Optimal Estimation of the Risk Premium for the Long Run and Asset Allocation: A Case of Compounded Estimation Risk
It 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.
Volume (Year): 3 (2005)
Issue (Month): 1 ()
|Contact details of provider:|| Postal: |
Fax: 01865 267 985
Web page: http://jfec.oxfordjournals.org/
More information through EDIRC
|Order Information:||Web: http://www.oup.co.uk/journals|
When requesting a correction, please mention this item's handle: RePEc:oup:jfinec:v:3:y:2005:i:1:p:37-55. See general information about how to correct material in RePEc.
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.