Jensen’s Measure

The Basics of Jensen's Measure

When it comes to evaluating the performance of investment portfolios, there are several metrics and measures that investors and financial analysts use. One such measure is Jensen's Measure, also known as Jensen's Alpha. Developed by Michael Jensen in 1968, Jensen's Measure is a widely recognized and respected tool for assessing the risk-adjusted performance of an investment portfolio.

Understanding Jensen's Measure

Jensen's Measure is a performance metric that helps investors determine whether a portfolio manager has generated excess returns above what would be expected given the level of risk taken. It takes into account both the portfolio's actual returns and the returns that would be expected based on the portfolio's exposure to systematic risk.

Systematic risk, also known as market risk, refers to the risk that cannot be diversified away. It is the risk associated with the overall market or a particular segment of the market. Jensen's Measure compares the actual returns of a portfolio to the returns that would be expected based on the portfolio's exposure to systematic risk, as measured by a benchmark index.

Calculating Jensen's Measure

The formula for calculating Jensen's Measure is as follows:

Jensen's Measure = Portfolio Return – (Risk-Free Rate + Beta * (Benchmark Return – Risk-Free Rate))

Let's break down the components of the formula:

• Portfolio Return: The actual return generated by the portfolio.
• Risk-Free Rate: The rate of return on a risk-free investment, such as a government bond.
• Beta: A measure of the portfolio's sensitivity to systematic risk. A beta of 1 indicates that the portfolio's returns move in line with the benchmark index, while a beta greater than 1 indicates higher volatility.
• Benchmark Return: The return of the benchmark index, which represents the overall market or a specific segment of the market.

By subtracting the expected return from the actual return, Jensen's Measure provides a measure of the portfolio manager's ability to generate excess returns above what would be expected given the level of risk taken.

An Example of Jensen's Measure in Action

Let's consider an example to illustrate how Jensen's Measure works. Suppose an investor has a portfolio with an actual return of 12%, a risk-free rate of 3%, a beta of 1.2, and a benchmark return of 10%. Using the formula, we can calculate Jensen's Measure:

Jensen's Measure = 12% – (3% + 1.2 * (10% – 3%))

Jensen's Measure = 12% – (3% + 1.2 * 7%)

Jensen's Measure = 12% – (3% + 8.4%)

Jensen's Measure = 12% – 11.4%

Jensen's Measure = 0.6%

In this example, the positive value of 0.6% indicates that the portfolio manager has generated excess returns above what would be expected given the level of risk taken. This suggests that the portfolio manager has added value through their investment decisions.

The Significance of Jensen's Measure

Jensen's Measure is a valuable tool for investors and financial analysts for several reasons:

• Risk-Adjusted Performance: Jensen's Measure takes into account the level of risk taken by a portfolio and provides a measure of the portfolio manager's ability to generate excess returns. This makes it a useful metric for evaluating the risk-adjusted performance of investment portfolios.
• Comparative Analysis: By comparing the Jensen's Measure of different portfolios or portfolio managers, investors can identify those who consistently outperform their peers or benchmarks.
• Portfolio Optimization: Jensen's Measure can help investors optimize their portfolios by identifying the optimal level of risk and return trade-off. It allows investors to assess whether the excess returns generated by a portfolio are worth the additional risk taken.

Limitations of Jensen's Measure

While Jensen's Measure is a widely used performance metric, it does have some limitations:

• Reliance on Historical Data: Jensen's Measure relies on historical data to calculate expected returns and beta. As a result, it may not accurately reflect future performance.
• Assumption of Linear Relationship: Jensen's Measure assumes a linear relationship between the portfolio's returns and the benchmark returns. In reality, the relationship may be more complex.
• Dependence on Benchmark Selection: The choice of benchmark index can significantly impact the calculation of Jensen's Measure. Different benchmarks may yield different results.

Conclusion

Jensen's Measure is a powerful tool for evaluating the risk-adjusted performance of investment portfolios. By comparing the actual returns of a portfolio to the returns that would be expected based on the portfolio's exposure to systematic risk, Jensen's Measure provides valuable insights into the portfolio manager's ability to generate excess returns. However, it is important to consider the limitations of Jensen's Measure and use it in conjunction with other performance metrics to make well-informed investment decisions.