σ = Total risk, standard deviation of portfolio return j
If Sj of the mutual fund scheme is greater than that of the market portfolio, the fund has
outperformed the market. The superiority of the Sharpe ratio over the Treynor ratio is, it
considers the point whether investors are reasonably rewarded for the total risk in comparison to
the market. A mutual fund scheme with a relatively large unique risk may outperform the market
in Treynor's index and may underperform the market in Sharpe ratio. A mutual fund scheme with
large Treynor ratio and low Sharpe ratio can be concluded to have relatively larger unique risk.
Thus the two indices rank the funds differently
Jensen's Measure
Jensen (1968) has given different dimension and confined his attention to the problem of
evaluating a fund manager's ability of providing higher returns to the investors. He measures the
performance as the excess return provided by the portfolio over the expected (CAPM) returns.
The performance measure, denoted by JP. He assumes that the investor expects at least CAPM
returns.
(Rp) = Rf + βj x [(Rm) – Rf]
Where,
(Rp) = Expected portfolio return during a particular period j
Rf = Risk free interest rate
Rm = return on market/benchmark portfolio
βj = Volatility of portfolio return against that of market Portfolio return or portfolio's market risk.
βj, is a measure of systematic risk of the portfolio and is calculated using following equation A
positive value of J would indicate that the scheme has provided a higher return over the CAPM
return and lies above Security Market Line (SML) and a negative value would indicate it has
provided a lower than expected returns and lies below SML. The Jensen model assumes that the
portfolio is fully invested and is subjected to the limitations of CAPM.