Hostname: page-component-cb9f654ff-qc88w Total loading time: 0 Render date: 2025-08-28T13:26:27.291Z Has data issue: false hasContentIssue false
  • English
  • Français

Small Sample Analysis of PerformanceMeasures in the Asymmetric ResponseModel

Published online by Cambridge University Press:  06 April 2009

Christian S. Pedersen  and
Stephen E. Satchell
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper reviews and extends definitions andproperties of the three classical performancestatistics (the Sharpe Ratio, the Treynor Index, andJensen's Alpha) by locating them in a more generalframework: the Asymmetric Response Mode. This allowsvarious notions of beta, which can be related todownside risk, to be employed, and includes, asspecial cases, a market timing model and themean-variance CAPM. Due to the general lack of dataon fund performance in practice, our emphasis is onsmall sample analysis where possible. We illustrateour results empirically using data on 15 U.S.-basedemerging markets investment funds.

Information

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 35 , Issue 3 , September 2000 , pp. 425 - 450
Copyright
Copyright © School of Business Administration, University of Washington 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

*

Pedersen, Oliver, Wyman and Company and HonoraryAssociate of the Financial Econometrics Project,Department of Applied Economics, CambridgeUniversity; Sagchell, Faculty of Economics andPolitics, Cambridge University, Austin RobinsonBuilding, Sidgwick Avenue, Cambridge CB3 9DD,Great Britain. The authors thank Akhtar Siddique(the referee) for helpful comments. This articleis completely independent of Oliver, Wyman andCompany and the opinions expressed are those ofthe authors alone.

