# Jensen's Alpha Calculator

By Wei Bin Loo
Last updated: Aug 06, 2021

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:

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%`.

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 benchmark?

A benchmark is an appropriate index to compare your investment against. For instance, if you are investing in the US stock market, the S&P 500 would be your benchmark. If you are investing in the UK stock market, the standard benchmark is the FTSE 100.

### What is Sharpe ratio?

Sharpe ratio is a widely used metric to compare the portfolio return to the risk-free return and divided by the standard deviation of portfolio return. It measures the amount of extra return you can get by taking on per unit of risk.

### What is excess return?

The excess return is defined as the difference between the portfolio return and the benchmark return. A positive excess return indicates that the portfolio manager has the skills to outperform the benchmark, whereas a negative excess return indicates that the return of the portfolio is less than the benchmark.

### Can information ratio be negative?

The short answer is yes. The information ratio can be negative. This happens when the portfolio return is lower than the benchmark return, creating a negative excess return. A negative information ratio indicates the lack of skills of the portfolio manager in generating superior returns compared to the benchmark.

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
%
People also viewed…

### Christmas tree

Welcome to the Christmas tree calculator, where you will find how to decorate your Christmas tree in the best way. Take a look at the perfect Christmas tree formula prepared by math professors and improved by physicists. Plan in advance how many lights and decorations you'll need!

### Sales tax

Sales tax calculator works out the tax imposed on the sale of goods and services. 