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The Jensen measure: This is the ratio of the portfolio’s return less the portfolio’s expected return as determined by the capital asset pricing model, or CAPM. The CAPM is an economic theory that describes the relationship between risk and the pricing of assets. The CAPM theory suggests that the only risk that is priced by investors is risk that cannot be diversified away. The CAPM in its most simple form shows that the expected return of a security or a portfolio is equal to the rate on a risk-free security plus the asset’s risk premium multiplied by the asset’s beta. The Jensen’s measure incorporates the CAPM into its calculation. The Jensen measure is calculated as follows.
Rp = Rf + (RMI – Rf) x β
Where,
Rp = Return on portfolio
RMI = Return on market index
Rf = Risk free rate of return
This measure is the ratio of the portfolio’s performance (rp) less the expected portfolio return as determined by CAPM or [rf + ßp (rm – rf)].
This measure by itself is sufficient to determine risk-adjusted performance. Since it is known that the market’s beta is 1.0 (by definition), and since the risk-free rate is both added and subtracted, the CAPM return is just the market return. Hence, if the Jensen’s measure is positive, the asset has outperformed on a risk-adjusted basis.
The Treynor measure is calculated dividing the portfolio risk premium by the portfolio risk as measured by the beta. An asset’s Treynor measure also must be measured against the market’s Treynor measure, which is calculated by dividing the market risk premium or the return on the market minus the risk-free rate by the beta of the market, which is 1.0. If the asset’s Treynor measure is greater than the market’s Treynor measure, the asset has outperformed on a risk-adjusted basis.
Like the Sharpe ratio, the Treynor ratio can be interpreted as the “quality” of portfolio return for the given level of risk but risk measured on a CAPM theory basis.
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