# Calculating Sharpe ratio for a long short portfolio

#### funtim

Hi!

I'm currently working on the backtesting of a long-short portfolio, and I need to calculate the Sharpe ratio of this portfolio. As you know, Sharpe ratio is (Expected return - Risk free rate)/(st dev of the returns of the portfolio).

Alright, but:
- easy question: what risk free rate am I suppose to use? I would say it's between 0 and a negative rate, according to the current market situation. I currently use 0 as reference. What do you think about it?

- challenging question: How do I calculate the returns? This might sound easy for a long only portfolio, but what is the method for a long short?
Basic example: I long $10k of stock A, short$10k of stock B. Stock A makes +2% and stock B doesn't move, I virtually have an infinite return!!! Using ($10k * 1.02 +$10k * 1)/($10k -$10k) -1
Am I suppose to calculate each return individually and then add them together? which would make 0.5*2% + 0.5*0% = 1% return ?

And last but not least, once I will have my vector with returns, Sharpe ratio should be:
Sh. ratio = Average(daily returns)/St dev (daily returns)

I mean I am not supposed to use any multiple such as sqrt(250) because I am using daily data?

#### Alexei

For a simple model you can do the following: take a year long treasury returns for a RF rate proxy. Next, use quantities to express holdings vs market value of positions. To compute position return, use the following formula: q * (Position Close Price - Position Open Price) * I, where I E(-1, 1) depending on a position type (short (-1), long (1)). Normalize returns to be expressed per year. Use 252 to compute returns and the volatility from daily values. Use \$-exposure in the denominator to get the return (abs value for a position type (long | short)). A more complex model includes a different methodology for Sharpe Ratio calculation.

#### funtim

So you mean that to get the sharpe ratio, I should use:
Sharpe ratio = AverageDailyReturn * sqrt(252) / DailyVolatility​
What do you mean by more complex models? Do you have any examples / links / papers I could look at?

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