In what returns adjusted to risk is concerned, they used the Sharpe Index (IS), the Treynor Index (T), the M2 Index, Jensen's Alpha
(a) and the Sortino Index (S).
ratios of: Sharpe, Treynor, Jensen (Jensen's alpha
), Sortino, Sharpe-Israelsen, Omega, potential excess return (UPR) and information (IR).
(iii) Jensen's alpha
: the buy-and-hold abnormal returns are obtained using the capital asset pricing model (CAPM).
The results are valid both for excess average return and for the Jensen's alpha
and the Sharpe ratio.
One would think that Jensen's research debunking the myth of consistently outperforming fund managers (measured by alpha, also known as Jensen's alpha
) would strike a blow in the remarkably efficient marketplace for actively managed mutual funds.
In order to achieve this it uses Jensen's alpha
to identify stocks that provide higher actual returns compared to their expected returns when considering systematic risk as derived by the capital asset pricing model.
This relationship is maintained using different measures of performance (raw return and Jensen's Alpha
) as shown by Sirri and Tufano (1998), Fant and O'Neal (2000) and Del Guercio and Tkac (2002), and its level of convexity is higher in smaller, younger mutual funds that demonstrate higher participation costs, according to Chevalier and Ellison (1997), Goriaev et al.
Earlier studies of fund performance evaluation are started with the models based on Jensen's alpha
(i.e., Jensen 1968), and are then extended by adding more variables as explanatory factors (i.e., Carhart 1997) to improve the models.
Point estimates of Jensen's alpha
provide some evidence of superior returns, although none of the individual point estimates is statistically significant at the 5% level.
These composite portfolio performance measures are the Sharpe ratio, the Treynor ratio, the Jensen's alpha
measure, and the information ratio.
The latter use either Jensen's alpha
as a single output or both the Sharpe ratio and Jensen's alpha
as outputs and some ETFs characteristics as inputs.
Redman, Gullett and Manakyan (2000) examined the risk-adjusted returns using Sharpe's Index, Treynor's Index, and Jensen's Alpha
for five portfolios of international mutual funds and for three time periods: 1985-1994, 1985-1989, and 1990-1994.