Jensen’s alpha (α): a tool for measuring investment performance

What is Jensen’s alpha

Jensen’s alpha is a key indicator for measuring the “risk-adjusted” performance of an investment fund or portfolio, highlighting the extra return that exceeds the expected return based on the systematic risk taken. Developed by economist Michael Jensen, this index compares the portfolio’s actual return with its theoretical return, considering its exposure to market risk, expressed by beta (β).

Calculating alpha is essential for understanding whether a fund manager has achieved a performance that justifies the risk incurred or whether, on the contrary, the returns achieved have not lived up to expectations for the level of risk. Its relevance is greatest for those wishing to assess the effectiveness of active management and is based on Capital Asset Pricing Model (CAPM) parameters.

The formula of the calculation is:

\(\alpha = R_p – (\beta \cdot R_m)\)

where:

\(\alpha\) : represents the risk-adjusted extra return

\(R_p\) : indicates the portfolio return net of the risk-free rate

\(\beta\) : is the beta coefficient and expresses the systematic riskiness of the portfolio

\(R_m\) : is the average market return

How Jensen’s alpha works in the context of the CAPM

Jensen’s alpha is based on the principles of the Capital Asset Pricing Model (CAPM), a financial theory that relates the expected return on a financial asset to its systematic risk. In CAPM, beta is a measure of the market risk associated with a portfolio or security relative to the entire market. If the alpha is positive, it means that the fund has outperformed the expected return, demonstrating effective management. Conversely, a negative alpha indicates performance below expectations, suggesting that the investment has not adequately compensated for the risk taken. This type of assessment allows investors to obtain accurate indications of the quality of fund management and the effectiveness of the strategies employed. With the use of Jensen’s alpha, return is then related to risk, allowing for a clearer recognition of whether a positive outcome is due to a winning strategy or pure chance.

Calculate Jensen’s alpha

This Jensen’s Alpha calculator allows you to evaluate a portfolio’s performance relative to the risk taken. By entering the portfolio’s return, beta, and market return, you can find out whether management has outperformed or underperformed.

Enter values to calculate Jensen’s alpha:

Average portfolio return (Rp) in %:

Beta (𝛽):

Average market return (Rm) in %:

Calculate Alpha

Result:

Evaluating investment choices

Measuring Jensen's alpha allows investors to better understand a fund's ability to generate outperformance relative to a benchmark, such as a market index, after accounting for risk. For example, if an equity fund has a beta of 1.2 and the market returns 10%, the expectation is that the fund will produce a return of 12% (10% x 1.2). If the fund's return is 14%, the alpha will be positive (+2%) and will indicate that the fund has outperformed expectations.

In high volatility environments, tracking error, which measures the deviation of a fund's return from the benchmark, becomes a complementary element to alpha, giving investors even more detailed insight. In addition, indicators such as Information Ratio and Appraisal Ratio can be integrated into the analysis for a comprehensive assessment, as they provide additional metrics of the quality of portfolio management and its efficiency relative to the risk taken.

Differences between Jensen's alpha and other performance indices

While Jensen's alpha focuses on return relative to systematic market risk, other indices such as Sharpe's Index and Treynor's Index offer different perspectives for evaluating performance.

• Sharpe's Index measures return relative to total volatility
• Treynor's Index analyzes return per unit of systematic risk.
• Modigliani Index: assesses performance relative to a benchmark
• Sortino Index: assesses the ability to achieve superior returns in situations of asymmetric risk.

Each indicator addresses specific analytical needs and allows investors to identify the approach most in line with their return objectives. Choosing one or more of these indices helps determine not only whether the investment generated outperformance, but also how this return was achieved, providing a more complete and personalized view of portfolio risk and performance.

The importance in managing diversified portfolios

Jensen's alpha plays a key role in the management of diversified portfolios, as it provides accurate indications of the manager's value added relative to the market. In active management, a positive alpha is a signal of the manager's ability to select securities capable of outperforming the benchmark.

In addition, tools such as the Treynor Index and Information Ratio can help to better understand the quality of the investment choices made. Within a broadly diversified portfolio, the risk premium is directly linked to additional performance relative to the market, and alpha becomes a valuable tool for quantifying its value.

This analysis gives investors a clear view of the additional return achieved and how the portfolio responds to systematic risk, facilitating more informed choices for optimal resource allocation.

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