Global Asset Allocation and Stock Selection

Forecasting International Returns

The Traditional Approach

The traditional approach to asset management input assumes that asset prices follow random walks (potentially with some drift). In these models, this month's price is the best forecast of next month's price. In the model with drift, the forecasted return is this month's price plus a constant. In both of these models, returns (differences in the log prices) are unforecastable.

           Pt = drift + Pt-1 + et


           Rt = drift + et

Notice that et is so-called white noise, which implies that the returns are not forecastable. The expected return is just the drift which is often measured as an average.

Traditional asset management will calculate historical average returns, historical average volatility and historical average covariance and apply these inputs in a mean-variance framework following Markowitz (1959).

This framework imposes the assumption that in a more general model:

             Rt = d0 + d1(Z1,t-1) + et    

where Zt-1 represents lagged information, the coefficient d1 is exactly zero. With this constraint, the R-square of the model is exactly zero. Hence, the traditional approach starts with the constraint that the R-square is zero.

The traditional approach provides a lower bound for our exercise. If we fail to forecast returns, we will also get a zero R-square. Hence, in failing we will fall back on the traditional approach. If we get a zero R-square, the forecasted return is a constant.

The General Setup

We will be interested in building models which explicitly incorporate conditioning information. The research protocol gives us a set of guidelines for avoiding specification problems and data mining traps. We will develop a parsimonious model which has been tested on an quasi-out-of-sample basis, i.e. we hold out some data for out-sample-testing (it is quasi because the data are know to us).

After developing the model, we implement using the following steps. Suppose the date is October 31.

  1. Fit regression with returns through October 31 and information variables through September 30.
  2. Save coefficients, d0,d1,...
  3. Use coefficients and information variables available October 31 to form an out-of-sample forecast for the return in November.

Information Variables

An Economic Model

In specifying information variables, we must be keenly aware of the data mining problem. Variables must make economic sense to be included in the regression model. Hence, we must start with an economic model. Usually, we use some variant of the Lucas (Econometrica, 1978) asset pricing model.

                 Forecasted Cash Flows into Future
Pricet = SUM -----------------------------------------
              Expected discount rates (for each period)

This is just the present value formula. However, it has some unique features compared to the Finance 101 version.

One could future decompose the expected discount rate into a part due to:

Each of these could change through time and may be different depending on the horizon of the forecasted cash flow.

Economic Categories

The following are a list of general categories:

Each of these categories has some relation to the general model. They are not mutually exclusive. That is, information variable may fit into more than one of these categories. Indeed, there can be correlation among the categories.

We will focus the discussion on the building of a model for a particular country. It will be generalized to an international setting.


Inflation itself is not that useful of a forecasting attribute because it measures past inflation. We are really interested in future inflation. This will affect both the numerator and the denominator of our valuation formula. Some candidate variables include.

Business Cycle

The business cycle affects the expected cash flows in the numerator. We need leading indicators of the business cycle. One might immediately go to index of leading indicators (LEI). However, this index has produced a remarkable number of false signals. It is better to go to the components and variants of the components. Among the macro economic information:

It is probably not wise to use last quarter's GDP growth. That is backward looking and we want something that promises to forecast the future.

There are also some financial variables that could be useful.

The dividend yield is very cyclical [see Fama and French (Journal of Financial Economics, 1989)] and is a traditional forecasting variable. Harvey (Journal of Financial Economics, 1988) shows that the term structure forecasts real economic activity. A number of authors, including Campbell (Journal of Financial Economics, 1987) show that the term structure also forecasts stock returns.

Fundamental Valuation

There is a long history of using fundamental - or accounting - based information in stock selection. Recently, Ferson and Harvey (1993, 1995) show the importance of certain country based fundamental valuation metrics in the cross-sectional stock selection problem. The variables of interest are:

The first four ratios are available through MSCI for developed countries and the IFC has coverage of all but the price to cash ratio. IBES has recently made available global aggregates of their survey data for a number of accounting aggregates. I have included the expected price to earnings ratio. However, there are many additional useful variables in the IBES database.


Fundamental values are historical or backward looking. It is often important to capture expectations. :

Some of these variables can be found in First Call or IBES data.

Default Risk

This category is correlated with the business cycle category. Default risk will change the discount rate in the denominator of the valuation equation. Default risk is highly correlated with the business cycle. A popular specification includes

Default risk increases before business cycle recessions and narrows during expansions. See Keim and Stambaugh (Journal of Financial Economics, 1986).

Microstructure of Market

The microstructure of the market could affect the discount rate applied to the firm in that market. That is, if the market is thinly traded, investors will demand a premium for transacting in that market. Some possible measures include:

World Integration

The degree of market integration will affect the expected discount rate. Integration means that the same risk project will require the same discount rate no matter where the project is located. In reality, some markets are segmented. As a result, a larger discount rate is required. Integration works on the denominator of the valuation formula. See Bekaert and Harvey (Journal of Finance, 1995). They propose two proxies for openess:

Bekaert and Harvey (1995) specify a functional form for the degree of integration which relies on these variables.

Bekaert and Harvey (1995) pursue the intuition that a market that appears segmented because of numerous investment restrictions could be integrated if investors can access the market in different ways. They examine country funds and American Depository Receipts (ADRs) as proxies for this accessibility.

Political Risk

Much has been written and talked about political risk but not much mentioned. Obviously, political risk could influence the discount rate in the denominator of the valuation formula. A negative political event could adversely affect the numerator (cash flows).

Erb, Harvey and Viskanta (1994, 1995) have examined a proxy for political risk using Institutional Investors' Country Credit Rating. Political Risk Services'(PRS) indices and subindices are available on a monthly basis.


There are various economic reasons why serial correlation in returns may arise. These reasons focus on the speed of adjusting production as a result of economic shocks. Momentum is often proxied by:


This factor will influence the expected cash flows and the discount rates. It is often measured by:

Model Building

For each country, the availability of data is determined. The next step is to conference with the research team. A small set of variables are pre-selected for each country. Small being 10-15 variables. The variables should have a theme. That is, the same type of variables should be chosen across different markets. The model building process then begins with strict adherance to the research protocol. Out-of-sample validation is critical to the success of this exercise.