Optimal Estimation of the Risk Premium for the Long Run and Asset Allocation: A Case of Compounded Estimation Risk
AbstractIt is well known that an unbiased forecast of the terminal value of a portfolio requires compounding at the arithmetic mean return over the investment horizon. However, the maximum-likelihood practice, common with academics, of compounding at the estimator of mean return results in upward biased and highly inefficient estimates of long-term expected returns. We derive analytically both an unbiased and a small-sample efficient estimator of long-term expected returns for a given sample size and horizon. Both estimators entail penalties that reduce the annual compounding rate as the investment horizon increases. The unbiased estimator, which is far lower than the compounded arithmetic average, is still very inefficient, often more so than a simple geometric estimator known to practitioners. Our small-sample efficient estimator is even lower. These results compound the sobering evidence in recent work that the equity risk premium is lower than suggested by post-1926 data. Our methodology and results are robust to extensions such as predictable returns. We also confirm analytically that parameter uncertainty, properly incorporated, produces optimal asset allocations, in stark contrast to conventional wisdom. Longer investment horizons require lower, not higher, allocations to risky assets. Copyright 2005, Oxford University Press.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Society for Financial Econometrics in its journal Journal of Financial Econometrics.
Volume (Year): 3 (2005)
Issue (Month): 1 ()
Contact details of provider:
Postal: Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK
Fax: 01865 267 985
Web page: http://jfec.oxfordjournals.org/
More information through EDIRC
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Maheu, John M. & McCurdy, Thomas H., 2009.
"How Useful are Historical Data for Forecasting the Long-Run Equity Return Distribution?,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 27, pages 95-112.
- John M Maheu & Thomas H McCurdy, 2007. "How useful are historical data for forecasting the long-run equity return distribution?," Working Papers tecipa-293, University of Toronto, Department of Economics.
- John M. Maheu & Thomas H. McCurdy, 2007. "How useful are historical data for forecasting the long-run equity return distribution?," Working Paper Series 19-07, The Rimini Centre for Economic Analysis, revised Jul 2007.
- Freeman, Mark C., 2010. "Yes, we should discount the far-distant future at its lowest possible rate: A resolution of the Weitzman-Gollier puzzle," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 4(13), pages 1-21.
- Freeman, Mark C., 2009. "Yes, we should discount the far-distant future at its lowest possible rate: a resolution of the Weitzman-Gollier puzzle," Economics Discussion Papers 2009-42, Kiel Institute for the World Economy.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Oxford University Press) or (Christopher F. Baum).
If references are entirely missing, you can add them using this form.