**Table of Contents**

## What is 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.

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.

Mathematically, the formula of Alpha is represented as,

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

or

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

### Explanation of the Alpha Formula

The calculation of the equation of alpha of a portfolio can be simply done by using the following steps:

**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.

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**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 an 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.

### Example of Alpha Formula (with Excel Template)

**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 Formula = 16% – 13.1%

**Alpha Calculation of Mutual Funds**

- Alpha = 2.9%

The alpha of the mutual fund is 2.9%.

### Relevance and Use of Alpha Formula

It is important to understand the concept of alpha formula because it is used to measure the risk-adjusted performance of a portfolio. Alpha formula 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).

Since alpha calulation is a reflection of the performance of a portfolio vis-à-vis a benchmark index, it is usually considered to be the value addition that a portfolio manager does to the portfolio’s return. In short, alpha can be seen as the return on an investment which is not due to general movement in the broader market. Consequently, an alpha value of zero is indicative of the fact that the portfolio is perfectly tracking the benchmark index and that the fund manager has not added any value to the portfolio as compared to the broader market.

Despite several performance tracking benefits, alpha also comes its own set of limitations which should be by an investor. One of the limitations is that although investors utilize this ratio for comparing various types of portfolios, which may include portfolios that are invested in different asset classes, this comparison could result in inaccurate or misleading numbers. The reason behind the variation is the diverse nature of the different funds that may impact the understanding of the ratio. First of all, the interpretation of alpha works best when applied to an investment in a stock market (not in other asset classes). Secondly, if the ratio is used as a tool to compare funds, then it is useful to evaluate similar funds.

For instance, it is better to compare two large-cap dividend mutual funds, rather than, comparing a large-cap dividend mutual fund with a mid-cap growth mutual fund. Another limitation of alpha for investors the selection of a benchmark index. The value of alpha is calculated and compared to a benchmark that is believed to be appropriate for the portfolio. As such, an investor should choose a relevant benchmark.

For instance, in the evaluation of a portfolio of stocks that are invested in the sector of transportation, a more suitable benchmark index would be the Dow Transportation index. In cases when there is no pre-existing benchmark index available, the analysts can use algorithms and other such models to simulate an index for comparative purposes.

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