suggests that "a truly outstanding manager" might have an information ratio of 1.33:

(6) A rough guideline for determining the required IC comes from Grinold !1989^. If you have N stocks, then a truly outstanding manager who has an information ratio of IR = 1.33 (corresponding to a t-stat of 3 over five years) will need an IC (for each stock!) given approximately by IC = {IR}/!(# of Stocks).sup.1/2^ = 1.33/!(500).sup.1/2^ = 0.06. Top quartile might have (let's be generous) an information ratio of IR = 0.90 (t-stat of 2 over five years); thus the IC of 0.04 = 0.9/!(500).sup.1/2^. These numbers are rough guidelines. The guideline can tell us that for 500 stocks and a quality manager ICs of 0.3 or 0.001 are out of range. The rough guideline will not help us tell if 0.03 or 0.04 is a better choice.

## Answer by valerio (score 4)

https://quant.stackexchange.com/a/4624

Perhaps check out Poti and Levich (2009), or in a different setting but from one of the same authors, Poti and Wang (2010) "The coskewness puzzle" in JBF. They directly address the issue of what level of SR is plausible.

## Answer by pyCthon (score 2)

https://quant.stackexchange.com/a/3887

This is a very common and serious problem among academic papers and with some hedge fund marketing materials, I can almost guarantee that the high ratio of 7 was without transaction costs and that when these are included this 7 will drop down somewhere between 0 and 1.