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Variance vs downside risk: Is there really that much difference? (English) Zbl 0935.91021
Summary: The popularity of downside risk among investors is growing and mean return-downside risk portfolio selection models seem to oppress the familiar mean-variance approach. The reason for the success of the former models is that they separate return fluctuations into downside risk and upside potential. This is especially relevant for asymmetrical return distributions, for which mean-variance models punish the upside potential in the same fashion as the downside risk.
The paper focuses on the differences and similarities between using variance or a downside risk measure, both from a theoretical and an empirical point of view. We first discuss the theoretical properties of different downside risk measures and the corresponding mean-downside risk models. Against common beliefs, we show that from the large family of downside risk measures, only a few possess better theoretical properties within a return-risk framework than the variance. On the empirical side, we analyze the differences between some US asset allocation portfolios based on variances and downside risk measures. Among other things, we find that the downside risk approach tends to produce on average – slightly higher bond allocations than the mean-variance approach. Furthermore, we take a closer look at estimation risk, viz. the effect of sampling error in expected returns and risk measures on portfolio composition. On the basis of simulation analyses, we find that there are marked differences in the degree of estimation accuracy, which calls for further research.

91B28 Finance etc. (MSC2000)
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[1] Arrow, K.J., 1970. Essays in the Theory of Risk-Bearing, North-Holland, Amsterdam · Zbl 0215.58602
[2] Baumol, W.J., An expected gain – confidence limit criterion for portfolio selection, Management science, 10, 1, 174-182, (1963)
[3] Bawa, V.S., Optimal rules for ordering uncertain prospects, Journal of financial economics, 2, 95-121, (1975)
[4] Bawa, V.S., 1978. Safety-first, stochastic dominance and optimal portfolio choice, Journal of Financial and Quantitative Analysis, 255-271
[5] Bawa, V.S.; Lindenberg, E.B., Capital market equilibrium in a mean – lower partial moment framework, Journal of financial economics, 5, 189-200, (1977)
[6] Best, M.J.; Grauer, R.G., Positively weighted minimum-variance portfolios and the structure of asset expected returns, The journal of financial and quantitative analysis, 27, 4, 513-537, (1992)
[7] Borch, K., A note on uncertainty and indifferent curves, Review of economic studies, 36, 1-4, (1969)
[8] Chamberlain, G., A characterization of the distributions that imply mean – variance utility functions, Journal of economic theory, 29, 185-201, (1983) · Zbl 0495.90009
[9] Choobineh, F.; Branting, D., A simple approximation for semivariance, European journal of operational research, 27, 364-370, (1986)
[10] Chow, K.; Denning, K.C., On variance and lower partial moment betas: the equivalence of systematic risk measures, Journal of business finance and accounting, 21, 2, 231-241, (1994)
[11] Feldstein, M.S., Mean – variance analysis in the theory of liquidity preference and portfolio selection, Review of economic studies, 36, 5-12, (1969)
[12] Fishburn, P.C., 1977. Mean-risk analysis with risk associated with below-target returns, The American Economic Review, 116-126
[13] Fisher, I., 1906. The Nature of Capital and Income, Macmillan, New York
[14] Frankfurter, G.M.; Phillips, H.E.; Seagle, J.P., Portfolio selection: the effect of uncertain means, variances, and covariances, The journal of financial and quantitative analysis, 6, 5, 1251-1262, (1971)
[15] Hakansson, N., Mean-variance analysis in a finite world, Journal of financial and quantitative analysis, 5, 1873-1880, (1972)
[16] Harlow, W.V.; Rao, R.K.S., Asset pricing in a generalised mean – lower partial moment framework: theory and evidence, Journal of financial and quantitative analysis, 3, 285-0311, (1989)
[17] Haugen, R.A., Baker, N.L., 1990. Dedicated stock portfolios, The Journal of Portfolio Management, Summer, 17-22
[18] Haugen, R.A., Baker, N.L., 1991. The efficient market inefficiency of capitalization-weighted stock portfolios, The Journal of Portfolio Management, Spring, 35-40
[19] Hicks, J.R., Liquidity, Economic journal, 72, 787-802, (1962)
[20] Hogan, W.W., Warren, J.M., 1972. Computation of the efficient boundary in the E-S portfolio selection model, Journal of Financial and Quantitative Analysis, 1881-1896
[21] Holthausen, D.M., A risk – return model with risk and return measured as deviations from a target, American economic review, 71, 1, 182-188, (1981)
[22] Homaifar, G.; Graddy, D.B., Variance and lower partial moment betas as alternative risk measures in cost of capital estimation: A defense of the CAPM beta, Journal of business finance and accounting, 17, 5, 677-688, (1990)
[23] Jorion, Ph., International portfolio diversification with estimation risk, The journal of business, 58, 3, 259-278, (1985)
[24] Jorion, Ph., 1992. Portfolio optimization in practice, Financial Analysts Journal, 68-74
[25] Kang, T.; Brorsen, B.W.; Adam, B.D., A new efficiency criterion: the Mean-separated target deviations model, Journal of economics and business, 48, 1, 47-66, (1996)
[26] Kataoka, S., A stochstic programming model, Econometrica, 31, 1-2, 181-196, (1963) · Zbl 0125.09601
[27] Kroll, Y.; Levy, H.; Markowitz, H.M., Mean – variance versus direct utility maximalization, Journal of finance, 39, 47-61, (1984)
[28] Lee, W.Y.; Rao, R.K.S., Mean – lower partial moment valuation and lognormally distributed returns, Management science, 4, 446-453, (1988) · Zbl 0638.90008
[29] Markowitz, H.M., Theories of uncertainty and financial behavior, Econometrica, 19, Chicago Meeting Report, 325-326, (1950)
[30] Markowitz, H.M., 1952. Portfolio selection, Journal of Finance, 7 (1), 77-91
[31] Markowitz, H.M., 1959. Portfolio Selection: Efficient Diversification of Investments, Wiley, New York
[32] Markowitz, H.M., Computation of mean – semivariance efficient sets by the critical line algorithm, Annals of operational research, 45, 307-317, (1993) · Zbl 0785.90017
[33] Meyer, J., Two-moment decision models and expected utility maximization, The American economic review, 77, 421-430, (1987)
[34] Michaud, R.O., 1989. The Markowitz optimization enigma: Is optimized optimal? Financial Analysts Journal, 31-42
[35] Nawrocki, D.N., Optimal algorithms and lower partial moments: ex post results, Applied economics, 23, 465-470, (1991)
[36] Owen, J.; Rabinovitch, R., On the class of ellipitical distributions and their applications to the theory of portfolio choice, The journal of finance, 38, 3, 745-752, (1983)
[37] Pratt, J., 1964. Risk aversion in the small and in the large, Econometrica, 122-136 · Zbl 0132.13906
[38] Rom, B.M., Ferguson, K.W., 1994. Post-modern portfolio theory comes of age, Journal of Investing Fall, 11-17
[39] Roy, A.D., 1952. Safety first and the holding of assets, Econometrica, 431-449 · Zbl 0047.38805
[40] Sharpe, W.F., 1963. A simplified model for portfolio analysis, Management Science, 277-293
[41] Telser, L., Safety-first and hedging, review of economic studies, 23, 1-16, (1955)
[42] Tsiang, S.C., The rationale of the mean – standard deviation analysis, skewness preference and the demand for money, The American economic review, 62, 3, 354-371, (1972)
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