Sharpe Ratio

Quarterly Report

 

Strategy: 
Expected Value: see below “How to calculate it?” – in this table we assume RFR is 0% (see simulation for RFR = 1% below)
Sharpe Index: see below “How to calculate it?

What is the Sharpe Ratio?

In finance, the Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) measures the performance of an investment such as a security or portfolio compared to a risk-free asset, after adjusting for its risk. It is defined as the difference between the returns of the investment and the risk-free return, divided by the standard deviation of the investment returns. It represents the additional amount of return that an investor receives per unit of increase in risk.

source: Wikipedia

How to calculate it?

Since its revision by the original author, William Sharpe, in 1994, the ex-ante Sharpe ratio is defined as:

S a = E [ R a R b ] σ a = E [ R a R b ] v a r [ R a R b ] , {\displaystyle S_{a}={\frac {E[R_{a}-R_{b}]}{\sigma _{a}}}={\frac {E[R_{a}-R_{b}]}{\sqrt {\mathrm {var} [R_{a}-R_{b}]}}},}

where

R a {\displaystyle R_{a}}

 is the asset return,

R b {\displaystyle R_{b}}

 is the risk-free return (such as a U.S. Treasury security).

E [ R a R b ] {\displaystyle E[R_{a}-R_{b}]}

 is the expected value of the excess of the asset return over the benchmark return, and

σ a {\displaystyle {\sigma _{a}}}

 is the standard deviation of the asset excess return.

The ex-post Sharpe ratio uses the same equation as the one above but with realized returns of the asset and benchmark rather than expected returns; see the second example below.

The information ratio is a generalization of the Sharpe ratio that uses as benchmark some other, typically risky index rather than using risk-free returns.

source: Wikipedia

What if RFR (risk-free return) is 1% per year?

(that is 0,25% per quarter)