# Sharpe Ratio

## Sharpe Ratio Definition

The sharpe ratio definition is the excess return or risk premium of a well diversified portfolio or investment per unit of risk. Measure sharpe ratio using standard deviation. You may also know this ratio as the reward to variability ratio or the reward to volatility ratio.

## Sharpe Ratio Explained

The sharpe ratio is a good measure for investors because it allows them to distinguish the amount of reward needed per unit of risk. This allows for risk averse investors to stay away from low reward high risk situation that they are uncomfortable with. The higher the ratio the better for an investor. It is also useful in establishing the ratio efficient frontier in which an investor can build a model for several different investments and build a portfolio that is exactly equal to the desired ratio. These efficient frontier models can distinguish down to the specific weights what an investor needs to do to build the desired portfolio.

## Sharpe Ratio Formula

Use the following sharpe ratio formula:

```SR = E(R-Rf)
σ```

Where:

R = asset return
Rf = Risk free return
E(R-Rf) = Expected return of the risk premium
σ = standard deviation of the risk premium

## Example

Tim is looking to invest in a stock that has an expected return of 12%. The risk free rate is 4%, and the standard deviation of the risk premium is 10%. Thus, the calculation is as follows:
Sharpe = (.12-.04)/.10 = .8
The .8 can be interpreted as meaning that for every unit of risk that you accept as an investor you will be taking on an additional one and a quarter amount of risk.

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