Risk-Adjusted Performance Measures from P&L Series

Summary

The document explains how to derive performance statistics when only a strategy P&L series is available. If the data are cumulative P&L levels, first difference them into period changes, such as daily P&L, to obtain a more suitable series for analysis. A basic ex post Sharpe ratio can then be calculated as average period P&L divided by its standard deviation, though percentage returns are preferable when available.

It recommends complementing that ratio with total and average P&L, hit rate, maximum drawdown, skewness, and kurtosis. Higher positive skew or lower kurtosis may be preferable for series with matching means and variances, but the exchange notes that preferences depend on the market view and confidence in it. P&L-based measures also lack the capital or exposure denominator available in return data, limiting comparisons across strategies or changing position sizes.

Key ideas

• Difference cumulative P&L levels to obtain period P&L changes before calculating performance statistics.
• The average period P&L divided by its standard deviation is a basic ex post Sharpe-style measure.
• Percentage returns are preferable when capital or exposure data are available.
• Use drawdown, hit rate, skewness, and kurtosis to add context to a Sharpe ratio.
• Comparing P&L-based measures across strategies can be difficult without capital or exposure information.

Tags

# performance measure using pnl series


# performance measure using pnl series












I have a time series of \$pnl of a strategy and nothing else. Can i use it to come up with some sort of a performance measure adjusted for risk? Is $$ \frac{average(\$pnl)} {sigma(\$pnl)}$$ ok to use here? Are there ways of improving it? Is it same as sharpe ratio?

## Answer by polarbear (score 2, accepted)

https://quant.stackexchange.com/a/40947

Adding to Attack68 answer- you can do a few things:

- calculate total and average pnl over a given time.

- calculate skew, kurtosis etc. as suggested above.

- calculate hit rate.

- calculate max drawdown.

- SR using daily pnl is fine but ideally the returns should be in %.

## Answer by Attack68 (score 1)

https://quant.stackexchange.com/a/40938

If you have a time series of accumulated/on going PnL figures, $X_t$, you should be careful to convert these into a more stationary data series of period PnL changes (probably daily changes):

$Y_t = X_t - X_{t-1} = (1-L)X_t \; , \text{for L the lag opertaor}$

Then you can consider the traditional ex post Sharpe Ratio:

$Sharpe = \frac{E[Y_t]}{\sigma_Y}$

You can also analyse the skewness and kurtosis of the period PnL by taking 3rd and 4th moments of $Y_t$ respectively. Presumably you will conclude that for two series with identical expectation and variance, you will prefer the one with positive skew or lower kurtosis, but maybe not depending on the confidence of the market view, etc..

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.