# Jensen’s Alpha Formula

## What is Jensen’s Alpha?

A Jensen’s alpha or Jensen’s performance index or ex-post alpha measures the portfolio’s excess returns compared to returns suggested by the CAPM (Capital Asset Pricing Model) model.  The value of the excess return may be positive, negative, or zero. Jensen’s alpha measures the real performance over a calculated return. It can be an asset, such as a bond, stock, or derivative.

The CAPM uses statistical methods to predict the suitable risk-adjusted return of an Asset. The returns are supposed to account for a certain asset’s riskiness factor, which means that it has to be ‘Risk-Adjusted.’

Michael Jensen first used the Jensen’s Alpha in 1968, where he wanted to evaluate the mutual fund managers. He wanted to know more about the emerging markets and see whether the mutual fund managers’ returns indicated an ability to outperform the market. One of these methods would have been a straightforward one where he could’ve compared the managers’ return to the market portfolio, but it would have been very misleading as the risk factor hadn’t been considered. He was adamant on learning that if the managers could add value over the long term, and this is how Jensen’s Alpha was born.

Jensen’s Alpha Formula represents the math equation for Alpha calculation based on the realized return of the portfolio or investment, realized a return of the appropriate market index, risk-free rate of return for the period, and a beta (systematic risk of the portfolio).

Jensen’s Alpha Formula is:

Alpha = R(portfolio) – (R(rate) + Beta x (R(index) – R(rate)))

where:

R(portfolio) = the realized return of the portfolio or investment

R(index) = the realized return of the appropriate market index

R(rate) = the risk-free rate of return for the period

Beta = the beta of the portfolio of investment concerning the chosen market index

## How does Jensen’s Alpha work?

So the formula involving Jensen’s Alpha is used to calculate the difference between a return that an asset provides and the theoretically calculated expected return. The formula can be applied to all kinds of assets such as a stock, bond, derivatives, etc. the expected return, in this case, is calculated using CAPM (Capital Asset Pricing Model), a model that can be based on average market return, interest rate and the multiplier, calculate the expected rate of return.

The simple formula which is used to calculate this is as follows:

Portfolio Return-[Risk Free Rate+portfolio beta x (market return-risk free rate)]

The beta multiplier represents the asset’s uncertainty as compared to market factors. The Alpha represents the returns that are generated more than the calculated return. A positive alpha indicates better performance, whereas a negative alpha indicates poor performance.

If an Asset’s return is even higher than the risk-adjusted or the predicted return, it is known as a positive alpha or an abnormal return. A negative alpha indicates that the fund has performed poorly or has provided lower than expected returns. This basically means that the fund manager has the skills to beat the market.

Why is it important?

Every individual or a fund manager invests in the market for a sole purpose which is a profit. For this, they should be aware of the risks that they’ll have to take while investing in a stock or a bond or any other asset. This is where Jensen’s alpha comes into the picture, which provides them a properly calculated measure of what they’re going to get out of that asset against the risk involved in it. The main challenge that a fund manager faces is that they need to go for securities that offer maximum returns with a minimum risk factor. Jensen’s Alpha helps them to achieve this.

For example, if two schemes offer a similar kind of return, the investor can go for the one that would be more lucrative for an investor, which offers the same return with a lesser amount of risk. Jensen’s Alpha helps the investor determine whether an asset’s returns are acceptable compared to the applicable risk.

## Limitations to Jensen’s Alpha

An Alpha aims to generate returns that are not in line with market performance. According to statistics, a fund generating higher yields is unlikely to do so at a later stage. Its prices fluctuate according to the performance and adjust accordingly to reflect their value.

Jensen’s Alpha is a great tool for measuring a certain stock’s performance and helps the fund managers maximize the individual’s or the company’s risk to return ratio. You can also use the same to your advantage to measure your fund’s performance and increase your profitability and decrease risks.

So that was our take on Jensen’s Alpha! But do not just go with our word; investments are a crucial element of ones’ life. Therefore it is essential to analyze, study and learn about them in great detail and then get to the action.  So, huddle up! Research and Learn: It’s time to get investing!

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Fxigor

Igor has been a trader since 2007. Currently, Igor works for several prop trading companies. He is an expert in financial niche, long-term trading, and weekly technical levels. The primary field of Igor's research is the application of machine learning in algorithmic trading. Education: Computer Engineering and Ph.D. in machine learning. Igor regularly publishes trading-related videos on the Fxigor Youtube channel. To contact Igor write on: igor@forex.in.rs

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