Sharpe Ratio Formula

Sharpe Ratio Formula (Table of Contents)

• Sharpe Ratio Formula
• Sharpe Ratio Formula Calculator
• Sharpe Ratio Formula in Excel (With Excel Template)

Sharpe Ratio Formula

The formula for Sharpe ratio is calculated by dividing the excess rate of return of the portfolio by the standard deviation of the portfolio return. The excess rate of return of the portfolio is calculated by deducting the risk free rate of return from the actual rate of return of the portfolio. Mathematically, the Sharpe ratio formula is represented as below,

where,

• R_p = Expected rate of return of the portfolio
• R_f = Risk-free rate of return
• ơ_p = Standard deviation of the portfolio return

In case the Sharpe ratio has been computed based on daily returns, it can be annualized by multiplying the ratio by the square root of 252 i.e. number of trading days in a year.

Explanation of the Sharpe Ratio Formula

The formula for the Sharpe ratio can be computed by using the following steps:

Step 1: Firstly, the daily rate of return of the concerned portfolio is collected over a substantial period of time i.e. monthly, annually, etc. The rate of return is calculated based on net asset value at the beginning of the period and at the end of the period. Then the average of all the daily return is determined which is denoted as R_p.

Step 2: Now, the daily yield of a 10-year government security bond is collected to compute the risk-free rate of return which is denoted by R_f.

Step 3: Now, the excess rate of return of the portfolio is computed by deducting the risk-free rate of return (step 2) from the rate of return of the portfolio (step 1) as shown below.

Excess rate of return = R_p – R_f

Step 4: Now, the standard deviation of the daily return of the portfolio is calculated which is denoted by ơ_p.

Step 5: Now, the Sharpe ratio is calculated by dividing the excess rate of return of the portfolio (step 3) by the standard deviation of the portfolio return (step 4).

Sharpe Ratio = (R_p – R_f) / ơ_p

Step 6: Finally, the Sharpe ratio can be annualized by multiplying the above ratio by the square root of 252 as shown below.

Sharpe Ratio = (R_p – R_f) / ơ_p * √252

Examples of Sharpe Ratio Formula

Let’s take an example to understand the calculation of Sharpe Ratio formula in a better manner.

Sharpe Ratio Formula – Example #1

Let us take an example of a financial asset with an expected rate of return of 10% while the risk-free rate of return is 4%. The standard deviation of the asset’s return is 0.04.

Sharpe Ratio is calculated using the below formula

Sharpe Ratio = (R_p – R_f) / ơ_p

• Sharpe Ratio = (10% – 4%) / 0.04
• Sharpe Ratio = 1.50

This means that the financial asset gives a risk-adjusted return of 1.50 for every unit of additional risk.

Sharpe Ratio Formula – Example #2

Let us take an example of two financial assets X and Y with the expected rate of return are 12% and 20% for both while the risk-free rate of return is 5%. However, the standard deviation of asset X and Y are 0.04 and 0.15. Figure out which is the better investment given the risk associated.

Sharpe Ratio for X is calculated using below formula

Sharpe Ratio = (R_p – R_f) / ơ_p

• Sharpe ratio for X = (12% – 5%) / 0.04
• Sharpe ratio for X = 1.75

Sharpe Ratio for Y is calculated using below formula

Sharpe Ratio = (R_p – R_f) / ơ_p

• Sharpe ratio for Y = (20% – 5%) / 0.15
• Sharpe ratio for Y = 1

This means that even though asset Y offers higher return compared to asset X (asset Y-20% asset X-12%), asset X is a better investment as it has higher risk-adjusted return indicated by Sharpe ratio of 1.75 compared to 1 of asset Y.

Relevance and Uses

It is quintessential to understand the concept of the Sharpe ratio as it is is a comprehensive tool to assess the performance of a portfolio against a certain level of risk. The ratio is usually used to capture the change in the overall risk-return characteristics of a portfolio after a new asset or asset class has been added to the portfolio. The ratio can also be utilized in the evaluation of a past performance of a portfolio by using actual returns of the portfolio in the formula. On the other hand, the ratio can also be used to assess the estimated Sharpe ratio based on expected portfolio performance. As per the Sharpe ratio, a higher value indicates the better risk-adjusted performance of the portfolio.

Sharpe Ratio Formula Calculator

You can use the following Sharpe Ratio Calculator.

Sharpe Ratio Formula in Excel (With Excel Template)

Now let us take the monthly return information of Sundaram Equity Hybrid Fund to illustrate in excel template below. The table provides the detailed calculation of the Sharpe ratio for Sundaram Equity Hybrid Fund.

Sharpe ratio is calculated by dividing the difference between the daily return of Sundaram equity hybrid fund and the daily return of 10 year G Sec bonds by the standard deviation of the return of the hybrid fund. Consequently, the Sharpe ratio based on the daily return is calculated as 0.272. Further, the Sharpe ratio has been analyzed by multiplying the previous result by the square root of 252.

Average of the daily return of Sundaram Equity Hybrid Fund

Average of the daily return of 10 year G-Sec

Standard Deviation

Sharpe Ratio is calculated as:

Sharpe Ratio for annual is calculated as:

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