Читать книгу Asset Allocation - William Kinlaw, Mark P. Kritzman - Страница 66

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.