References

Bawa, V.; Brown, S.; and Klein, R.. “Asymmetric Response Asset Pricing Modls: Testable Alternatives o Mean-variance.” Mimeo (1981).Google Scholar
Bawa, V., and Lindenberg, E.. “Capital Market Equilibrium in a Mean-Lower Partial Moment Framework.” Journal of Financial Economics, 5 (1977), 189–200.10.1016/0304-405X(77)90017-4Google Scholar
Chen, N. Copeland, T.; and Mayers, D.. “A Comparison of Single and Multifactor Portfolio Performance Methodologies.” Journal of Financial Quantitative Analysis, 22 (12 1987), 401–417.10.2307/2330792S0022109000012758Google Scholar
Chen, S. “An Examination of Risk-Return Relationship in Bull and Bear Markets Using Time-Varying betas.” Journal of Financial and Quantitative Anylysis, 17 (06 1982), 258–286.Google Scholar
Connor, G., and Korajczyk, R.. “Performance Measurement with the Arbitrage Pricing Theory.” Journal of Financial Economics, 15 (1986), 373–394.10.1016/0304-405X(86)90027-9Google Scholar
Eftekhari, B., and Satchell, S.. “Non-Normality of Returns in Emerging Markets.” Research in International Business and Finance, Supplement 1 (1996), 267–277.Google Scholar
Fabozzi, F., and Francis, J.. “Stability Tests for Alphas and Betas over Bull and Bear Market Conditions.” Journal of Finance, 32 (09 1977), 1093–1099.10.2307/2326515Google Scholar
Fabozzi, F., and Francis, J.. “Mutual Fund Systematic Risk for Bull and Bear Markets: An Empirical Investigation.” Journal of Finance, 34 (12 1979), 1243–1250.10.2307/2327248Google Scholar
Fabozzi, F. Francis, J.; and Lee, C.. “General Functional Forms for Mutual Fund Returns.” Journal of Financial and Quantitative Analysis, 15 (12 1980), 1107–1120.10.2307/2330174S0022109000014046Google Scholar
Ferson, W., and Schadt, R.. “Measuring Fund Strategy and Performance in Changing Economic Conditions.” Journal of Finance, 51 (06 1996), 425–461.10.2307/2329367Google Scholar
Fieller, E. “Some Problems in Interval Estimation.” Journal of the Royal Statistical Society, 45 (1954), 175.Google Scholar
Hansen, B. E. “Autoregressive Conditional Density Estimation.” International Economic Review, 35 (1994), 705–730.10.2307/2527081Google Scholar
Harlow, W., and Rao, R.. “Asset Pricing in a Generalized Mean-Lower Partial Moment Framework: Theory and Evidence.” Journal of Financial and Quantitative Analysis, 24 (1989), 285–311.10.2307/2330813S0022109000013557Google Scholar
Harvey, C., and Siddique, A.. “Autoregressive Conditional Skewness.” Journal of Financial and Quantitative Analysis, 34 (12 1999), 465–487.10.2307/2676230S0022109000001277Google Scholar
Harvey, C., and Siddique, A.. “Conditional Skewness in Asset Pricing Tests.” Journal of Finance, 55 (06 2000), 1263–1295.10.1111/0022-1082.00247Google Scholar
Henriksson, R. “Market Timing and Mutual Fund Performance: An Empirical Investigation.” Journal of Business, 57 (1984), 73–96.10.1086/296225Google Scholar
Henriksson, R., and Merton, R.. “On Market Timing and Investment Performance. II. Statistical Procedures for Evaluating Forecasting Skills.” Journal of Business, 54 (10 1981), 513–533.10.1086/296144Google Scholar
Jarque, C. M., and Bera, A. K.. “Efficient Tests for Normality, Homoskedasticity and Serial Dependence of Regression Residuals.” Economic Letters, 6 (1980), 255–259.10.1016/0165-1765(80)90024-5Google Scholar
Jensen, M. “The Performance of Mutual Funds in the Period 1945–64.” Journal of Finance, 19 (05 1964), 389–416.Google Scholar
Jensen, M.. “Capital Markets: Theory and Evidence.” Bell Journal of Economics and Management Science, 3 (Fall 1972), 357–398.10.2307/3003029Google Scholar
Jobson, J., and Korkie, B.. “Performance Hypothesis Testing with the Sharpe and Treynor Measures.” Journal of Finance, 36 (09 1981), 889–908.10.2307/2327554Google Scholar
Jorion, P. Value at Risk. New York, NY: McGraw-Hill (1997).Google Scholar
Kim, M., and Zumwalt, J.. “An Analysis of Risk in Bull and Bear Markets.” Journal of Financial and Quantitative Analysis, 14 (12 1979), 1015–1025.10.2307/2330303S0022109000005949Google Scholar
Koschat, M. “A Characterization of the Fieller Solution.” Annals of Statistics, 15 (1987), 462.10.1214/aos/1176350282Google Scholar
Kothari, S. B., and Warner, J. B.. “Evaluating Mutual Fund Performance.” Working Paper, Massachusetts Institute of Technology (1997).Google Scholar
Leland, H. “Beyond Mean-Variance: Performance Measurement in a Nonsymmetric World.” Financial Analysts Journal (01/02 1999), 27–36.Google Scholar
Lintner, J. “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” Review of Economics and Statistics, 47 (1965), 13–37.10.2307/1924119Google Scholar
McCann, J.; Morey, R.; and Raturi, A.. “Confidence Intervals for the Total Advertising Impact and its Mean Duration under Koyck Models.” Journal of the Academy of Marketing Science, 19 (1991), 333–340.10.1007/BF02726508Google Scholar
Miller, R., and Gehr, A.. “Sample Bias and Sharpe's Performance Measure: A Note.” Journal of Financial and Quantitative Analysis, 13 (12 1978), 943–946.10.2307/2330636S0022109000014216Google Scholar
Morey, R., and McCann, J.. “Estimating the Confidence Interval for the Optimal Marketing Mix: An Application to Lead Generation.” Marketing Science, 2 (1983), 193–202.10.1287/mksc.2.2.193Google Scholar
Morris, P., and Pope, P.. “The Jensen Measure of Portfolio Performance in an Arbitrage Pricing Theory Context.” Journal of Business Finance and Accounting, 8 (1981), 203–220.10.1111/j.1468-5957.1981.tb00814.xGoogle Scholar
Mossin, J. “Security Pricing and Investment Criteria in Competitive Markets.” American Economic Review, 59 (1969), 749–756.Google Scholar
Pedersen, C. “Four Essays on Risk in Finance.” Ph.D. Diss., Cambridge Univ., England (1999).Google Scholar
Pedersen, C.. “Empirical Tests for Differences in Equilibrium Risk Measure with Application to Downside Risk in Small and Large U.K. Companies.” Cambridge Discussion Papers in Accounting and Finance, 41 (1998).Google Scholar
Roy, S., and Potthoff, R.. “Confidence Bounds on Vector Analogues of the ‘Ratio of Means’ and the ‘Ratio of Variances’ for Two Correlated Normal Variates and Some Associated Tests.” Annals of Mathematical Statistics, 29 (1958), 829–841.10.1214/aoms/1177706539CrossRefGoogle Scholar
Sargan, J. The Existence of the Moments of the Estimated Reduced Form Coefficients, Vol. 2. Cambridge, England: Cambridge Univ. Press (1988).Google Scholar
Sharpe, W. “Capital Asset Prices: A Theory of Capital Market Equilibrium under Conditions of Risk.” Journal of Finance, 19 (1964), 425–442.10.2307/2977928Google Scholar
Sharpe, W.. “Mutual Fund Performance.” Journal of Business, 34 (01 1966), 119–138.Google Scholar
Sortino, F., and Price, L.. “Performance Measurement in a Downside Risk Framework.” Journal of Investing (Fall 1994), 59–65.Google Scholar
Stuart, A., and Ord, K.. Kendall's Advanced Theory of Statistics, Vol. 2, Edward Arnold, fifth ed. (1991).Google Scholar
Treynor, J. “How to Rate Management of Investment Funds.” Harvard Business Review, (01–02 1965), 63–75.Google Scholar