Jensen's Alpha

Jensen's Alpha (or Jensen's Alpha) is a ratio that measures the ability of an investment portfolio manager to achieve returns above the benchmark risk-adjusted stock index.

Therefore, it measures the profitability that a manager has in an investment fund, demonstrating a better ability the higher and more positive it is compared to its competitors.

Jensen's Alpha Formula

Its calculation formula is as follows:

We can deduce that it is the real achieved profitability differential (subtracting the risk-free asset) adjusted for the systematic risk, which is measured by the beta. By using only the risk measured by beta, it is a ratio that does not measure the degree of diversification of the portfolio, as the sharpe ratio does.

Total risk = Systematic risk + Non-systematic risk

Where:

Rc: Portfolio profitability.

Rf: Is he risk free asset (in English Risk Free).

Rm: Market profitability, measured by the Stock index reference.

Bc: Portfolio beta.

Values ​​that Alfa de Jensen can take

It can take the following values:

α> 0: It is the option that every manager wants. If statistically it achieves results above 0, and also beats the average of its competitors, the manager is providing added value by beating the market.

α = 0: In this case the manager is replicating the profitability of the market.

α The manager is not even achieving the profitability that corresponds to him due to the systematic risk assumed.

Jensen's Alpha Example

Imagine that a portfolio manager in Europe "A" manages the fund "ABC" with the following data:

• The profitability achieved in 2015 = 6%.
• The risk-free asset in Europe is the German bund = 1%.
• The index to beat is the Eurostoxx, which has had an annual return of = 4%.
• The beta of the portfolio of manager «A» is = 0.5

α (ABC) = (6% -1%) - (4% -1%) * 0.5 = 3.5

Imagine that a portfolio manager in the United States "B" manages the fund "DEF" with the following data:

• The profitability achieved in 2015 = 8%.
• The risk-free asset in the US is the T bond = 2.5%.
• The index to beat is the S & P500, which has had an annual profitability of = 6%.
• The beta of the portfolio of manager «A» is = 1.5

α (DEF) = (8% -2.5%) - (6% -2.5%) * 1.5 = 0.25

Manager "A" has a Jensen Alpha of 3.5, while manager "B" has a Jensen Alpha of 0.25. Which is the best manager?

Clearly manager "A" is a much better manager, even achieving a lower annual return on their ABC fund, they are doing it assuming a lower risk measured by the beta which is 0.5 versus 1.5.