Introduction to Portfolio Construction Using Asset Classes

Now that we understand the importance of asset allocation, and how to estimate the target real rate of return you’ll have to earn to reach your accumulation goals, let's take a closer look at the different approaches that can be used to construct a portfolio of asset classes.

Historically, the most commonly used approach to asset allocation and portfolio construction is a methodology called "mean variance optimization" (MVO), which is an application of linear programming.

MVO starts with three assumptions about each asset class: the average rate of annual return it is expected to provide in the future, the expected standard deviation of its returns (i.e., the extent to which actual returns are distributed around the expected average), and the correlation of its returns with those on other asset classes (i.e., the extent to which asset class returns linearly move together). MVO then calculates an optimal asset allocation solution, that either minimizes expected risk (defined as portfolio standard deviation) for a target level of expected annual return, or that maximizes return for a target level of risk.

Unfortunately, the theoretically "optimum" portfolios produced by MVO have too often produced disappointing real world results. There are two broad reasons for this: problems with the methodology itself, and problems with the inputs it uses.

Criticisms of the MVO methodology include the following:

• Standard deviation does not align with most investors' intuitive understanding of risk, which is better described as the distribution of returns below the expected average, or the probability of failing to achieve some threshold portfolio return (and hence the goals and dreams that depend on that return).

• Correlation only captures linear (but not non-linear) relationships between asset class returns, and does a poor job of capturing the relationships between returns in the tails of a distribution (where contagion and herding across asset classes under extreme conditions can cause many correlations to sharply increase).

• MVO assumes that asset returns are normally distributed - that is, when plotted on a graph they have the familiar symmetrical bell-curve shape. In fact, most financial asset returns are not normal, are more tilted in a positive or negative direction (technically, they "skewed"), and have fatter tails than the normal distribution (i.e., they have a greater proportion of extreme returns, or, technically, greater "kurtosis").

• While MVO is a one period technique, most investors' goals extend across long time horizons. When the returns on an asset class vary (i.e., when standard deviation is greater than zero), the long term geometric average return will be less than the arithmetic average return used in most MVO analyses (this difference will be roughly equal to the arithmetic return less two times the standard deviation squared). Moreover, across multiple periods, asset class weights will not always equal the weights assumed by the MVO analysis, as rebalancing only happens at intervals.

• Returns, standard deviations and correlations aren't stable over time; for example, they have been quite different in the past under different economic conditions. The averages that are typically used in MVO analyses can assume away serious problems that can (and have) occur under adverse regimes (e.g., ones involving high uncertainty or high inflation).

• Too often, MVO analyses use historical data as the basis for calculating return, risk and correlation inputs. What is often not acknowledged is that these historical samples are only estimates of the true values of the returns, standard deviations and correlations produced by the underlying return generating process. For example, statistical software that calculates the historical average or mean return of a time series of asset returns also typically calculates the standard error of this estimate. The standard error is equal to the sample standard deviation divided by the square root of the number of data points used in the estimate. Assuming that the data come from a normal distribution (that is, one in the shape of the bell curve), there is a 67% chance that the true mean will lie within plus or minus one standard error of the sample mean, and a 95% chance that it will lie within two standard errors. Given the relatively short historical data series available for most asset classes, these standard errors are typically quite large relative to the sample mean. All else being equal, this should introduce a substantial amount of uncertainty into the MVO calculation - yet this uncertainty is seldom acknowledged or disclosed.

• A similar problem occurs in the case of standard deviation. The use of the sample standard deviation in an MVO analysis assumes that the underlying series of financial returns are independent from each other (technically, that they have zero autocorrelation). Yet this is seldom the case. As a result, assets whose returns have positive autocorrelation have underestimated standard deviations, while assets with negative autocorrelations have overestimates standard deviations.