Issue link: https://resources.envestnet.com/i/1527493
2 Asset Class Portfolio Update I. Asset Class Portfolio Construction: Overview 1a Modern Portfolio Theory More than half a century has passed since Markowitz (1952, 1959) introduced the Nobel Prize-winning theory of optimal portfolio allocation in the mean-variance framework that was later dubbed Modern Portfolio Theory (MPT). Markowitz's approach to the computation of an optimal portfolio is very elegant and, given the computational constraints at the time, analytically accessible. Despite its academic success, PMC believes the use of MPT in the finance industry is limited. When in fact used, typically either a large set of constraints is applied or some type of methodological improvement (see below) is employed. The reason for this has to do with the extreme fluctuations of MPT optimal portfolios over time and across the risk spectrum. To illustrate this problem, consider the following example. Suppose there are two assets in the portfolio: A and B. The correlation between the assets is assumed to be 0.9. Table 1 below displays the optimal mean-variance allocations. These results highlight the following problems inherent to MPT: (A) the optimal portfolio weight changes are extreme; and (B) the changes in the associated portfolio expected returns/standard deviations are very slight. These problems have also been widely documented in literature. Jobson et al (1979) and Jobson & Korkie (1980) show that mean-variance portfolios are highly sensitive to small deviations in the estimates of means and covariances (correlations and standard deviations). Best & Grauer (1991) show that optimal portfolios are very sensitive to the level of expected returns. For example, they note that "a surprisingly small increase in the mean of just one asset drives half the securities from the portfolio. Yet the portfolio's expected return and standard deviation are virtually unchanged." 1b Estimation Risk There are several assumptions that are necessary for MPT to be relevant, one of which is that the means and covariances are known with certainty. Thus, if we knew the parameters with certainty and if minimizing variance while maximizing the mean of the portfolio, regardless of the resulting portfolio turnover, were the right criteria to use for our portfolio, then the above portfolio weights, however extreme, would present an appropriate strategy. Of course, we do not know the input parameters with certainty. In fact, as noted by several authors, the estimation of these parameters is fraught with difficulty. Merton (1980) points out the expected return estimation problems by noting that a very long time series of data is required to achieve precise estimates. Similar problems can also affect the covariance estimates (Green and Hollifield, 1992; Ledoit and Wolf, 2003). Thus, when running mean-variance optimization, the inherent instability of the suggested optimal weights is greatly exacerbated by the fact that we have to estimate the inputs, usually with a high degree of error. FOR ONE-ON-ONE USE WITH A CLIENT'S FINANCIAL ADVISOR ONLY © 2024 Envestnet. All rights reserved. Table 1. Scenario 1 Scenario 2 Scenario 3 mean std.dev. allocation mean std.dev. allocation mean std.dev. allocation Asset A 8.00% 20.00% 50.00% 8.00% 20.00% 100.00% 8.00% 20.00% 200.00% Asset B 8.00% 20.00% 50.00% 8.01% 20.00% 0.00% 7.99% 20.00% -100.00% Portfolio 8.00% 19.49% 100.00% 8.00% 20.00% 100.00% 8.01% 23.66% 100.00%