Abstract
Previous studies show that combining a power utility portfolio selection model with the empirical probability assessment approach (EPAA) to estimate the joint return distribution frequently generates economically and statistically significant abnormal returns. In this paper, we examine additional ways of estimating joint return distributions that allow us to explore the stationary/nonstationary tradeoffs implicit in “expanding” versus “moving” window estimation methods; the benefits of alternative methods of allowing for the “memory loss” inherent in the moving-window EPAA; and the possibility that weighting more recent observations more heavily may improve investment performance.
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Notes
- 1.
- 2.
Solnik (1993) explores the use of conditioning variables to predict the means in a mean-variance portfolio selection framework. Merton (1971, 1973) points out that if returns are predictable, investors may wish to hedge against shifts in the opportunity set. Kandel and Stambaugh (1996), Brennan et al. (1997), and Barberis (2000), among others, employ a continuous-time framework to examine whether the optimal portfolio weights of an investor with a long horizon are different from those of an investor with a short horizon.
- 3.
Lowenstein (2000) provides an extremely readable account of the rise and fall of Long-Term Capital. In addition to the quote by Merton Miller, he includes comments by Paul Samuelson, Eugene Fama, and William Sharpe, that question the idea that “real world” risk can ever be completely eliminated.
- 4.
Results based on 40-quarter and from 8- to 15-year estimating periods have also been discussed.
- 5.
Note that we say one way to alleviate the problem. It seems clear that no model can completely overcome the problem of a truly unforeseen event.
- 6.
The solvency constraint (12.5) is not binding for the power functions, with γ < 1, and discrete probability distributions with a finite number of outcomes because the marginal utility of zero wealth is infinite. Nonetheless, it is convenient to explicitly consider (12.5) so that the nonlinear programming algorithm used to solve the investment problems does not attempt to evaluate an infeasible policy as it searches for the optimum.
- 7.
The nonlinear programming algorithm employed is described in Best (1975).
- 8.
The realized borrowing rate is calculated as a monthly average.
- 9.
Note that if k = 32 is under quarterly revision, then the first quarter for which a portfolio can be selected is b + 32, where b is the first quarter for which data is available.
- 10.
There is no practical way to take maintenance margins into account in our programs. In any case, it is evident from the results that they would come into play only for the more risk-tolerant strategies (and even for them only occasionally) and the net effect would be relatively neutral.
- 11.
If the number of assets were equal to the number of states, there would be a complete market. In the absence of constraints other than the budget constraint, the optimizer would then think it could achieve any arbitrary return distribution.
- 12.
- 13.
For consistency with the geometric mean, the standard deviation is based on the log of one plus the rate of return. This quantity is very similar to the standard deviation of the rate of return for levels less than 25 percent.
- 14.
Figure 12.1 also contains the compound return-standard deviation pairs for a combined approach discussed in Section 12.9.
- 15.
We note, however, that the starting point for the all-of-history estimation period is 1926 in the industry dataset and 1960 in the global dataset.
- 16.
The differences are even more pronounced in an equal-weighted industries universe, reported in the first version of the paper.
- 17.
In the equal-weighted industries universe, all the power policies perform extremely well—especially in the 1968–90 period where the highly statistically significant abnormal returns range from approximately 45 to over 60 percent of excess returns.
- 18.
These results are consistent with Grauer and Shen (2000), who find that ex ante the policies of more risk-averse investors subject to fewer constraints are preferred to policies subject to more constraints. Nonetheless the policies subject to more constraints are preferred ex post.
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Acknowledgments
We thank the Social Sciences Research Council of Canada and the Centre for Accounting Research and Education for financial support. The paper was presented at the University of British Columbia, the Northern Finance Association meetings in London Ontario, and the Pacific Northwest Finance Conference in Seattle. We thank C.F. Lee, William Ziemba, and seminar participants for valuable comments, and Reo Audette, Christopher Fong, Maciek Kon, Jaspreet Sahni, William Ting, and Jeffrey Yang for most capable assistance.
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Grauer, R.R., Shen, F.C. (2010). On Estimation Risk and Power Utility Portfolio Selection. In: Lee, CF., Lee, A.C., Lee, J. (eds) Handbook of Quantitative Finance and Risk Management. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-77117-5_12
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