Optimal Portfolio Choice with Parameter Uncertainty

2007 ◽  
Vol 42 (3) ◽  
pp. 621-656 ◽  
Author(s):  
Raymond Kan ◽  
Guofu Zhou
Keyword(s):  
Portfolio Choice ◽  
Parameter Uncertainty ◽  
Minimum Variance ◽  
Optimal Portfolio ◽  
Estimation Risk ◽  
Out Of Sample ◽  
Minimum Variance Portfolio ◽  
Riskless Asset ◽  
Fund Portfolio ◽  
Global Minimum Variance Portfolio

AbstractIn this paper, we analytically derive the expected loss function associated with using sample means and the covariance matrix of returns to estimate the optimal portfolio. Our analytical results show that the standard plug-in approach that replaces the population parameters by their sample estimates can lead to very poor out-of-sample performance. We further show that with parameter uncertainty, holding the sample tangency portfolio and the riskless asset is never optimal. An investor can benefit by holding some other risky portfolios that help reduce the estimation risk. In particular, we show that a portfolio that optimally combines the riskless asset, the sample tangency portfolio, and the sample global minimum-variance portfolio dominates a portfolio with just the riskless asset and the sample tangency portfolio, suggesting that the presence of estimation risk completely alters the theoretical recommendation of a two-fund portfolio.

Optimal Portfolio Choice with Estimation Risk: No Risk-Free Asset Case

2021 ◽  
Author(s):  
Raymond Kan ◽  
Xiaolu Wang ◽  
Guofu Zhou
Keyword(s):  
Portfolio Choice ◽  
Exact Distribution ◽  
Optimal Portfolio ◽  
Portfolio Construction ◽  
Estimation Risk ◽  
Choice Problem ◽  
Out Of Sample ◽  
Mean Variance Portfolio ◽  
Mean Variance ◽  
Explicit Expressions

We propose an optimal combining strategy to mitigate estimation risk for the popular mean-variance portfolio choice problem in the case without a risk-free asset. We find that our strategy performs well in general, and it can be applied to known estimated rules and the resulting new rules outperform the original ones. We further obtain the exact distribution of the out-of-sample returns and explicit expressions of the expected out-of-sample utilities of the combining strategy, providing not only a fast and accurate way of evaluating the performance, but also analytical insights into the portfolio construction. This paper was accepted by Tyler Shumway, finance.

scholarly journals Does GMVP Strategy Reduce Risk? A Global Asset Approach

2014 ◽  
Vol 30 (6) ◽  
pp. 1873
Author(s):  
Arben Zibri ◽  
Agim Kukeli
Keyword(s):  
Risk Reduction ◽  
Covariance Matrix ◽  
Minimum Variance ◽  
Portfolio Constraints ◽  
Stock Portfolios ◽  
Sample Covariance ◽  
Out Of Sample ◽  
Bond Portfolios ◽  
Minimum Variance Portfolio ◽  
Global Minimum Variance Portfolio

<p>This paper studies the out of sample risk reduction of global minimum variance portfolio. The analysis are drown from the discussions of Jagannathan and Ma (2003) regarding the risk reduction in US stock portfolios using portfolio constraints. We estimate the covariance matrix using the sample covariance matrix approach and derive optimal minimum variance portfolios considering upper/lower bounds and no restrictions. Results are shown under different revision frequency and transaction costs assumed. The data used are monthly indices of stocks, bonds, gold oil and spreads from 1996 until 2013. Unconstrained GMVPs result in the lowest out of sample variance, while unconstrained GMVPs of global bond portfolios performs the best in terms of risk reduction. Diversification through global asset classes result in a better strategy than international stock diversification regarding risk, as suggested by the literature.</p>

Properties of the beta coefficient of the global minimum variance portfolio

2020 ◽  
Vol 8 (1) ◽  
pp. 11-21
Author(s):  
S. M. Yaroshko ◽  
◽  
M. V. Zabolotskyy ◽  
T. M. Zabolotskyy ◽  
◽  
...  
Keyword(s):  
Confidence Interval ◽  
Asymptotic Distribution ◽  
Global Minimum ◽  
Asset Returns ◽  
Minimum Variance ◽  
Benchmark Portfolio ◽  
Beta Coefficient ◽  
Minimum Variance Portfolio ◽  
Global Minimum Variance Portfolio ◽  
Daily Returns

The paper is devoted to the investigation of statistical properties of the sample estimator of the beta coefficient in the case when the weights of benchmark portfolio are constant and for the target portfolio, the global minimum variance portfolio is taken. We provide the asymptotic distribution of the sample estimator of the beta coefficient assuming that the asset returns are multivariate normally distributed. Based on the asymptotic distribution we construct the confidence interval for the beta coefficient. We use the daily returns on the assets included in the DAX index for the period from 01.01.2018 to 30.09.2019 to compare empirical and asymptotic means, variances and densities of the standardized estimator for the beta coefficient. We obtain that the bias of the sample estimator converges to zero very slowly for a large number of assets in the portfolio. We present the adjusted estimator of the beta coefficient for which convergence of the empirical variances to the asymptotic ones is not significantly slower than for a sample estimator but the bias of the adjusted estimator is significantly smaller.

