Jensen Ratio – What Is It And How Is It Calculated? (Jensen’s Performance Index in Finance)

As an investor, you would want to know whether your investment’s return is worth the risk. There are different methods you can use to measure the risk-adjusted performance of your portfolio, and the Jensen Ratio (Jensen’s Performance Index) is one of them. But what is the Jensen Ratio?

Named after the renowned economist Michael Jensen who formulated it in 1968, Jensen’s Performance Index, or simply called Jensen’s Alpha or Jensen’s Ratio is a formula for calculating a portfolio’s returns after adjusting for risk. It measures the returns earned in excess of or below the expected return based on the Capital Asset Pricing Model (CAPM), given the portfolio’s beta, the overall market returns, and the risk-free rate of return.

After understanding the R-squared, Beta, and Standard Deviation in our earlier posts, let’s look into the ratios and trading strategy and system performance metrics that can be used to evaluate the risk-adjusted performance of an investment. In this post, our focus is on the Jensen’s measure, and we will be discussing it under the following headings:

  • What does Jensen’s Ratio mean?
  • How is the Jensen’s alpha calculated?
  • The Significance of Jensen’s alpha
  • How Jensen’s alpha is used in financial analysis
  • The criticisms of the Jensen’s measure

What does Jensen’s Ratio mean?

By way of definition, the Jensen’s alpha, or Jensen’s measure, is a risk-adjusted performance measure that represents the average return on a portfolio or investment, above or below that predicted by the capital asset pricing model (CAPM), given the portfolio’s or investment’s beta and the average market return.

The Jensen’s measure is a statistical measurement of the portion of a security’s or portfolio’s return that is not explained by the market movement and how the portfolio is expected to move relative to the market movement. It shows how much the portfolio has performed above or below its expected performance given its risk level relative to the market.

This theoretical expected return/performance is predicted by a market model known as the capital asset pricing model (CAPM). The model uses statistical methods to estimate the appropriate risk-adjusted return of an asset. The Jensen’s alpha, simply referred to as alpha, measures how much the investment returned above or below this expected return.

For a managed portfolio, Jensen’s alpha shows the manager’s risk-adjusted performance relative to the market returns. It is the degree with which a manager outperforms or underperforms the market, putting into account the portfolio’s systemic risk relative to the broad market as measured by the beta. Beating the market is to deliver an alpha. Hence, alpha is a measure of a portfolio manager’s skills.

How is the Jensen’s alpha calculated?

As you can deduce from our discussion so far, Jensen’s alpha, also known as the Jensen’s Performance Index, is a measure of the excess returns earned by the portfolio compared to returns suggested by the CAPM. So mathematically, alpha can be calculated from the CAPM formula.

The formula for Jensen’s alpha can be presented as follows:

α = Rp – [Rf + β(Rm – Rf)]

Where:

α = Jensen’s alpha

Rp = Portfolio’s Realized Return

Rf = Risk-Free Rate

β = Beta of the Portfolio

Rm = Expected Market Return

Rf = Risk-Free Rate

Note that the portfolio’s minimum expected return can be written as:

E(R) = Rf + β(Rm – Rf)

Hence,

α = Rp – E(R)

To put it in words, the formula goes like this:

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

Or

Jensen’s Alpha = Portfolio’s Realized Return – Expected Return

The Significance of Jensen’s alpha

Jensen’s alpha can have a positive or negative value. A positive value suggests that the portfolio’s return is more than the expected return, while a negative value shows that the portfolio earned less than the expected return. The more positive (bigger) the value of alpha, the better the return compared to the expected.

To understand how Jensen’s alpha works, you need to realize that the higher a portfolio’s risk (as measured by Beta), the greater the value of its expected return. What it means is that investors are supposed to be rewarded with a higher return for taking a bigger risk. So when a portfolio earns more than the expected risk-adjusted value — as reflected by a positive alpha value — the portfolio can be said to have performed very well, earning more than the level predicted by the market. The portfolio’s manager can be said to have beat the market.

How Jensen Ratio is used in financial analysis

In finance, Jensen’s alpha is used to determine the abnormal return of a security or portfolio of investment earned in excess of the expected return calc