Sharpe Ratios and Performance Measures for Intraday P&L
Summary
The document discusses how to assess a market-making strategy that starts and ends each day flat, using a series of daily dollar profit and loss figures. One response says the annualized Sharpe formula based on mean and standard deviation is appropriate if the capital base stays constant and leverage does not change. It also points out that account capital provides a basis for interpreting P&L as returns.
A second response cautions that dollar P&L alone may not support a meaningful Sharpe ratio when the strategy has no defined capital basis or leverage convention. It suggests describing income with measures such as mean, standard deviation, skewness, winning-day frequency, average win relative to average loss, or profit factor. Resampling may be more useful for path-dependent measures such as maximum drawdown or recovery time. The answers differ in emphasis, underscoring that metric choice depends on capital and leverage assumptions; no empirical comparison or bootstrap study is supplied.
Key ideas
- An annualized Sharpe based on daily P&L can be used when the capital base and leverage are held constant.
- A Sharpe ratio requires a clear capital basis to interpret risk and performance.
- Dollar-income strategies without a meaningful capital denominator may be better described with distributional and win-loss measures.
- Bootstrapping may help assess path-dependent measures such as drawdown and recovery time.
- The document gives practitioner opinions rather than empirical evidence comparing these evaluation methods.
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Full text
# How do I calculate Sharpe ratio from P&L?
# How do I calculate Sharpe ratio from P&L?
Say I have a market-making strategy that trades intraday. I start with a flat position and finish flat too. I end up with a daily P&L $p_{today}$. Over a year of trading I get $\vec{p} = (p_1,\dots,p_{252})$.
There is no way to calculate returns here. As such I calculate $$Sharpe = S(\vec{p}) = \sqrt{252} \cdot \frac{\mathbb{E}[\vec{p}]}{\sqrt{\mathbb{V}[\vec{p}]}} = \sqrt{252} \cdot \frac{mean(p)}{sd(p)}$$
My questions are :
- Am I right to do it like this?
- Do you usually bootstrap your Sharpe? (I do not but I am interested in your view of it.)
## Answer by chrisaycock (score 7)
https://quant.stackexchange.com/a/9480
> There is no way to calculate returns here.
Let me stop you right there. You didn't open a brokerage account with zero dollars. The money you put-up for margin is your starting position. After a year of trading, you have a stopping position represented by a different amount of money in your account. The change from your starting position to your stopping is your return.
> Am I right to do it like this?
Your formula for annualized Sharpe ratio is correct, assuming you didn't introduce more margin into your brokerage account to do bigger trades. For a fair comparison using P&L, you must have the same amount of capital that you started with.
> Do you usually bootstrap your Sharpe?
I've never heard of resampling applied to performance metrics like this. At least not by industry practitioners.
## Answer by feetwet (score 4)
https://quant.stackexchange.com/a/12979
It is true that intraday/market-making strategies don't have a reasonable "return" metric. For this reason you can't characterize them with the Sharpe Ratio, which depends on a capital basis and how that basis is leveraged (not to mention the risk-free rate on the capital basis).
What you're asking is how to characterize the performance of a daily stream of dollar income that doesn't have a capital basis. Typically I would start with mean, standard deviation, and skewness. Or I might ask for %Winning days and AvgWin/AvgLoss, or Profit Factor. Bootstrapping your data does not benefit any of these measures.
Then I would go to other metrics where bootstrapping (i.e., resampling the returns to generate different return paths) could be beneficial. E.g., max drawdown, or max time to recover (i.e., return to high water mark).Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.