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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?

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

  1. calculate total and average pnl over a given time.
  2. calculate skew, kurtosis etc. as suggested above.
  3. calculate hit rate.
  4. calculate max drawdown.
  5. SR using daily pnl is fine but ideally the returns should be in %.
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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..

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