Jensen’s Measure

Jensen’s Measure Formula

In the context of portfolio management, alpha (α) is defined as the incremental returns from a portfolio of investments, typically consisting of equities, above a certain benchmark return.

Under Jensen’s Measure, the chosen benchmark return is the capital asset pricing model (CAPM), rather than the S&P 500 market index.

The formula for alpha under Jensen’s Measure is shown below:

Jensen’s Alpha Formula

Jensen’s Alpha = rp – [rf + β * (rm – rf)]

• rp = Portfolio Return
• rf = Risk-Free Rate
• rm = Expected Market Return
• β = Portfolio Beta

Interpreting Jensen’s Alpha

The value of alpha – the excess returns – can range from being positive, negative, or zero.

• Positive Alpha: Outperformance
• Negative Alpha: Underperformance
• Zero Alpha: Neutral Performance (i.e. Tracks Benchmark)

The CAPM model calculates risk-adjusted returns – i.e. the formula adjusts for the risk-free rate to account for risk.

Therefore, if a given security is fairly priced, the expected returns should be the same as the returns estimated by CAPM (i.e. alpha = 0).

However, if the security were to earn more than the risk-adjusted returns, the alpha will be positive.

By contrast, negative alpha suggests the security (or portfolio) fell short in achieving its required return.

For return-oriented portfolio managers, a higher alpha is nearly always the desired outcome.

Jensen’s Measure Calculation Example

Now, to move to an example calculation of Jensen’s alpha, let’s use the following assumptions:

• Beginning Portfolio Value = $1 million
• Ending Portfolio Value = $1.2 million
• Portfolio Beta = 1.2
• Risk-Free Rate = 2%
• Expected Market Return = 10%

The first step is to calculate the portfolio return, which can be calculated using the formula below.

Portfolio Return Formula

• Portfolio Return = (Ending Portfolio Value / Beginning Portfolio Value) – 1

If we divide $1.2 million by $1 million and subtract one, we arrive at 20% for the portfolio return.

Next, the portfolio beta was stated as 1.2 while the risk-free rate is 2%, so we have all the necessary inputs.

In closing, the estimated alpha for our example scenario is equal to 8.4%.