Dynamic Asset Allocation in a Mean-Variance Framework

Bajeux‐Besnainou, Isabelle; Portrait, Roland

doi:10.1287/mnsc.44.11.s79

Cited by 114 publications

(60 citation statements)

References 16 publications

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“…When c = 0, the efficient frontier coincides with that found by Richardson (1989), Bajeux-Besnainou & Portait (1998) and Zhou & Li (2000) for self-financing portfolios.…”

Section: Definition 1 An Investment Strategy Y(·) Is Said To Besupporting

confidence: 73%

“…The main reason of this delay in solving such a relevant problem, since Markowitz (1952) and Markowitz (1959), lies in the difficulty inherent in the extension from single-period to multi-period or continuous-time framework. In the portfolio selection literature the problem of finding the minimum variance trading strategy in continuous time has been solved by Richardson (1989) and by Bajeux-Besnainou & Portait (1998) via the martingale approach. Regarding the use of stochastic control theory to solve a mean-variance optimization problem, a real breakthrough was made by Li & Ng (2000) in a discrete-time multiperiod framework and Zhou & Li (2000) in a continuous-time model.…”

Section: Introductionmentioning

confidence: 99%

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On efficiency of mean–variance based portfolio selection in defined contribution pension schemes

Vigna

2012

Quantitative Finance

103

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We consider the portfolio selection problem in the accumulation phase of a defined contribution (DC) pension scheme. We solve the mean-variance portfolio selection problem using the embedding technique pioneered by Zhou & Li (2000) and show that it is equivalent to a targetbased optimization problem, consisting in the minimization of a quadratic loss function. We support the use of the target-based approach in DC pension funds for three reasons. Firstly, it transforms the difficult problem of selecting the individual's risk aversion coefficient into the easier task of choosing an appropriate target. Secondly, it is intuitive, flexible and adaptable to the member's needs and preferences. Thirdly, it produces final portfolios that are efficient in the mean-variance setting.We address the issue of comparison between an efficient portfolio and a portfolio that is optimal according to the more general criterion of maximization of expected utility (EU). The two natural notions of Variance Inefficiency and Mean Inefficiency are introduced, which measure the distance of an optimal inefficient portfolio from an efficient one, focusing on their variance and on their expected value, respectively. We illustrate the general procedure for finding the mean-variance inefficiency for the HARA class of utility functions, and then focus on the popular classes of CARA and CRRA utility functions. In these cases we prove the intuitive but not trivial results that the mean-variance inefficiency decreases with the risk aversion of the individual and increases with the time horizon and the Sharpe ratio of the risky asset. As a byproduct we prove that the CARA and CRRA optimal portfolio are not mean-variance efficient.Numerical investigations stress the impact of the time horizon on the extent of mean-variance inefficiency of CARA and CRRA utility functions. While at instantaneous level EU-optimality and efficiency coincide (see Merton (1971)), we find that for short durations they do not differ significantly. However, for longer durations -that are typical in pension funds -the extent of inefficiency turns out to be remarkable and should be taken into account by pension fund investment managers seeking appropriate rules for portfolio selection. Indeed, we see this result as a fourth reason for supporting the use of the target-based approach in DC pension schemes.

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“…When c = 0, the efficient frontier coincides with that found by Richardson (1989), Bajeux-Besnainou & Portait (1998) and Zhou & Li (2000) for self-financing portfolios.…”

Section: Definition 1 An Investment Strategy Y(·) Is Said To Besupporting

confidence: 73%

Section: Introductionmentioning

confidence: 99%

On efficiency of mean–variance based portfolio selection in defined contribution pension schemes

Vigna

2012

Quantitative Finance

103

View full text Add to dashboard Cite

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“…Institutional portfolio management has significantly increased over the past four decades 1 . The risk-adjusted performance measurement is an important factor for fund investors when selecting fund managers, and for deciding on the ways for compensating them.…”

Section: Introductionmentioning

confidence: 99%

Implications of Sharpe Ratio as a Performance Measure in Multi-Period Settings

2007

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We study effects of using Sharpe ratio as a performance measure for compensating money managers in a dynamic and frictionless market setting. First, we demonstrate that with such a performance measure, the manager's focus on the short horizon performance is detrimental to the investor's long horizon performance. Numerical experiments illustrate that when returns are iid, the performance loss is significant, even when the investor's investment horizon is not much longer than the manager's. When expected returns are mean reverting, the performance loss is exacerbated. Second, we show that Sharpe ratio maximization strategies tend to increase (decrease) the risk in the later part of the optimization period after a bad (good) performance in the earlier part of the optimization period. As illustrated by a simulation exercise, this prediction is in agreement with empirical observations, and it presents a rational expectations alternative to the prevalent tournament theory explanation.

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“…2 Early essays in this directions were for instance proposed in Smith (1967), Mossin (1968), Merton (1969), Samuelson (1969), and more recently Duffie and Richardson (1991), Grauer and Hakansson (1993), and Schweizer (1995). Bajeux-Besnainou and Portait (1998) obtained an explicit dynamic asset allocation in a continuous-time mean-variance framework using martingale techniques. Li, Zhou and Lim (2002) study the solutions of a continuous time mean-variance portfolio optimization problem under short-selling constraints on stocks.…”

Section: Introductionmentioning

confidence: 99%