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.

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.

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.

It’s All in the Timing: Simple Active Portfolio Strategies that Outperform Naïve Diversification

2012 ◽  
Vol 47 (2) ◽  
pp. 437-467 ◽  
Author(s):  
Chris Kirby ◽  
Barbara Ostdiek
Keyword(s):  
Transaction Costs ◽  
Asset Allocation ◽  
Estimation Risk ◽  
Portfolio Strategies ◽  
Out Of Sample ◽  
Volatility Timing ◽  
Naïve Diversification ◽  
Mean Variance Portfolio ◽  
Timing Strategies ◽  
Mean Variance

AbstractDeMiguel, Garlappi, and Uppal (2009) report that naïve diversification dominates mean-variance optimization in out-of-sample asset allocation tests. Our analysis suggests that this is largely due to their research design, which focuses on portfolios that are subject to high estimation risk and extreme turnover. We find that mean-variance optimization often outperforms naïve diversification, but turnover can erode its advantage in the presence of transaction costs. To address this issue, we develop 2 new methods of mean-variance portfolio selection (volatility timing and reward-to-risk timing) that deliver portfolios characterized by low turnover. These timing strategies outperform naïve diversification even in the presence of high transaction costs.

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

Humans, Econs and Portfolio Choice

2016 ◽  
Vol 07 (02) ◽  
pp. 1750001 ◽  
Author(s):  
Michael J. Best ◽  
Robert R. Grauer
Keyword(s):  
Prospect Theory ◽  
Portfolio Choice ◽  
Loss Aversion ◽  
Asset Allocation ◽  
Power Utility ◽  
Numerical Example ◽  
Portfolio Choices ◽  
Out Of Sample ◽  
Finance Theory ◽  
Mean Variance

We compare the portfolio choices of Humans — prospect theory investors — to the portfolio choices of Econs — power utility and mean-variance (MV) investors. In a numerical example, prospect theory portfolios are decidedly unreasonable. In an in-sample asset allocation setting, the prospect theory results are consistent with myopic loss aversion. However, the portfolios are extremely unstable. The power utility and MV results are consistent with traditional finance theory, where the portfolios are stable across decision horizons. In an out-of-sample asset allocation setting, the power utility and portfolios outperform the prospect theory portfolios. Nonetheless the prospect theory portfolios with loss aversion coefficients of 2.25 and 2 perform well.

Topics in finance and risk management

2018 ◽  
Author(s):  
Hans Fehr ◽  
Fabian Kindermann
Keyword(s):  
Portfolio Choice ◽  
Market Price ◽  
Theoretical Background ◽  
Optimal Portfolio ◽  
Corporate Bond ◽  
Choice Problem ◽  
Risk And Return ◽  
Risky Assets ◽  
Credit Risk Measurement ◽  
Portfolio Structure

This chapter introduces basic concepts of modern finance theory and demonstrates how to apply them in complex real-world problems. Financial deals and investment decisions are typically determined under uncertainty.Therefore, although this chapter is self-contained, we have to expect some theoretical background in individual decisionmaking and optimal investment under uncertainty. We organize our discussion into four central sections. The starting point is a portfolio choice problem, where an investor has to choose between different assets with specific risk and return characteristics. We then move on to some option pricing applications. We first derive analytical formulas and then evaluate numerical procedures for pricing European and American options as well as more exotic option products. The third section elaborates on credit risk measurement and management using a corporate bond portfolio as example. In the last section we discuss mortality risk and the optimal portfolio structure of a life insurance company. This section provides different numerical approaches to find an optimal portfolio structure with many risky assets. It begins with simple measures of risk and return of a single asset and then develops decision rules to choose optimal portfolios that maximize expected utility of wealth in worlds without and with riskless borrowing and lending opportunities. The purpose of this section is to optimize a portfolio of equity shares and a risk-free investment opportunity. The investor faces the most basic two-period investment choice problem: He buys assets in the first period and these assets pay off in the next period. The problem of the investor is to choose from i = 1, . . . ,N risky assets which may be shares, bonds, real estate, etc. The gross return of each asset i is denoted by rit = qit/qit−1 − 1, where qit−1 is the first-period market price and qit − qit−1 the second-period payoff.

scholarly journals Continuous-Time Mean-Variance Portfolio Selection under the CEV Process

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Hui-qiang Ma
Keyword(s):  
Portfolio Selection ◽  
Continuous Time ◽  
Stock Price ◽  
Efficient Frontier ◽  
Optimal Portfolio ◽  
Portfolio Strategy ◽  
Cev Process ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Mean Variance

We consider a continuous-time mean-variance portfolio selection model when stock price follows the constant elasticity of variance (CEV) process. The aim of this paper is to derive an optimal portfolio strategy and the efficient frontier. The mean-variance portfolio selection problem is formulated as a linearly constrained convex program problem. By employing the Lagrange multiplier method and stochastic optimal control theory, we obtain the optimal portfolio strategy and mean-variance efficient frontier analytically. The results show that the mean-variance efficient frontier is still a parabola in the mean-variance plane, and the optimal strategies depend not only on the total wealth but also on the stock price. Moreover, some numerical examples are given to analyze the sensitivity of the efficient frontier with respect to the elasticity parameter and to illustrate the results presented in this paper. The numerical results show that the price of risk decreases as the elasticity coefficient increases.

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