## Formula to Calculate Alpha of a Portfolio

Alpha is an index which is used for determining the highest possible return with respect to the least amount of the risk and according to the formula, alpha is calculated by subtracting the risk-free rate of the return from the market return and multiplying the resultant with the systematic risk of the portfolio represented by the beta and further subtracting the resultant along with the risk-free rate of the return from the expected Rate of the return on the portfolio.

The formula for calculation of alpha can be done first by calculating the expected rate of return of the portfolio based on the risk-free rate of return, a beta of the portfolio and market risk premium, and then deducting the result from the actual rate of return of the portfolio.

**Alpha of portfolio = Actual rate of return of portfolio – Expected Rate of Return on Portfolio**

or

**Alpha of portfolio = Actual rate of return of portfolio – Risk-free rate of return – β * (Market return – Risk-free rate of return)**

### Alpha of a Portfolio Calculation (Step by Step)

**Step 1:**Firstly, figure out the risk-free rate which can be determined from the average annual return of government security, say Treasury bonds, over a substantial period of time.**Step 2:**Next, figure out the market return which can be done by tracking the average annual return of a benchmark index, say S&P500, over a substantial period of time. Consequently, the market risk premium is computed by deducting the risk-free rate of return from the market return.**Market risk premium = Market return – Risk rate of return****Step 3:**Next, the beta of a portfolio is determined by assessing the movement of the portfolio compared to the benchmark index.**Step 4:**Now, based on the risk-free rate of return (step 1), a beta of the portfolio (step 3) and market risk premium (step 2), the expected rate of return of the portfolio is calculated as below.**Expected rate of return of portfolio = Risk-free rate of return + β * (Market return – Risk-free rate of return)****Step 5:**Next, the actual rate of return achieved by the portfolio is calculated based on its current value and the previous value.**Step 6:**Finally, the formula for calculation of alpha of the portfolio is done by deducting the expected rate of return of the portfolio (step 4) from the actual rate of return of the portfolio (step 5) as above.

### Examples

**Let us take the example of a mutual fund which has realized a return of 16% during last year. The appropriate benchmark index for the fund has book annual return of 11%. Further, the beta of the mutual fund vis-à-vis that benchmark index is 1.3while the risk-free rate of return is 4%. Do the Calculation of the alpha of the mutual fund.**

As per the question, the following is the data for the calculation of alpha formula.

**Expected Rate of Return **

Expected rate of return = Risk-free rate of return + β * (Benchmark return – Risk-free rate of return)

- = 4% + 1.3 * (11% – 4%)
- = 13.1%

Therefore, Calculation of Alpha of the mutual fund will be as follows –

- Alpha of the mutual fund = Actual rate of return – Expected rate of return
- Alpha = 16% – 13.1%

**Alpha Calculation of Mutual Funds**

- Alpha = 2.9%

The alpha of the mutual fund is 2.9%.

### Relevance and Uses of Alpha Formula

- The term Alpha refers to the index which is used in many financial models, say the CAPM (capital asset pricing model), to assess the highest possible return from an investment with the least amount of risk. Alpha is also known as Jensen Index.
- It is important to understand the concept of alpha formula because it is used to measure the risk-adjusted performance of a portfolio.
- It is also recognized as the excess return or the abnormal rate of return of a portfolio. The figure demonstrates how much worse or better a fund had performed with regard to a benchmark. This variance is then credited to the judgments made by the fund manager. Active portfolio managers predominantly strive to generate alpha in a diversified portfolio (diversification is intended towards the elimination of unsystematic risk).

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