Efficient Asset Management: A Practical Guide to Stock Portfolio Optimization and Asset Allocation.

Michaud, Richard O.; Ma, Tongshu

doi:10.1093/rfs/14.3.901

Cited by 206 publications

(201 citation statements)

References 4 publications

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“…We observe that the inequality φ T Dφ ≤ t is equivalent to the third constraint of (33), which together with Lemma 4.3, implies that (24) is equivalent to (33). The conclusion immediately follows from this result and the fact that (22) is equivalent to (24).…”

Section: Cone Programming Reformulationsupporting

confidence: 54%

“…One of the main reasons is that the optimal portfolios determined by the mean-variance model are often sensitive to perturbations in the parameters of the problem (e.g., expected returns and the covariance matrix), and thus lead to large turnover ratios with periodic adjustments of the problem parameters; see for example Michaud [24]. Various aspects of this phenomenon have also been extensively studied in the literature, for example, see [9,7,8,10].…”

Section: Introductionmentioning

confidence: 99%

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Robust portfolio selection based on a joint ellipsoidal uncertainty set

2011

Optimization Methods and Software

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The "separable" uncertainty sets have been widely used in robust portfolio selection models (e.g., see [16,15,28]). For these uncertainty sets, each type of uncertain parameters (e.g., mean and covariance) has its own uncertainty set. As addressed in [21,22], these "separable" uncertainty sets typically share two common properties: (i) their actual confidence level, namely, the probability of uncertain parameters falling within the uncertainty set is unknown, and it can be much higher than the desired one; and (ii) they are fully or partially box-type. The associated consequences are that the resulting robust portfolios can be too conservative, and moreover, they are usually highly nondiversified as observed in the computational experiments conducted in [21,22] and [28]. To combat these drawbacks, we consider a factor model for the random asset returns. For this model, we introduce a "joint" ellipsoidal uncertainty set for the model parameters and show that it can be constructed as a confidence region associated with a statistical procedure applied to estimate the model parameters. We further show that the robust maximum risk-adjusted return (RMRAR) problem with this uncertainty set can be reformulated and solved as a cone programming problem. The computational results reported in [21,22] demonstrate that the robust portfolio determined by the RMRAR model with our "joint" uncertainty set outperforms that with Goldfarb and Iyengar's "separable" uncertainty set proposed in the seminal paper [16] in terms of wealth growth rate and transaction cost; and moreover, our robust portfolio is fairly diversified, but Goldfarb and Iyengar's is surprisingly highly non-diversified.

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Section: Cone Programming Reformulationsupporting

confidence: 54%

Section: Introductionmentioning

confidence: 99%

Robust portfolio selection based on a joint ellipsoidal uncertainty set

2011

Optimization Methods and Software

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“…Since the population means and covariance matrix must always be estimated in financial applications, estimation error is an unavoidable aspect of practical portfolio management. While a number of authors have explored the impact of estimation error on portfolio optimization, 6 and alternatives such as Bayesian inference (Brown, 1976), robust portfolio optimization (Fabozzi et al, 2007), and resampling (Michaud, 1998) have been developed in response, none of these methods addresses the impossibility of the population mean-variance-efficient frontier.…”

Section: Estimation Errormentioning

confidence: 99%

Impossible Frontiers

Brennan

2010

Management Science

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A key result of the Capital Asset Pricing Model (CAPM) is that the market portfoliothe portfolio of all assets in which each asset's weight is proportional to its total market capitalization-lies on the mean-variance-efficient frontier, the set of portfolios having mean-variance characteristics that cannot be improved upon. Therefore, the CAPM cannot be consistent with efficient frontiers for which every frontier portfolio has at least one negative weight or short position. We call such efficient frontiers "impossible", and show that impossible frontiers are difficult to avoid. In particular, as the number of assets, n, grows, we prove that the probability that a generically chosen frontier is impossible tends to one at a geometric rate. In fact, for one natural class of distributions, nearly one-eighth of all assets on a frontier is expected to have negative weights for every portfolio on the frontier. We also show that the expected minimum amount of shortselling across frontier portfolios grows linearly with n, and even when shortsales are constrained to some finite level, an impossible frontier remains impossible. Using daily and monthly U.S. stock returns, we document the impossibility of efficient frontiers in the data.

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“…This use has a long history in financial theory. For example, Sharpe (1963) used historical average returns to estimate expected returns, and Michaud (1998) argued for the superiority of a resampled frontier based on historical averages. Even those who argue for Bayes-Stein estimation methods use historical averages in their null hypothesis.…”

Section: Different Ratios Of Momentum To Valuementioning

confidence: 99%

Simulating Security Markets in Dynamic and Equilibrium Modes

Jacobs

Levy

Markowitz³

2010

Financial Analysts Journal

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An asynchronous discrete-time model run in "dynamic mode" can model the effects on market prices of changes in strategies, leverage, and regulations, or the effects of different return estimation procedures and different trading rules. Run in "equilibrium mode," it can be used to arrive at equilibrium expected returns.nalysts in the natural sciences, manufacturing, logistics, and warfare frequently rely on asynchronous discrete-time models. Such models are less well known in finance, where analysts have tended to rely on continuoustime models.1 But in finance, as in these other areas, discrete-time models offer several important advantages over continuous-time models. Both continuous-time and discrete-time models are a form of dynamic model. Dynamic models allow one to represent the evolution of a system, such as a financial market, over time. In continuoustime dynamic models, the system changes continuously over time; in discrete-time dynamic models, an internal system clock advances in discrete increments. Discrete-time models can be further classified into synchronous and asynchronous models. Synchronous discrete-time models use system clocks that advance by fixed increments, such as a day or a year, with the status of the system updated at each increment. Asynchronous discrete-time models use system clocks that advance from one event to the next, whereby the time intervals between events are typically not constant. Asynchronous models can provide a more realistic representation of markets than synchronous models. 2 The most commonly used dynamic models in finance assume that security prices follow a continuous-time process. This process is frequently assumed to be random and is modeled as a Brownian motion or as a function of a Brownian motion. A major advantage of continuous-time models is that some of them can be solved explicitly, which allows one to evaluate investment strategies analytically. Most familiar, perhaps, are optionpricing models that can be solved given a fixedprice process for the underlying security.Most discrete-time models cannot be solved analytically; large and detailed asynchronous models that attempt to model complex systems require computer simulation. Asynchronous discrete-time models, however, can provide insights not available from purely analytical procedures. They can be used to examine the mechanisms behind price movements and can thus be used to test the effects on security prices of such real-world events as changes in investors' strategies, modifications in overall leverage, and switches in regulatory regimes.Consider how continuous-time and discretetime models deal with so-called liquidity black holes. On Black Monday, 19 October 1987, liquidity disappeared from the market as large numbers of investors all attempted to sell at the same time. Similar black holes developed in connection with the collapse of the hedge fund Long-Term Capital Management in 1998 and, more recently, during the 2008-09 credit crisis (see, e.g., Jacobs 1999, 2009. In these and other, less extre...

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Efficient Asset Management: A Practical Guide to Stock Portfolio Optimization and Asset Allocation.

Cited by 206 publications

References 4 publications

Robust portfolio selection based on a joint ellipsoidal uncertainty set

Robust portfolio selection based on a joint ellipsoidal uncertainty set

Impossible Frontiers

Simulating Security Markets in Dynamic and Equilibrium Modes

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