Economic Tracking Portfolios

TLDR: An economic tracking portfolio is a portfolio of assets with returns that track an economic variable as mentioned in this paper, which is useful in forecasting post-war US output, consumption, labor income, inflation, stock returns, bond returns, and Treasury bill returns.

Abstract: An economic tracking portfolio is a portfolio of assets with returns that track an economic variable. Monthly returns on stocks and bonds are useful in forecasting post-war US output, consumption, labor income, inflation, stock returns, bond returns, and Treasury bill returns. These forecasting relationships define portfolios that track market expectations about future economic variables. Using tracking portfolio returns as instruments for future economic variables substantially raises the estimated sensitivity of asset prices to news about future economic variables. Out-of-sample results show that tracking portfolios are useful in forecasting macroeconomic variables and hedging economic risk.

Figures

Table 3 Forecasting ability and descriptive statistics for tracking portfolios, 1947-1994

Table 1: Summary Statistics for Target Variables, Control Variables, and Base Asset Returns, 1947:1-1994:12

Figure 1 Industrial Production Growth

Table 4 Correlation matrix for innovations: Tracking portfolios vs. vector autoregressions Panel A VAR innovations from Campbell and Ammer (1993)

Figure 2 Inflation

Table 8 Out-of sample results using rolling regressions

Full text

Economic Tracking Portfolios - Page 1
Changes in asset prices reflect, among other things, changing information about future
economic conditions. Identifying the impact of different macroeconomic shocks on asset prices
is important because it can reveal sources of economic fluctuations, measure risk premia, and
help predict future economic fluctuations. Economic tracking portfolios are a way of connecting
asset prices with news about economic variables. An economic tracking portfolio is a portfolio
of assets whose returns track an economic variable, such as expected output, inflation, or returns.
The portfolios constructed here have unexpected returns with maximum correlation with
news about future macroeconomic variables. I call these "economic tracking" portfolios, rather
than "factor mimicking" portfolios, to make clear that these portfolios are not only useful for
explaining the statistical properties (means and covariances) of asset returns, but are
fundamentally economic in nature.
Empirical finance has a long tradition of explaining current returns with other current
returns. A second tradition is to try to explain returns with contemporaneous economic
variables, or with future economic variables, or with both (e.g. Chen, Roll, and Ross (1986),
Fama (1990), and Campbell and Ammer (1993)). Economic tracking portfolios represent a
middle ground between these two alternatives. On the one hand, tracking portfolios are asset
returns. On the other hand, they are returns with an interpretable economic content.
Constructing economic tracking portfolios is a way of using current asset returns as instruments
for changes in expectations of future variables. The use of instruments is required because
realized variables are noisy measures of innovations in expectations.
This paper builds on Breeden, Gibbons, and Litzenberger (1989). They construct
economic tracking portfolios (which they call "maximum correlation portfolios") for current

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consumption, in order to test the Consumption Capital Asset Pricing Model (CCAPM). This
paper has several differences. First, and most importantly, it constructs tracking portfolios for
future (not current) economic variables, since asset returns reflect information about future cash
flows and discount rates. Second, as a consequence, it uses only the unexpected component of
returns (not total returns) in constructing the tracking portfolios. Last, it constructs tracking
portfolios for a variety of economic variables (not just consumption).
Tracking portfolios have several uses. One use is measuring risk premia. If tracking
portfolios earn risk premia, then the signs of the risk premia and the identities of the premia-
generating economic variables can reveal which state variables are important determinants of
expected returns, and can help evaluate asset pricing models. Tracking portfolio have (at least)
three other uses that do not rely on the portfolios earning non-zero risk premia.
First, tracking portfolios can serve as hedging tools for individuals who wish to insure
themselves against a particular economic risk. For example, individuals who wish to insure
against inflation could take a position in the inflation tracking portfolio. Second, tracking
portfolios forecast economic variables. Since asset returns are available on a daily basis,
tracking portfolios can provide daily information about the market's expectations about future
economic variables. Third, by measuring innovations in expectations, tracking portfolios
illuminate the structure of the economy and the reaction of prices to economic news. This paper
concentrates on this last use of tracking portfolios, and studies the reaction of stock and bond
prices to news about future production, interest rates, and expected returns.
These three uses are empirically testable, and do not depend on a particular asset pricing
model. For example, suppose the CAPM is true. In that case, an economic tracking portfolio

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would have an expected return that is a linear function of covariance with the market, but its
unexpected return would still reveal news about future economic variables. Alternatively,
suppose that asset markets are inefficient, irrational sentiment affects market prices, and returns
are partially predictable. In this case, as long as asset prices reflect some information about
future economic variables, tracking portfolio returns will still be useful for hedging, forecasting,
and understanding the economy.
This paper is organized as follows. Section 1 defines tracking portfolios, states their
statistical properties, and introduces the notation. Section 2 discusses the relation of tracking
portfolios to previous research. Section 3 describes the data. Section 4 shows the properties of
the estimated tracking portfolios. Section 5 uses tracking portfolios to test hypotheses about the
effect of news on asset prices. Section 6 shows the out-of-sample tracking ability of the
portfolios, and performs robustness tests. Section 7 concludes by summarizing the results and
discussing possible applications and extensions of tracking portfolios.
1. Definitions and basic properties
Simple tracking portfolios
A tracking portfolio for any variable y can be obtained as the fitted value of a regression
of y on a set of base asset returns. The portfolio weights for the economic tracking portfolio for
y are identical to the coefficients of an OLS regression. If y happens to be to be a state variable
for asset pricing, then a multi-factor model holds with one of the factors being y's tracking
portfolio (Breeden, 1979). However, even if y is not a state variable for asset pricing, its
tracking portfolio is still an interesting economic object, since it reveals changes in market
expectations about y.

Frequently asked questions

Q1. What is the risk premia of the economic tracking portfolios?

The positive risk premia is one measure of the cost of business cycles: investors demand high returns on assets exposed to macroeconomic fluctuations. 

Q2. What is the reason for the consumption portfolio's mispricing by the CAPM?

Theprimary reason for the consumption portfolio's mispricing by the CAPM is that returns on one of the base assets (the one-year treasury bond portfolio) is also mispriced by the CAPM. 

Q3. What is the effect of the second regression on stock returns?

Since the tracking portfolio for production is constructed only using bond returns, the second regression shows the ability of long bond returns to explain stock returns. 

Q4. What is the key assumption for the use of tracking portfolios?

A crucial assumption for the use of tracking portfolios, in equation (1), is that returnsreflect revisions in expectations about the target variable. 

Q5. How are the correlations with baseline portfolios calculated?

The correlations with baseline portfolios are calculated using monthly returns, where the portfolio weights come from the regression using quarterly returns. 

Q6. What could be the reason why stock prices do not react to macroeconomic announcements?

It could be that stock prices do not react because competing effects on future discount rates and cash flows cancel out in aggregate. 

Q7. What are the other rows of Panel A?

The other rows of Panel A test whether three subsets of returns forecast the targetvariable (given the other returns): the 12 returns excluding the market portfolio, the eight industry portfolios, and the four bond portfolios. 

Q8. What is the correlation between the tracking portfolios and the base assets?

Before discussing the results, a statistical fact: since the tracking portfolios are linear combinations of the base assets, the α's of the trackingportfolios are linear combination of the α's of the base assets.