## Sharpe Ratio

Sharpe ratio is a metric that evaluates risk and returns together in order to help investors in the selection of such investment that generates higher returns for the optimal risk taken. This ratio provides the investor with a perception of return earned on per unit of risk he takes. Sharpe ratio calculator is an online tool for calculating Sharpe ratio in the blink of an eye. The ratio has got its title from the name of William F. Sharpe who has developed the formula of Sharpe’s Ratio.

It helps the management in analyzing whether adding any asset helps in generating higher returns or not. Also, it is of great use in ranking and comparing different portfolios.

## Formula for Calculating Sharpe Ratio

The formula for calculating Sharpe’s ratio is as follows:

**Sharpe’s Ratio **= (*x̄ *– *R _{f}*) /

*σ*

Where,

*x̄ _{ }*= Mean Portfolio Return of Portfolio

*R _{f }* = Risk-Free Rate of Return

*σ* = Standard Deviation

## About the Sharpe Ratio Calculator / Features

This Sharpe’s Ratio calculator effortlessly calculates the Sharpe’s Ratio or risk-adjusted return by simply inputting following details to it:

- Mean portfolio return
- Risk-free rate of return
- Standard deviation

## Calculator

## How to Calculate using Calculator

For calculating Sharpe’s Ratio, simply provide the following data to the calculator:

### Mean Portfolio Return

It is the average of return on portfolio. It can be based on past as well as future data. The formula for calculating the mean portfolio return from past data is as follows:

* x̄* = ∑x / n

And for calculating mean portfolio return from future data, the formula is as follows:

* x̄* = ∑P(x)

Where, x = Return on Portfolio (%)

n = Number of Years

P = Probability

### Risk-Free Rate of Return

The risk-free rate of return is a rate on investment having no risk. It works as a benchmark for various other interest rates. Investment in treasury bills, government bonds are considered as risk-free investment.

Therefore, **( x̄ – R_{f})** gives a result of returns generated by taking risk.

### Standard Deviation

Standard deviation is amount by which returns may fluctuate in corelation with its average return or mean. It is the expected risk of portfolio. It represents volatility around the mean.

Formula for calculating standard deviation is:

- From past data,

* σ *= √[∑(x –

*x̄*)

^{2}/n]

- From future data,

* σ* = √[∑P(x –

*x̄*)

^{2}]

## Example of Sharpe Ratio

Suppose there are two portfolios: Portfolio A and Portfolio B

The details of both the portfolios are as follows:

Particulars | Portfolio A | Portfolio B |

Average return (R)_{p} | 15% | 12% |

Risk-free rate (R)_{f} | 6% | 6% |

Standard deviation (σ) | 6 | 3 |

Sharpe’s Ratio of Portfolio A = (15 – 6) / 6 = 1.5

Sharpe’s Ratio of Portfolio B = (12 – 6) / 3 = 2

### Interpretation

A higher Sharpe Ratio is always considered better. In the example above, A has a ratio of 1.5 while that of B is equal to 2. Hence, portfolio B is better than A as it has higher Sharpe Ratio. Higher ratio signifies higher returns.

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