Asset Allocation. William Kinlaw

in passive asset class benchmarks. They then measured the return associated with deviations from the policy mix assuming investment in passive benchmarks, and they attributed this component of return to timing. Finally, they measured the return associated with deviations from the passive benchmarks within each asset class and attributed this component of return to security selection. For each of the 91 funds, they regressed total return through time on these respective components of return. These regressions revealed that asset allocation policy, on average across the 91 funds, accounted for 93.6% of total return variation through time and in no case less than 75.5%.

      Fundamental Flaw

This methodology is flawed because it presents no notion of a normal or a default asset mix. Their analysis implicitly assumes that the pension plans' funds would otherwise be uninvested, perhaps contained in a very large coffee can. Because the authors failed to net out an average or typical asset mix, most of the variation in performance that they attributed to asset allocation policy arose not from the choice of a portfolio's asset mix but, instead, from merely the decision to invest. The authors simply demonstrated that we incur risk when we invest in risky assets.

      A Practical View on Importance

      To illustrate our point, consider a portfolio that consists of 75% technology stocks and 25% US bonds. From 2006 to 2013, what percentage of this portfolio's return variation is explained by asset allocation?

      We begin by obtaining monthly historical returns for the actual portfolio. Next, we split the returns into two parts. The first part equals the monthly returns of a portfolio that holds 75% in a broad stock market index and 25% in US bonds. It mimics the asset allocation but ignores security selection. The second part equals the monthly returns of the actual portfolio – which contains a large concentrated position in technology stocks – in excess of the returns of the first part. It reflects the incremental return associated with security selection.

      This separation allows us to decompose the portfolio's monthly return variation into its two component parts. We do so by calculating the fractional contribution to total variance (FCTV), as follows:

(3.1)

In Equation 3.1, Σ is the covariance matrix of return components, 1 is a column vector of ones, and ʹ denotes the matrix transpose. The sum of FCTV across components always equals one (as can be seen from Equation 3.1, where the numerator will equal the denominator after pre-multiplying by 1ʹ).

      In this example, the asset allocation component appears to explain 73% of the total return variation, dwarfing the 27% explained by security selection. This conclusion mirrors the logic of Brinson, Hood, and Beebower. Intuitively, it seems surprising that such a dramatic security selection tilt carries so little relative importance. In fact, this approach incorrectly implies that asset allocation is more important than security selection because it considers all market volatility to be the result of an asset allocation decision.

Now, let us propose a different perspective. In the absence of any skill, effort, or careful consideration, investors can still default to a broadly diversified portfolio such as 60/40 stocks and bonds. The default might represent, for example, the average allocation across a pool of similar investors. The returns of this default asset mix reflect the decision to invest. They do not reflect an asset allocation decision for the simple reason that it was chosen without any care or consideration at all.

The relevant question for investors is: how much impact can I have on return outcomes by deviating from the default asset allocation, as opposed to deviating from the default security selection? The answer to this question helps to allocate scarce time and attention across competing investment activities. Figure 3.1 shows that when we account for the return variation explained by the default asset mix, our conclusion is reversed. Only 16% of the return variation is due to asset allocation, which means it is less important than security selection in this example. More than half of the portfolio's variation in returns comes from the mere decision to invest.

FIGURE 3.1 Fractional contribution to total variance.

      Reductio ad Absurdum

To stress our point even further, it is possible to construct a simple yet extreme example of the Brinson, Hood, and Beebower methodology that leads to an obvious contradiction. Kritzman (2006) describes an imaginary world with two stocks and two bonds.² The first stock always produces the same return as the first bond, and the second stock always produces the same return as the second bond. Thus, stocks and bonds as asset classes always have identical returns, which means that the weights assigned to stocks versus bonds have no impact. In other words, asset allocation is completely irrelevant to returns. Security selection does matter, though. Suppose that the second stock and second bond have returns that are always twice as large as those of the first stock and first bond. The punch line is that an investor who allocates entirely to the second stock and second bond will earn twice the return of an investor who allocates to the first stock and first bond, but both of their returns will be 100% correlated to their asset allocation benchmarks (equivalent to an R-squared of 100% in a regression of returns). The methodology proposed by Brinson, Hood, and Beebower would conclude that asset allocation explains 100% of performance variation across the two investors, but we know the opposite to be true: asset allocation is irrelevant in this example.

THE BEHAVIORAL BIAS OF POSITIVE ECONOMICS

The Brinson, Hood, and Beebower methodology has another feature that limits its ability to separate the relative importance of various investment activities, which is also common to other methodologies that address this question. Most studies analyze the actual performance of funds.³ In this sense, they are positive, as opposed to normative; they rely on actual returns that reflect some combination of the relative importance of alternative investment choices as well as the behavior of investors; that is, the extent to which investors choose to engage in various investment activities.

      For example, some investors choose to invest in actively managed funds with high tracking error relative to the norm, but choose an asset mix that is close to the norm, such as the average asset mix of a relevant universe. Other investors choose actively managed funds with low tracking error relative to the norm, but choose an asset mix that is substantially different from the normal asset mix. In the former case, security selection will be seen to be more important than it is normally thought to be, whereas asset allocation will be seen to be less important than it is typically construed to be. In the latter case, the opposite will be true. But these conclusions could be misleading, because they may reflect as much or more about the investors' choices to emphasize asset allocation over security selection than the potential impact asset allocation and security selection have on portfolio performance.

To separate the intrinsic importance of an investment choice from an investor's decision to emphasize that choice, we need to measure the potential for an investment choice to cause dispersion in wealth. Dispersion is important to investors who believe they are skillful because it enables them to increase wealth beyond what they could expect to achieve by passive investment or from average performance. Dispersion is also important to