Estimation Risk and Optimal Portfolio Choice.

1981 ◽  
Vol 36 (1) ◽  
pp. 202
Author(s):  
Larry J. Merville ◽  
Vijay S. Bawa ◽  
Stephen J. Brown ◽  
Roger W. Klein
Keyword(s):  
Portfolio Choice ◽  
Optimal Portfolio ◽  
Estimation Risk

Abstract: The Effect of Limited Information and Estimation Risk on Optimal Portfolio Diversification

1977 ◽  
Vol 12 (4) ◽  
pp. 669-669 ◽  
Author(s):  
Roger W. Klein ◽  
Vijay S. Bawa
Keyword(s):  
Portfolio Choice ◽  
Joint Probability ◽  
Optimal Portfolio ◽  
Joint Probability Distribution ◽  
Sufficient Information ◽  
Limited Information ◽  
Multivariate Normal ◽  
Estimation Risk ◽  
Conjugate Priors ◽  
Mean Variance

This paper analyzes the effect of limited information and estimation risk on optimal portfolio choice when the joint probability distribution of security returns is multivariate normal and the underlying parameters (means and variance-covariance matrix) are unknown. We first consider the case of limited, but sufficient information (the number of observations per security exceeds the number of securities or the prior distribution of the underlying parameters is “sufficiently” informative). We show that for a general family of conjugate priors, the admissible set of portfolios, taking estimation risk into account, may be obtained by the traditional mean-variance analysis. As a result of estimation risk the optimal portfolio choice differs from that obtained by traditional analysis.

scholarly journals Incorporating Economic Objectives into Bayesian Priors: Portfolio Choice under Parameter Uncertainty

2010 ◽  
Vol 45 (4) ◽  
pp. 959-986 ◽  
Author(s):  
Jun Tu ◽  
Guofu Zhou
Keyword(s):  
Euler Equation ◽  
Portfolio Choice ◽  
Loss Function ◽  
Parameter Uncertainty ◽  
Economic Problem ◽  
Certainty Equivalent ◽  
Portfolio Strategies ◽  
Out Of Sample ◽  
Bayesian Priors ◽  
Function Measure

AbstractThis paper proposes a way to allow Bayesian priors to reflect the objectives of an economic problem. That is, we impose priors on the solution to the problem rather than on the primitive parameters whose implied priors can be backed out from the Euler equation. Using monthly returns on the Fama-French 25 size and book-to-market portfolios and their 3 factors from January 1965 to December 2004, we find that investment performances under the objective-based priors can be significantly different from those under alternative priors, with differences in terms of annual certainty-equivalent returns greater than 10% in many cases. In terms of an out-of-sample loss function measure, portfolio strategies based on the objective-based priors can substantially outperform both strategies under alternative priors and some of the best strategies developed in the classical framework.

scholarly journals Seleção de carteiras ótimas sob restrições nas normas dos vetores de alocação: uma avaliação empírica com dados da BM&FBOVESPA

2015 ◽  
Vol 13 (3) ◽  
pp. 504
Author(s):  
Paulo Ferreira Naibert ◽  
João Caldeira
Keyword(s):  
Stock Market ◽  
Covariance Matrix ◽  
Portfolio Selection ◽  
Stock Exchange ◽  
Minimum Variance ◽  
Average Risk ◽  
Short Sale ◽  
Performance Indexes ◽  
Out Of Sample ◽  
Minimum Variance Portfolio

In this paper, we study the problem of minimum variance portfolio selection based on a recent methodology for portfolio optimization restricting the allocation vector proposed by Fan et al. (2012). To achieve this, we consider different conditional and unconditional covariance matrix estimators. The main contribution of this paper is one of empirical nature for the brazilian stock market. We evaluate out of sample performance indexes of the portfolios constructed for a set of 61 different stocks traded in the São Paulo stock exchange (BM&FBovespa). The results show that the restrictions on the norms of the allocation vector generate substantial gains in relation to the no short-sale portfolio, increasing the average risk-adjusted return (larger Sharpe Ratio) and lowering the portfolio turnover.

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