What is the Jensen’s Alpha Formula?

Flame_Towers_Baku_Azerbaijan What is the Jensen's Alpha Formula?

Flame Towers, Baku, Azerbaijan

The higher the risk associated with an asset, the greater is the value of its expected return. This high return is supposed to be the reward for investors who dare to invest in riskier assets. This makes the calculation of an asset’s or a portfolio’s risk-adjusted performance detrimental in making investment decisions. Jensen’s Alpha, also known as “Alpha”, “Jensen’s Measure” and “Jensen’s Performance Index” is one of the many ways a trader can calculate the risk-adjusted value of an investment.

When you are using Alpha, the risk-adjusted performance of the investment option is calculated in relation to its expected market return. The expected market return used in this context is based on the capital asset pricing model. Higher value of Alpha indicates that your portfolio has performed better, earning more than the level predicted by the market. It also shows how the option you are evaluating fares compared to other options in terms of risk-return balance.

Who Created the Jensen’s Alpha Formula?

The Jensen’s Alpha formula was used for the first time by Michael Jensen back in 1986. Jensen is a well-known economist who specializes in dealing with financial economics. Initially, he discovered this measure to track the performance of a hedge fund manager. The purpose of this formula was to gauge whether hedge fund managers can outperform markets on a consistent basis. After a comprehensive study, Jensen’s results stated that the events of hedge fund managers outperforming the markets were quite rare.

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 – [Rf + ?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

Rf = 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. The theoretical expected return in this case is mostly calculated using the capital asset pricing model (CAPM). 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.  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.

Why Is Jensen’s Measure Important for Investors?

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 options 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.