# What is the Jensen’s Alpha?

Jensen’s measure, or Jensen’s alpha, developed by Michael Jensen in 1968, is used to calculate the return on a portfolio in excess of its theoretical expected return. The idea behind this ratio is that any investment that performs better than its projected or expected risk-adjusted return shows that the manager is able to extract more mileage from his investments.

In  other words, Jensen’s Alpha is the difference between actual returns of a fund and those that could have been earned on a benchmark portfolio with the same amount of market risk (e.g. the same Beta). Jensen’s Alpha measures the return earned by a portfolio above or below that demanded by the market for its risk class.

The measure was developed to try to determine how much active management can increase returns above those that are purely a reward for bearing market risk.

It therefore becomes an important tool in the mutual fund analyst’s toolkit to decipher which funds to recommend to investors – apart from other important ratios like Sharpe, Treynor which shall be covered in separate posts.

The Jensen’s Alpha Formula

Alpha is calculated using a simple formula:

Jensen’s Alpha = Expected Portfolio Return – [Risk Free Rate + Beta of the Portfolio * (Expected Market Return – Risk Free Rate)]

The formula is also represented as:

?p = Rp – [R+ ?p * (Rm – Rf)]

Where,

?p = Jensen’s Alpha

Rp = Expected Portfolio Return

Rf = Risk Free Rate

?p = Beta of the Portfolio

Rm = Expected Market Return

R= Risk Free Rate How Does This Formula Work?

This formula is used to calculate the difference between the abnormal return of an asset and its expected return that was calculated theoretically. The formula can be applied to any type of asset including securities, bonds, stocks and derivatives. This is a financial model that calculates the expected return of a security based on average market return, risk-free interest rate and the beta of the security as a multiplier.

The beta multiplier is a representation of an asset’s volatility in comparison to the overall market factors (it measures typical jump or fall in the fund versus market expressed as times – example, XYZ Mutual Fund fluctuates by “1.4 times” the market fluctuation) . A beta of less than 1.0 will indicate that the scheme is less volatile than the benchmark index; while beta of more than 1.0 will indicate that the scheme is more volatile than the benchmark index.

The Alpha, on the other hand, represents the excess return an asset generated over the return calculated using the CAPM (. At times, an asset generates a return that is either more or less than what was calculated using the CAPM. These are the instances when a positive or negative alpha value is recorded. A higher positive value indicates better performance of the asset compared to the expectations while a negative value indicates that the asset performed poorly than expected.

An Illustration

let us assume a portfolio realized a return of 17% in the previous year. The approximate market index for this fund returned 12.5%. The beta of the fund versus the same index is 1.4 and the risk-free rate is 4%. The risk free rate may be the safest investment the client can make – typically the GOI Securities T Bill rate or savings account interest may be taken here.

Thus, in above case, Jensen’s Alpha = 17 – [4 + 1.4 *(12.5-4)]

= 17 – [4 + 1.4* 8.5] = = 17 – [4 + 11.9]

= 1.1%

Given, the Beta of 1.4, the fund is expected to be risky than the market index and thus earn more. A positive alpha is an indication that the portfolio manager earned substantial return to be compensated for the additional risk taken over the course over the year. If the fund would have returned 15%, the computed alpha would be -0.9%. A negative alpha indicates that the investor was not earning enough returns for the quantum of risk which was borne.

Why Is Jensen’s Measure Important?

For every investor, it is important to understand the risks they would be taking when they invest in a particular asset. For that, they need a properly calculated measure of the total return of an investment against the risk involved in it. The aim of investors is to go for securities that offer maximum returns with minimal risks.

This means that between two mutual fund schemes that are offering similar returns, the one with less risk would be more lucrative for investors than the one with higher risk. The Jensen’s Alpha can help investors determine if the return an asset is generating on average is acceptable compared to the risks it is offering, which is commonly known as risk-adjusted return. A positive alpha indicating an abnormal return is what investors are looking for when they are using this formula.

So, if you are considering some investment options, make sure you have calculated the risk-adjusted returns these options offer to understand what you are really getting into. The higher the alpha value, the more lucrative an option is. If you are dealing with options that generate a negative alpha value, investing in them might not be a wise choice.

Our Mutual Fund research desk takes into account a wide variety of factors and ratios before recommending schemes to you – Do write in to us at mfss@plindia.com for more information or any queries or investing ideas. 