Testing for Mean-Coherent Regular Risk Spanning

Melenberg, Bertrand; Polbennikov, Simon

doi:10.2139/ssrn.807805

Cited by 1 publication

(10 citation statements)

References 42 publications

(66 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this paper we follow the approach developed by Huberman and Kandel (1987) for the mean-variance spanning and by Polbennikov and Melenberg (2005) for the mean-CRR spanning. The mean-variance spanning test is 12 based on the notion that the restrictions on the tangent portfolio weights can be expressed as moment restrictions on excess returns of assets in the portfolio.…”

Section: Iic Mean-variance and Mean-crr Spanning Testsmentioning

confidence: 99%

“…Our simulation study confirms that for portfolios with asymmetric distributions of returns, such as portfolios of derivatives or credit instruments, an optimization based on a coherent risk measure behaves differently as it accounts mostly for negative returns 3 . As second contribution, we implement spanning tests for the mean-coherent risk efficient frontiers as developed by Polbennikov and Melenberg (2005). These tests can be regarded as an analog for the usual mean-variance spanning tests, see DeRoon and Nijman (2001) for a survey of the mean-variance tests.…”

Section: Introductionmentioning

confidence: 99%

“…These moment restrictions can be reformulated in terms of restrictions in an OLS regression, see, for example also, DeRoon and Nijman (2001). Polbennikov and Melenberg (2005) develop a test similar to Huberman and Kandel (1987) for mean-CRR spanning, expressed in terms of restrictions on an IV regression coefficients.An alternative approach to the spanning test is followed by Britten-Jones (1999), who formulates the spanning hypothesis in the mean-variance framework in terms of restrictions on the tangent portfolio weights. These weights can be found as OLS regression coefficient.…”

mentioning

confidence: 99%

“…These weights can be found as OLS regression coefficient. Results from the previous subsection can be used to implement this approach in the mean-CRR setup with the restrictions on the OLS regression coefficients in Britten-Jones (1999) replaced by restrictions on the corresponding mean-CRR portfolio weights.In this paper we follow the approach developed by Huberman and Kandel (1987) for the mean-variance spanning and by Polbennikov and Melenberg (2005) for the mean-CRR spanning. The mean-variance spanning test is 12 based on the notion that the restrictions on the tangent portfolio weights can be expressed as moment restrictions on excess returns of assets in the portfolio.…”

mentioning

confidence: 99%

“…Thus, the spanning test in case of the mean-variance portfolio is equivalent to the significance test of the intercept α in OLS regression, 12 and the mean-CRR spanning test is equivalent to the significance test of the intercept α in the IV regression. The asymptotic properties of the IV intercept coefficient are discussed in Polbennikov and Melenberg (2005). …”

mentioning

confidence: 99%

See 4 more Smart Citations

Mean-Coherent Risk and Mean-Variance Approaches in Portfolio Selection: An Empirical Comparison

Polbennikov

Melenberg

2005

SSRN Journal

Self Cite

View full text Add to dashboard Cite

We empirically analyze the implementation of coherent risk measures in portfolio selection. First, we compare optimal portfolios obtained through mean-coherent risk optimization with corresponding mean-variance portfolios. We find that, even for a typical portfolio of equities, the outcomes can be statistically and economically different. Furthermore, we apply spanning tests for the mean-coherent risk efficient frontiers, which we compare to their equivalents in the meanvariance framework. For portfolios of common stocks the outcomes of the spanning tests seem to be statistically the same.Keywords: portfolio choice, mean variance, mean coherent risk, comparison. JEL Classification: G11. I IntroductionThere is an ongoing debate in the financial literature on which risk measure to use in risk management and portfolio choice. As some risk measures are more theoretically appealing, others are easier to implement practically. For a long time, the standard deviation has been the predominant measure of risk in asset management. Mean-variance portfolio selection via quadratic optimization, introduced by Markowitz (1952), used to be the industry standard (see, for instance, Tucker et al. (1994)). Two justifications for using the standard deviation in portfolio choice can be given. First, an institution can view the standard deviation as a measure of risk, which needs to be minimized to limit the risk exposure. Second, a mean-variance portfolio maximizes expected utility of an investor if the utility index is quadratic or asset returns jointly follow an elliptically symmetric distribution. 1 Despite the computational advantages, the variance is not a satisfactory risk measure from the risk measurement perspective. First, mean-variance portfolios are not consistent with second-order stochastic dominance (SDD) and, thus, with the benchmark expected utility approach for portfolio selection. Second, but not independently, as a symmetric risk measure, the variance penalizes gains and losses in the same way. Artzner et al. (1999) give an axiomatic foundation for so-called coherent risk measures. They propose that a "rational" risk measure related to capital requirements 2 should be monotonic, subadditive, linearly homogeneous, and translation invariant. Tasche (2002) and Kusuoka (2001) demonstrate that a Choquet expectation with a concave distortion function represents a general class of coherent risk measures. Moreover, with some additional regularity restrictions, as imposed by Kusuoka (2001), the class of coherent risk measures becomes consistent with the second order stochastic dominance principle and thus generates portfolios consistent with the expected utility paradigm, see, for example, Ogryczak andRuszczyński (2002) andDe Giorgi (2005).The class of coherent risk measures generalizes expected shortfall, a co- Ingersoll (1987). 2 The capital requirements are relevant for asset management since they are directly applied to financial institutions, see the Basel Accord (1999).3 herent risk measure which received a...

show abstract

Section: Iic Mean-variance and Mean-crr Spanning Testsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 3 more Smart Citations