Jensen's Alpha Calculator

Created by Wei Bin Loo
Reviewed by Dominik Czernia, PhD candidate and Steven Wooding
Last updated: Apr 06, 2022

We have designed this Jensen's alpha calculator to help you calculate your portfolio's performance. Jensen's alpha is one of the most widely used metrics in the industry of measuring investment performance. It also tells you if your investment portfolio outperforms the market.

By reading this article, you will understand what Jensen's alpha is and how to calculate it using the Jensen's alpha formula. We will also use some examples to help you understand the concept better. But first, let's make sure we understand the fundamentals, namely the definition of Jensen's alpha.

What is Jensen's alpha?

Jensen's alpha, or Jensen's measure, is a performance metric that measures a portfolio's excess return when compared to the market. In other words, it tells you if your investments beat the market and by how much.

Unlike the total return, Jensen's alpha measures the risk-adjusted measure of a portfolio. The reason that this metric is important is based on the assumption that, given the same return, investors will prefer the less risky fund. Hence, it is vital to adjust a fund's return by the risks it takes to evaluate its performance better.

Now, let's look at how to put this concept into practice.

How to calculate Jensen's alpha? Jensen's alpha calculation example

Let's assume that you have invested in a portfolio with the following information:

  • Beginning portfolio value: $1,000,000
  • Ending portfolio value: $1,200,000
  • Portfolio beta: 1.12
  • Risk-free rate: 2%
  • Market rate of return: 11%

Calculating Jensen's alpha requires 5 steps:

  1. Determine your portfolio's return.

The first step is to determine your portfolio's return, which can be calculated by using the formula below:

portfolio return = (ending portfolio value - beginning portfolio value) / beginning portfolio value

For our example, portfolio return is ($1,200,000 - $1,000,000) / $1,000,000 = 20%.

  1. Determine the risk-free rate.

The risk-free rate is often assumed to be the yield of a 10-year US bond as it is considered to have minimal credit risk since the US government can always print more money to repay its debt. This information can be found on the Federal Reserve website.

In this example, the risk-free rate is assumed to be 2%.

  1. Calculate your portfolio's beta.

The next step is to calculate the portfolio beta. The portfolio beta is merely the weighted average of the betas of the portfolio's holdings.

The portfolio beta for our portfolio is 1.12.

  1. Calculate the market rate of return.

The average annual rate of return of a broad market index can be used as the market rate of return. S&P 500 is the most commonly used index.

As the average annual return of the S&P 500 is about 11%, we will use this as our market rate of return.

  1. Calculate Jensen's alpha.

The last step of this Jensen's alpha calculation example is to calculate it. This can be done using the Jensen's alpha formula:

Jensen's alpha = pr - (rf + b * (rm - rf))

where:

  • pr — Portfolio return;
  • rf — Risk-free rate;
  • rm — Market rate of return; and
  • b — Portfolio beta.

In the example, we obtain Jensen's alpha = 7.92%, what means the investment returns beat the market. 💰

Why is it essential to understand Jensen's alpha?

Now that we understand how to calculate Jensen's alpha, let's discuss the importance of Jensen's measure.

The main reason that Jensen's alpha is useful in assessing investment performance is that the total return is often misleading. Given the same return, the fund with lower risk is usually preferred. Hence, Jensen's alpha is perfect for helping us compare investment performance fairly.

Besides, Jensen's alpha can inform you if your investment portfolio does outperform the market on a risk-adjusted basis. If Jensen's alpha is positive, it means that your portfolio has beaten the market.

However, it is risky to claim that you have outperformed the market if you have a positive Jensen's alpha for one year. Outperforming the market may be luck instead of skill if it does not happen consistently. Hence, it is recommended that you keep track of your historical performance when assessing your investment performance.

FAQ

What is a good Jensen's alpha?

In general, the higher the Jensen's alpha the better. A positive Jensen's alpha is considered good, as it indicates that you have outperformed the market.

Can Jensen's alpha be negative?

Yes, Jensen's alpha can be negative. If Jensen's alpha is negative, it means your portfolio is performing worse than the market.

What is the difference between Jensen's alpha and total return?

The two metrics are used to calculate investment performance differently. The total return is the gross return, whereas Jensen's alpha is a return metrics adjusted by the risk of the portfolio.

What is the risk in using Jensen's alpha?

Luck often plays a massive part in investment performance, so it is important to make sure that the positive Jensen's alpha is not merely a one-off occurrence. It is not uncommon for investors to think that they are skillful once they have achieved a positive Jensen's alpha.

Wei Bin Loo
Portfolio's return
Beginning portfolio value
$
Ending portfolio value
$
Portfolio's return
%
Jensen's alpha
Risk-free rate
%
Portfolio's beta
Market rate of return
%
Jensen's alpha
%
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