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I have a pairs strategy that I am trying to calculate the sharpe ratio for. Currently I am using python for my analysis and calculation. I have a dataframe that contains the cumulative returns in $'s for each day. I am confused on how to convert this information into something that I can calculate the sharpe ratio from.

Could anyone point me in the right direction on how to use cumulative returns (in $'s) to find the sharpe ratio? Any help is appreciated! Thanks

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Let's say your cumulative return series is $\{R_i \mid i=0,1,...,N-1\}$ of length $N$ days.

There's 3 conventional ways to do this at this stage. You may convert the cumulative dollar return curve into arithmetic returns:

$\displaystyle{r_i}= \dfrac{R_i-R_{i-1}}{R_{i-1}}$

Or dollar returns:

$\displaystyle{r_i=R_i-R_{i-1}}$

Then take the ratio:

$\displaystyle{SR_{1d} = \dfrac{E\{r_i\}-r_f}{std\{r_i\}} }$

where the risk-free rate $r_f$ is often taken to be $0$. Finally, you annualize it:

$\displaystyle{SR_{1y}=SR \cdot \sqrt{252}}$

Here's an example of how you can do it in Python:

import numpy as np
import pandas as pd

# Simulate cumulative returns of 100 days
N = 100
R = pd.DataFrame(np.random.normal(size=100)).cumsum()

# Approach 1
r = (R - R.shift(1))/R.shift(1)

# Approach 2
r = R.diff()

sr = r.mean()/r.std() * np.sqrt(252)
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    $\begingroup$ I still seem to be getting an abnormally large value for my sharp ratio (~5). I should mention that this is being calculated from returns on a pairs trading strategy. Is there anything that would change because of this, or should I assume that something among my prior calculations is off. $\endgroup$ – jod51 May 15 '18 at 23:54
  • $\begingroup$ It doesn't matter what kind of strategy you're testing this on. 5 isn't unusual, for strategies like that you probably just have wrong slippage assumptions. $\endgroup$ – madilyn May 16 '18 at 1:16
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    $\begingroup$ @madilyn is this python code missing the annualization of the SR? Because I'm getting something ridiculous after converting to an annualized ratio. $\endgroup$ – cheez Nov 15 '18 at 14:31
  • $\begingroup$ You are right, the last line should read sr = r.mean()/r.std() * np.sqrt(252). $\endgroup$ – madilyn Nov 16 '18 at 3:02
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    $\begingroup$ You should include that in the answer above, some people (myself included) don't always read the comments and might miss it, thanks. $\endgroup$ – Goose Jan 30 at 5:49

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