Staying ahead on downside risk 159
when the same signal is used. An important question is whether it is possible
to limit the downside without sacrificing the upside of portfolio returns. As for
the theory, it would be possible to develop a model in which the objective func-
tion consists of a linear combination of several expectiles. This would allow
the portfolio manager to incorporate his or her preferences on the shape of the
distribution of returns in the asset allocation process.
References
Acerbi , C. ( 2004 ). Coherent representations of subjective risk aversion. In G. Szeg ö
(Ed.) , Risk measures for the 21st century (pp. 147 – 207 ). Chichester: Wiley.
Artzner , P. , Delbaen , F. , Eber , J.-M. , & Heath , D. ( 1999 ). Coherent measures of risk.
Mathematical Finance , 9 , 203 – 228.
Basset , G. W. , Koenker , R. , & Kordas , G. ( 2004 ). Pessimistic portfolio allocation and
Choquet expected utility. Journal of Financial Econometrics , 2 ( 4 ) , 477 – 492.
De Rossi, G. (2009). Time varying expectiles and dynamic asset allocation, Working
paper.
De Rossi, G., & Harvey, A.C. (2006). Time-varying quantiles, Cambridge Working
Papers in Economics, 0649.
De Rossi, G., & Harvey, A.C. (2009). Quantiles, expectiles and splines. Journal of
Econometrics , Forthcoming.
Engle , R. , & Rangel , J. G. ( 2008 ). The spline GARCH model for low frequency vol-
atility and its global macroeconomic causes. Review of Financial Studies , 21 ,
1187 – 1222.
Granger , C. W. J. , & Sin , C. Y. ( 2000 ). Modelling the absolute returns of different stock
indices: Exploring the forecastability of an alternative measure of risk. Journal of
Forecasting , 19 , 277 – 298.
Grinold , R. C. , & Kahn , R. N. ( 2000 ). Active portfolio management. New York :
MGraw-Hill.
Jondeau , E. , & Rockinger , M. ( 2006 ). Optimal portfolio allocation under higher
moments. European Financial Management , 12 , 29 – 55.
Kuan, C.-M., Yeh, J.H., & Hsu, Y.-C. (2009). Assessing value at risk with CARE, the
Conditional AutoRegressive Expectile Models. Journal of Econometrics , Volume
150(2), pp. 261 – 270.
Ledoit , O. , & Wolf , M. ( 2004 ). Honey, I shrunk the sample covariance matrix. Journal
of Portfolio Management , 30 , 110 – 119.
Madan , D. B. ( 2006 ). Equilibrium asset pricing: With non-Gaussian factors and expo-
nential utilities. Quantitative Finance , 6 ( 6 ) , 455 – 463.
Manganelli, S. (2007). Asset allocation by penalized least squares. ECB Working paper 723.
Menc ì a, J,. & Sentana, E. (2008). Multivariate location-scale mixtures of normals
and mean – variance – skewness portfolio allocation. Journal of Econometrics ,
Forthcoming.
Meucci , A. ( 2006 ). Beyond Black – Litterman: Views on non-normal markets. Risk
Magazine , 19 ( 2 ) , 96 – 102.
Newey , W. K. , & Powell , J. L. ( 1987 ). Asymmetric least squares estimation and testing.
Econometrica , 55 , 819 – 847.