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 the 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 – Rf) / σ
Where,
x̄ = Mean Portfolio Return of Portfolio
Rf = 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 the 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 a 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 and government bonds is considered as a risk-free investment.
Therefore, (x̄ – Rf) gives a result of returns generated by taking risks.
Standard Deviation
Standard deviation is the amount by which returns may fluctuate in correlation with its average return or mean. It is the expected risk of a portfolio. It represents volatility around the mean.
The 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 (Rp) | 15% | 12% |
| Risk-free rate (Rf) | 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 a higher Sharpe Ratio. A higher ratio signifies higher returns.
