Global Asset Allocation:

The BARRA Altis System™
and World Markets Model

Researching global asset allocation strategies for institutional investors is a three-step process: forecasting asset class expected returns, building optimal portfolios, and testing their out-of-sample performance.

The new BARRA Altis System can be used to estimate models linking fundamental economic variables to asset class returns. These models can then be used to forecast asset class returns as part of a tactical asset allocation (TAA) strategy.

Altis includes comprehensive in- and out-of-sample analysis which—when combined with the empirical backtesting capability of the World Markets Model—quantifies and assesses the value added by a particular strategy. We will illustrate the benefits of Altis with a comprehensive case study.

Case study: How to beat the EAFE?

The equity market selection policy was based on forecast expected asset class returns generated using a quantitative model. This model was derived from the relationship between underlying fundamental economic variables and the asset returns. All of the analysis was generated by a combination of the new Altis System and the BARRA World Markets Model.

Model construction

Table 1

The model was estimated separately for each of the 20 equity markets within the Morgan Stanley EAFE universe. A linear regression was run over the period from January 1985 to December 1992 for each country, in which the monthly local excess returns were regressed on the variable values (we define excess returns as those returns above the risk-free return in each market).

The asset class excess monthly returns r(t) were explained using a set of explanatory variables {x_j(t)}. The explanatory variables were known at the beginning of period t. The coefficients b_j were estimated to relate the explanatory variables to the returns.

In-sample model results

Table 2: In-sample model results

Despite the fact that there are likely to be in-sample biases in these results, they remain sufficiently encouraging to proceed with the out-of-sample testing. (Please refer to the discussion of how to avoid biases in TAA model-building in this Newsletter.)

Although our model is quantitative, it also provides qualitative insight and intuition into market behavior. The relationship between the economic variables and the expected returns should be intuitive. The model can help to identify which variables are relatively more important for market returns and which help to predict market direction.

The January dummy effect was positive for every country. This suggests that returns are on average higher in January than in all other months for every country. For five of the countries, the January dummy variable is significant at the 90% level.

The coefficients for dividend yield were positive in all but two of the countries. Higher dividend yield implies higher expected returns: in the U.K., each 1% increase in dividend yield raises the expected monthly U.K. excess return by 2.97%.

At first glance this result could be construed as being counterintuitive, since an increase in dividend yield could follow from a fall in share prices. However, it could also be explained using a discounted cash flow argument: An increase in dividend payments would increase the net present value and hence the price of the shares.

The coefficients for the local exchange rate (U.S. dollars per local currency) were almost always positive. This means that as the dollar appreciates relative to the local currency, the expected return increases.

The coefficients for the earnings estimates were positive in half of the markets and negative in the others. This is counterintuitive since one would expect a positive coefficient, an increase in the upwards earnings revisions leading to a higher return. However, this result is perhaps explained by the fact that only one of the coefficient estimates was significant, at the 90% level.

Out-of-sample model results

The R² ranged between 0.3% and 11% for the 20 countries, with an average of 4%. These are fairly typical results for the out-of-sample period.

We can also look at a comparison of the out-of-sample forecast returns and the actual returns. Figure 1 displays the cumulative forecast and actual returns for the U.K.

Figure 1: U.K. cumulative forecast and actual return

Empirical backtest

Figure 2 shows the cumulative returns of the optimal portfolio created using the out-of-sample forecast returns. This portfolio was constrained to be fully hedged into a U.S. dollar perspective. Figure 2 also shows the cumulative returns to the benchmark and the active return. Active return is defined as the difference between the portfolio return and the benchmark return. The graph clearly shows that a global asset allocation strategy based on the forecast returns generated using the model led to portfolio outperformance.

Figure 2: Cumulative returns to optimal portfolio constructed using Altis forecasts in the World Markets Model Optimizer

These returns are stated before transaction costs. To minimize turnover and costs, the optimal portfolio was constrained so that its active weights reflected a typical investment range.

We can further extend the performance attribution analysis to consider the modelÕs risk-adjusted performance. Table 3 shows that the annualized active return is 1.29%, with an associated tracking error of 2.24%. The information ratio is a high 0.58. This means that the strategy added 58 basis points of outperformance for every 100 basis points of risk.

Table 3: Return vs. risk of optimal portfolio constructed using Altis and the World Markets Model

Based on mutual fund research at BARRA, the typical before-costs distribution of information ratios suggests that this fund would have been in the top performing quartile.

As a final step in the analysis, we can examine the return contributions for each country in terms of both an average and a timing element. Table 4 shows that the outperformance was achieved as a result of positive contributions from 13 of the 20 countries. The most successful average country tilt was the underweighting in Japan, although the timing decisions around this average position were the most unsuccessful. The best timing policy was achieved on the French market, with a positive contribution of 59 basis points.

Table 4: Country contributions to model performance

Summary

The new BARRA Altis System covers all stages of quantitative model development, and allows you to develop and test quantitative investment strategies for international asset allocation. With Altis, you can identify the relative importance and directional impact of particular variables and use them as the basis for predicting market movements.