Table I. Performance metrics Name Risk... | Emerald Publishing

Table I.

Performance metrics

Name	Risk metric	Portfolio theory	Formula
Absolute return	No risk adjustment	None	R_p
Excess return on benchmark	No direct risk adjustment	None	R_p − R_b
Sharpe ratio	Standard deviation	Modern*	$\frac{R_{p} - R_{f}}{σ_{p}}$
Treynor ratio	Beta CAPM	Modern	$\frac{R_{p} - R_{f}}{b_{p}}$
Jensen’s alpha	Beta CAPM	Modern	R_p − (R_f + b_p (R_m − R_f)
Information ratio	Standard deviation of residual or tracking error	Modern*	$\frac{α_{p}}{σ_{ε p}}$
Modigliani and Modigliani – M²	Beta CAPM	Modern*	$(\frac{R_{p} - R_{f}}{σ_{p}}) σ_{m} - R_{f}$
Sortino ratio	Semivariance	Post-modern	$\frac{R_{p} - R_{f}}{\sqrt{{S V}_{p}}}$
Return relative to VaR	VaR	Post-modern	$\frac{R_{p} - R_{f}}{{V a R}_{}}$

Name	Risk metric	Portfolio theory	Formula
Absolute return	No risk adjustment	None	R_p
Excess return on benchmark	No direct risk adjustment	None	R_p − R_b
Sharpe ratio	Standard deviation	Modern*	$\frac{R_{p} - R_{f}}{σ_{p}}$
Treynor ratio	Beta CAPM	Modern	$\frac{R_{p} - R_{f}}{b_{p}}$
Jensen’s alpha	Beta CAPM	Modern	R_p − (R_f + b_p (R_m − R_f)
Information ratio	Standard deviation ofresidual or tracking error	Modern*	$\frac{α_{p}}{σ_{ε p}}$
Modigliani and Modigliani – M²	Beta CAPM	Modern*	$(\frac{R_{p} - R_{f}}{σ_{p}}) σ_{m} - R_{f}$
Sortino ratio	Semivariance	Post-modern	$\frac{R_{p} - R_{f}}{\sqrt{{S V}_{p}}}$
Return relative to VaR	VaR	Post-modern	$\frac{R_{p} - R_{f}}{{V a R}_{}}$

Note:

*

The empirical tests reported in Section 4 compare the adoption of these performance measures based on the modern theory of portfolios with the adoption of the Sortino index and the return relative to VaR