The Library

On empirical risk measurement with asymmetric returns data

Tools

Pedersen, Christian S. and Hwang, Soosung (2002) On empirical risk measurement with asymmetric returns data. Working Paper. Coventry: Warwick Business School, Financial Econometrics Research Centre. Working papers (Warwick Business School. Financial Econometrics Research Centre) (No.02-).

Preview

PDF
WRAP_Pedersen_fwp02-03.pdf - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (1105Kb)

Official URL: http://www2.warwick.ac.uk/fac/soc/wbs/research/wfr...

Abstract

By formulating a nested test of the asymmetric response model of Bawa, Brown, and Klein (1981), the mean-lower partial moment CAPM (LPMCAPM) of Bawa and Lindenberg (1977) and the mean-variance CAPM of Sharpe (1963, 1964), Lintner (1965) and Mossin (1969), this paper investigates the relative merits of symmetric and asymmetric risk measures using UK equity data for differently sized companies and at different frequencies. Our analysis shows that, when equity returns are not normal - which is the case for most daily and weekly returns, and for a large portion of smaller firms - the CAPM is rejected in 30%-50% of cases, and the optimal choice of alternative model is LPM-CAPM in over two thirds of these. These, and our further results, have strong consequences for the accurate measurement of equity risk, performance and prices, as downside and/or asymmetric risk measures often outperform the traditional CAPM framework, thus rendering it’s related and widely-used current approaches sub-optimal for some company sizes/data frequency combinations.

Item Type:

Working or Discussion Paper (Working Paper)

Subjects:

H Social Sciences > HG Finance
H Social Sciences > HD Industries. Land use. Labor > HD61 Risk Management

Divisions:

Faculty of Social Sciences > Warwick Business School > Financial Econometrics Research Centre
Faculty of Social Sciences > Warwick Business School

Library of Congress Subject Headings (LCSH):

Risk management, Rate of return, Small business -- Finance, Distribution (Probability theory)

Series Name:

Working papers (Warwick Business School. Financial Econometrics Research Centre)

Publisher:

Warwick Business School, Financial Econometrics Research Centre

Place of Publication:

Coventry

Official Date:

29 August 2002

Dates:

Date	Event
29 August 2002	Published

Number:

No.02-

Number of Pages:

Status:

Not Peer Reviewed

Access rights to Published version:

Open Access

References:

