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4 FOR ONE-ON-ONE USE WITH A CLIENT'S FINANCIAL ADVISOR ONLY © 2024 Envestnet. All rights reserved. Asset Class Portfolio Update II. Asset Class Portfolio Construction: Process STEP 1: Specification of the Constraints The first step in our estimation process is to set up portfolio constraints. While an over-constraining optimization problem (i.e., setting the constraints to obtain the desired outcome) is counterproductive, imposing a set of guiding constraints that nevertheless allow the optimization to take its course is very useful. For example, Jagannathan & Ma (2003) note the following: "It is well recognized in the literature that imposing portfolio weight constraints leads to superior out-of-sample performance of mean-variance efficient portfolios…These constraints are likely to be wrong in population and hence they introduce specification error. According to our analysis, these constraints can reduce sampling error. Therefore, gain from imposing these constraints depends on the trade-off between the reduction in sampling error and the increase in specification error." To avoid over-constraining the optimization problem, we have imposed a number of relative constraints that are guided by the observed market capitalizations of the various asset classes. These constraints ensure that the relative sizes of the exposures in the optimized portfolio track those in the observed market portfolio, while allowing the risk/return trade-off properties of the various asset classes to shape the final portfolio. Also, we have restricted the allocation to Value and Growth to be the same, which, combined with the above size constraints, allows us to mimic the market portfolio in largely avoiding either a style- or size-bias in our Asset Class Portfolios. Finally, we add an absolute constraint that at a 50/50 equity/fixed-income split, Intermediate Bonds should occupy no larger than 25 percent of the portfolio. STEP 2: Bootstrap Estimation of the Mean-Variance Portfolios It turns out that estimation risk can be expressed as equaling the bias squared of the estimated portfolio weights (when compared to the true, but unknown and unknowable portfolio weights) plus the variance of the estimated portfolio weights. 1 If we knew the true means and covariances, the Mean Squared Error (MSE) would equal zero. The goal of our estimation methodology then is to reduce the MSE as much as possible. Application of a bootstrap allows us to estimate and adjust for the bias in the mean-variance optimal weights. The bootstrap statistical technique was first proposed by Efron (1979). Horowitz (2001) describes the bootstrap as follows: "The bootstrap is a method for estimating the distribution of an estimator or test statistic by resampling one's data or a model estimated from the data." In other words, the essence of the bootstrap is to attempt to estimate the distribution of an estimator (in our case the portfolio weights), and to do this we can employ either resampling or model-based approaches. Resampling usually turns out to be more general and expedient than the model-based approach, but we should not confuse the resampling with the general approach of the bootstrap. Thus, the application of bootstrap statistical techniques allows us to estimate and correct for the estimation bias in the portfolio weights. We carry out this adjustment at every portfolio across the mean-variance frontier. 2 Finally, we use empirical copulas (see Meucci (2011) for a brief introduction in copula statistical approach) to generate the bootstrap sample. The reason for using a copula approach is two-fold. First, it allows us to incorporate the forward-looking assumptions on means and covariances. Second, it allows us to more realistically reflect the observed idiosyncrasies (e.g., skewness, kurtosis and asymmetric tail dependence; see Patton 2004) of the return distributions. 1 The quantity bias squared plus variance is called the Mean Squared Error (MSE). MSE is widely used in statistics as a criterion for evaluating the performance of an estimation methodology. Ordinary Least Squares (OLS) regressions are an example of being optimal in MSE sense. 2 See, for example, Jorion (1992) or Lai, Xing, & Chen (2010) for the details on how to carry out this bootstrap bias adjustment.

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