QQ 102, 2 min read
The Sharpe ratio
After this lesson you can
- Compute and annualise a Sharpe ratio
- Spot three ways the number gets inflated
- Know what to check before comparing two Sharpe ratios
The Sharpe ratio asks how much return you were paid for each unit of volatility.
Sharpe = (mean return - risk-free rate) / standard deviation of returns
Measured on daily returns it is a daily number. It is annualised the same way as volatility:
annual Sharpe = daily Sharpe x square root of 252
A Sharpe of 1 means the average excess return equals the volatility. Higher is better, all else equal.
Three ways the number gets inflated
The risk-free rate is left out. Many tools skip it. When interest rates are near zero it hardly matters. When they are 5% it matters a lot.
The wrong number of periods. Annualising hourly returns as if the market traded every hour of the year gives a larger Sharpe than counting only the hours it was open. Two tools can report different Sharpe ratios for the same trades for this reason alone.
It was picked from many. If you test a hundred variations and report the best Sharpe, that number is biased upward by the search itself. The next module covers this, and the terminal's deflated Sharpe check exists because of it.
What the terminal does
The terminal states its choices: which returns it uses, whether a risk-free rate is subtracted, and how it annualises. They are in The statistics. Read them before comparing its Sharpe with one from another tool.
What Sharpe cannot tell you
It uses standard deviation, so it inherits every blind spot from the last lesson. A strategy that collects small gains and occasionally loses a great deal can show an excellent Sharpe for years before the large loss arrives.
Key points
- Sharpe is excess return divided by volatility
- The annualisation convention changes the answer
- A Sharpe chosen from many tries is biased upward
Check your understanding
Mean daily return 0.05%, daily standard deviation 1%, risk-free rate taken as zero. What is the annualised Sharpe?
You test 100 variants and report the best Sharpe. What is wrong with that number?
Further reading
- Sharpe, W. F. (1994). "The Sharpe Ratio." Journal of Portfolio Management 21(1).
- Lo, A. W. (2002). "The Statistics of Sharpe Ratios." Financial Analysts Journal 58(4). How uncertain a measured Sharpe ratio is.
- Bailey, D. H. and Lopez de Prado, M. (2014). "The Deflated Sharpe Ratio: Correcting for Selection Bias, Backtest Overfitting, and Non-Normality." Journal of Portfolio Management 40(5).