Jensen's Index

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Jensen's Index

A measure of the return on a portfolio over what the capital asset pricing model predicts, given the beta and market return on that portfolio. The index also adjusts for risk. It is also called Jensen's alpha or Jensen's measure. It is calculated as:

Jensen's Index = ((Portfolio's return - Risk-free return) + (Market return - Risk-free return)) * Beta
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Jensen (1967) also created a portfolio performance measurement tool called Jensen Alpha. Jensen Alpha is a special measurement for risk-adjusted returns from portfolio performance which specifically emphasizes a systematic risk.
All of these variables were important to calculate the Sharpe Index, Treynor Ratio, Jensen Alpha, and Information Ratio.
The Jensen alpha index is a measure indicating the absolute benefits or lack of benefits from the investment.
The analysis has been made on the basis of mean return, beta risk, co-efficient of determination, Sharpe ratio, Treynor ratio and Jensen Alpha. The overall analysis finds Franklin Templeton and UTI being the best performers and Birla SunLife, HDFC and LIC mutual funds showing poor below-average performance.
All the sample schemes were not well diversified as depicted by the differences in the Jensen alpha and Sharpe's Differential return.
To explore this dimension of the analysis we use the Sharpe ratio, Jensen alpha and the Treynor ratio measures.
As for its relation with other evaluation measures, IR can be expressed in terms of Jensen alpha (raw fund return less return predicted by CAPM) when excess returns are estimated with historical data using the single-factor regression equation mentioned in the previous section, while Sharpe ratio (fund risk premium divided by standard deviation of fund return) is a special case of IR (Goodwin, 1998).
The average Jensen alpha is -0.00052 with a minimum value of -0.00969 and a maximum value of 0.00482, showing that on average the CBs issuance firms earn about 0.052% less per day than they should have earned given their level of systematic risk.
Due to the significant correlations among portfolios in the residuals, we employ the GRS multivariate statistics, instead of focusing on the Jensen alpha in the following discussion of abnormal performance of various portfolios.(12)
The Jensen Alpha, which is based on the Capital Asset Pricing Model (CAPM), looks at investment performance by calculating the intercept ([a.sub.p]) of the regression line: [R.sub.p] - [R.sub.f] = [a.sub.p] + [[beta].sub.p]([R.sub.m] - [R.sub.f]) + [e.sub.t].
Table 2 summarizes the Jensen alphas obtained for the DSI over the entire period 1986 through 1994 and the two subperiods respectively.