[1] Akaike, H., 1973, Information theory and an extension of the Maximum Likelihood Principle. Akademiai Kaido.
[2] Balzer, L., Fall 1984, Measuring investment risk: a review. The Journal of Investing, 47-58.
[3] Bawa, V., 1975, Optimal rules for ordering uncertain prospects. Journal of Financial Economics, 2, 95—121.
[4] Bawa, V., Brown, S. and R. Klein, 1981, Asymmetric response asset pricing models: Testable alternatives to mean-variance. Mimeo.
[5] Bawa, V. and E. Lindenberg, 1977. Capital market equilibrium in a mean-lower partial moment framework. Journal of Financial Economics 5, 89—200.
[6] Chamberlain, G., 1983, A characterisation of the distributions that imply meanvariance utility functions. Journal of Economic Theory, 185-201.
[7] Chen, S., June 1982, An examination of risk-return relationship in bull and bear markets using time-varying betas. Journal of Financial and Quantitative Analysis 17, 265-286.
[8] Chow, K. and K. Denning, 1994, On variance and lower partial moment betas and the equivalence of systematic risk measures. Journal of Business, Finance and Accounting, 231-241.
[9] Cosh, A. and A. Hughes, September 1995, Failures, acquisitions and post-merger success: The comparative financial characteristics of large and small companies. ESRC Centre for Business Research, University of Cambridge, Working Paper No. 18.
[10] Davidson, R. and J. MacKinnon, 1993, Estimation and inference in econometrics. Oxford University Press.
[11] DeGroot, M., 1989, Probability and Statistics. Addison Wesley, 2nd edition.
[12] Dimson, E., and P. Marsh, 1998, The Hoare Govett smaller companies index 1995-1997. Technical report, ABN Amro Hoare Govett.
[13] Dittmar, R., August 2000, Nonlinear Pricing Kernles, Kurtosis Preferences, and Evidence from the Cross-Section of Equity Returns. Working Paper, Indiana University.
[14] Eftekhari, B. and S. Satchell, 1996, Non-normality of returns in emerging markets. Research in International Business and Finance, Supplement 1, 267-277.
[15] Fabozzi, F. and J. Francis, December 1979, Mutual fund systematic risk for bull and bear markets: an empirical investigation. Journal of Finance 34, 1243-1250.
[16] Fabozzi, F. and J, Francis, September 1977, Stability tests for alphas and betas over bull and bear market conditions. Journal of Finance 32, 1093-1099.
[17] Fishburn, P., 1980. Foundations of risk measurement : I. Risk as a probability of loss. Management Science 30, 396—406.
[18] Grauer, R., 1981, Investment policy implications of the capital asset pricing model. Journal of Finance 36, 127-141.
[19] Harlow, W. and R. Rao, 1989, Asset-pricing in a generalised mean-lower partial moment framework : Theory and evidence. Journal of Financial and Quantitative Analysis, 24, 285—311.
[20] Harvey, C.R. and A. Siddique, 1999, Autoregressive Conditional Skewness. Journal of Financial and Quantitative Analysis 34 (4), 465-488.
[21] Henriksson, R., 1984, Market timing and mutual fund performance: An empirical investigation. Journal of Business 57, 73-96.
[22] Henriksson, R. and R. Merton, Oct. 1981, On market timing and investment performance. II statistical procedures for evaluating forecasting skills. Journal of Business 54, 513-533.
[23] Homaifar, G. and D.B. Graddy, Winter 1990, Variance and lower partial moment betas as alternative risk measures in cost of capital estimation: A defence of the CAPM beta. Journal of business finance and accounting 17, 677-688.
[24] Hughes, A. and D. Storey, 1994, Finance and the small firm. Routledge, London.
[25] Hwang, S. and S. E. Satchell, 2001, The Asset Allocation Decision in a Loss Aversion World, Financial Econometrics Research Centre, Working Paper WP01-7, City University Business School.
[26] Ingersoll, J., 1987, Theory of financial decision making. Rowman and Littlefield Publishers Inc.
[27] Jagannathan, R. and E. McGrattan, Fall 1995, The CAPM debate. Federal Reserve Bank of Minneapolis Quarterly Review 19, 2-17.
[28] Jensen, M., 1972. Capital markets : Theory and evidence. Bell Journal of Economics and Management Science 3, 357—398.
[29] Judge, G., Griffiths, W., Carter-Hill, R. and T. Lee, 1985, The Theory and Practice of Econometrics. Wiley and sons, 2nd edition.
[30] Kijima, K., Ohnishi, M., 1993. Mean-risk analysis of risk aversion and wealth effects on optimal portfolios with multiple investment opportunities. Annals of Operations Research 45, 147—163.
[31] Kim, M. and J. Zumwalt, December 1979, An analysis of risk in Bull and Bear markets. Journal of Financial and Quantitative Analysis 14, 1015-1025.
[32] Knight, J., Satchell, S. and K. Tran, 1995, Statistical modelling of asymmetric risk in asset returns. Applied Mathematical Finance 2, 155—172.
[33] Lintner, J., 1965, The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics 47, 13—37.
[34] Maddala, G.S., 1992, Introduction to Econometrics. Macmillan.
[35] Markowitz, H., 1952, Portfolio selection. Journal of Finance 7, 77—91.
[36] Menezes, C., Geiss, C. and J. Tressler, 1980, Increasing downside risk. The American Economic Review, 921—932.
[37] Mossin, J., 1969, Security pricing and investment criteria in competitive markets. American Economic Review 59, 749—756.
[38] Pedersen, C., 1998, Empirical tests for di!erences in equilibrium risk measure with application to downside risk in small and large UK companies. Cambridge Discussion Papers in Accounting and Finance, No. 41.
[39] Pedersen, C., 1999a, Four Essays on Risk in Finance. PhD thesis, Trinity College, University of Cambridge, England.
[40] Pedersen, C., 1999b, Separating risk and return in the CAPM: A general utility-based approach. European Journal of Operational Research (forthcoming), (AF39).
[41] Pedersen, C. and S. Satchell, 1998, An extended family of financial risk measures. Geneva Papers on Risk and Insurance: Theory 23, 89-117.
[42] Pedersen, C. and S. Satchell, 1999, Small sample analysis of performance measures in the asymmetric response model. Institute for Financial Research Discussion Papers, Birkbeck College, London (forthcoming).
[43] Price, K., Price, B. and T. Nantell, 1982, Variance and lower partial moment measures of systematic risk: Some analytical and empirical results. Journal of Finance 37, 843-855.
[44] Roll, R., June 1973, Evidence on the ’growth-optimum’ model. Journal of Finance 28, 551-566.
[45] Satchell, S., 1996. Lower partial moment capital asset pricing model : A reexamination. IFR Birkbeck College Discussion Paper No. 20.
[46] Schwartz, G., 1978, Estimating the dimension of a model. The Annals of Statistics 6, 461-464.
[47] Sharpe, W., January 1963, A Simplified model for portfolio analysis. Management Science, 277-293.
[48] Sharpe, W., 1964, Capital asset prices : A theory of capital market equilibrium under conditions of risk. Journal of Finance 19, 425—442.
[49] Sharpe, W., 1996. Mutual fund performance. Journal of Business, 119—138.
[50] Sortino, F. and R. Van der Meer, Summer 1991. Downside risk. The Journal of Portfolio Management, 27—31.
[51] Sortino, F., and L. Price, Fall 1994, Performance measurement in a downside risk framework. The Journal of Investing, 59—65.
[52] Storey, S., Keasey, K., Watson, P. and P. Wynarczyk, 1987, The performance of small firms. Croom Helm.
[53] Treynor, J., 1965, How to rate management of investment funds. Harvard Business Review, 63—75.