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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:

$S_{a}={\frac {E[R_{a}-R_{b}]}{\sigma _{a}}}={\frac {E[R_{a}-R_{b}]}{\sqrt {\mathrm {var} [R_{a}-R_{b}]}}},$

where

$R_{a}$

is the asset return,

$R_{b}$

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

$E[R_{a}-R_{b}]$

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

${\sigma _{a}}$

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)