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3 Asset Class Portfolio Update Jorion (1992) introduces the following definition for this phenomenon that he calls estimation risk (also known as measurement error, estimation error and parameter uncertainty): "The possibility of errors in the portfolio allocations due to imprecision on the estimated inputs to the portfolio optimization." Michaud (1989) comments on the consequences of the optimal portfolios calculated using the traditional mean-variance optimization, calling them "estimation-error maximizers". 1c Consequences of the Estimation Risk What are the consequences of the estimation risk? Chopra & Ziemba (1993) investigate this question and find that errors in means are about ten times as important as errors in variances, and errors in variances are about twice as important as errors in covariances. This suggests that estimation risk can substantially impact the mean- variance optimization results. In fact, several studies have demonstrated that the estimation risk inherent in mean-variance optimization is so large as to overwhelm any optimality of MPT optimization altogether. For example, Demiguel, Garlappi, & Uppal (2007) and Herold & Mauer (2006) show that due to the estimation error the 1/N and the market portfolio, respectively, are the best available portfolios. The basic reason for this is that the mistakes caused by using the suboptimal 1/N portfolio turn out to be smaller than the error caused by using weights from MPT (and especially the estimates of the expected rate of return) that are subject to high estimation risk. Jagannathan & Ma (2003) argue that the minimum variance portfolio performs better than the mean-variance efficient portfolio. They note that "the sample mean is an imprecise estimator of the population mean. The estimation error in the sample mean is so large that nothing much is lost in ignoring the mean altogether when no further information about the population mean is available." A recent thought-provoking study from the University of Chicago (Pastor & Stambaugh, 2012) argues that even the "stocks for the long run" maxim does not hold true due to estimation risk. Previously, Campbell & Viceira (2005) had demonstrated that the "time diversification" holds when there is negative serial correlation in equity returns, but Pastor & Stambaugh (2012) show that this effect gets overwhelmed by the estimation risk inherent in the parameters. 1d Methods for Dealing with Estimation Risk There are various approaches to dealing with the above problem. The three main methods, mentioned by Demiguel, Garlappi, & Uppal (2007) and Herold & Mauer (2006), are Bayesian estimation, bootstrap statistical approach and "heuristic" approaches. A Bayesian approach allows the analyst to account for estimation risk by specifying the likely values of the parameters and the associated probabilities. This information is then used in a self-consistent portfolio optimization framework that accounts for all the available information, including estimation risk. For example, Harvey et al. (2010) propose a Bayesian framework within which to deal with the estimation risk as well as to incorporate higher moments of the return distributions. The "heuristic" group of approaches contains various heuristic ways of dealing with the estimation error. An example of this is Jagannathan & Ma (2003) who investigate the effect of non-negativity constraints on the performance of the efficient portfolios. The bootstrap approach accounts for estimation risk in portfolio weights by attempting to estimate this risk directly (see details of this method below). We follow the bootstrap route in constructing Envestnet's Asset Class Portfolios (ACPs). FOR ONE-ON-ONE USE WITH A CLIENT'S FINANCIAL ADVISOR ONLY © 2024 Envestnet. All rights reserved.

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