Jensen's Measure

Jensen's measure is a statistical measure of the performance of an investment manager. It is calculated by taking the difference between the return on an investment and the return on a benchmark index, and then dividing that difference by the standard deviation of the investment's returns.

Jensen's measure is used to measure the active return of an investment manager, which is the return that is in excess of the return of the benchmark index. An active return can be positive or negative, and a positive active return indicates that the investment manager has outperformed the benchmark index.

Jensen's measure is a useful tool for evaluating the performance of an investment manager, but it has some limitations. One limitation is that it does not take into account the risk of the investment. Another limitation is that it is based on historical data, and there is no guarantee that an investment manager will continue to outperform the benchmark index in the future.

Despite its limitations, Jensen's measure is a valuable tool for evaluating the performance of an investment manager. It can be used to compare the performance of different investment managers, and it can help investors to identify those managers who are consistently able to outperform the benchmark index.

Here is a more mathematical explanation of Jensen's measure:

Jensen's measure is calculated as follows:

$$Jensen's\ Measure = \frac{R_i - R_f}{\sigma_i}$$

where:

* $R_i$ is the return on the investment
* $R_f$ is the risk-free rate of return
* $\sigma_i$ is the standard deviation of the investment's returns

Jensen's measure can be used to compare the performance of different investments, and to identify those investments that have outperformed the market. It can also be used to evaluate the performance of investment managers, and to identify those managers who have consistently outperformed the market.

Jensen's measure is a useful tool for investors, but it is important to understand its limitations. One limitation is that Jensen's measure does not take into account the risk of the investment. Another limitation is that Jensen's measure is based on historical data, and there is no guarantee that an investment will continue to outperform the market in the future.

Despite its limitations, Jensen's measure is a valuable tool for investors. It can be used to identify investments that have the potential to outperform the market, and it can be used to evaluate the performance of investment managers.