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While Chen et al. (1986) are credited with being the first to employ proxies for unidentified risk factors to explain expected returns, it was Chan et al. (1985) who laid the groundwork for this approach citing the APT as their motivation in an investigation of the firm size effect for firms listed on the NYSE over the January 1953 to December 1977 period. Chan et al.

(1985) postulate that returns are sensitive to changes in the economic environment and these changes are indicative of the risks that investors can hedge against. A theory linking stock prices to pre-specified factors is proposed whereby prices are assumed to be determined by expected cash flows and the discount rate - a pricing equation informing the choice of factors.

Factors identified by Chan et al. (1985) in this manner are the monthly growth rate in industrial production, the unanticipated inflation rate, changes in expected inflation, changes in the term structure of interest rates, the default spread and changes in the business cycle as measured by the growth rate of Net Business Formation (NBF). The equally-weighted NYSE Index serves as a proxy for returns on the market. While it is recognized that innovations (unexpected changes) in these factors should be used in empirical tests, the authors choose not to use innovations and warn that the generation of innovations through pre-whitening²⁶ may lead to a loss of information. Time series relationships between returns and the candidate risk factors are established by examining the correlation between aggregate returns, as measured by returns on the equally-weighted NYSE Index and the set of risk factors. Table 3.1 reproduces the correlation matrix in Chan et al. (1985) to demonstrate the approach undertaken in identifying factors that are correlated with returns over time and to provide insight into potential time series relationships. Although this approach reveals the presence of time series relationships between returns and factors, macroeconomic APT studies give little direct consideration to these relationships.

26 A process whereby the unexpected components of a series are extracted.

Table 3.1: Correlation among factors

– Growth Rate of industrial production from month t to t+1 (seasonally adjusted) – Unanticipated inflation, defined as CPI less expected inflation.

– Change in expected inflation.

– Difference in return on long-term government bond portfolio and the one-month T-bill.

– Growth rate of the Net Business Formation series from t to t+1. Seasonally adjusted.

– Difference in return of ‘under BAA’ (rated by Moody) bond portfolio and long-term government bond portfolio.

Source: Chan, Chen & Hsieh (1985)

As evident from Table 3.1, all factors show some level of correlation with each other and with returns on the equally-weighted NYSE Index over time. In macroeconomic APT studies, the presence of correlation between returns on a market aggregate and candidate risk factors, is often cited as a justification for the inclusion of specific factors in the return generating process and consideration in cross-sectional tests (see Van Rensburg, 2000). Chan et al.

(1985) proceed to estimate factor loadings for use in cross-sectional tests by first regressing 60 months of returns on size sorted portfolios on the candidate risk factors and then performing month-by-month cross-sectional regressions in the second stage over each month in the subsequent year.²⁷ The first stage is important. Regressing returns on macroeconomic factors to obtain factors loadings requires a formulation of a multifactor model of the return generating process. However, as asset pricing is of primary concern in the study, this aspect of the APT framework is not considered further by Chan et al. (1985).²⁸ The focus upon the implications of the cross-sectional APT model in this study is indicative of the focus of most macroeconomic APT studies. In these studies, the only (and limited) insight into the structure of the return generating process is provided by the correlation matrix.

Chan et al. (1985) find that three factors are priced over the entire sample period, namely the default spread, the growth rate in industrial production and unanticipated inflation. Together, these factors explain 35 percent of the cross-sectional variation in expected returns. Other factors that are priced over the sub-periods considered, aside from these three factors, are the

27 This two-stage procedure is consistent with the Fama-Macbeth approach and represents the thrust of early macroeconomic APT literature (see Fama & Macbeth, 1973; Chen et al., 1986; Hamao, 1988).

28 A two-step procedure need not be followed to establish which factors are priced. However, regardless of the approach undertaken in estimating factor loadings and risk premia, the APT framework consists of two components; a time series model and the APT model.

changes in expected inflation (1968-1977) and the term structure of interest rates (1958-1972). In a first test of the validity of the model, the authors consider whether a firm size effect is reflected in the residuals of the APT model. The differences between the residuals of the largest and smallest portfolio, and the top and bottom quintiles are statistically insignificant suggesting that macroeconomic factors used in place of unidentified APT factors account for systematic risk and risk that is associated with firm size. It is suggested that the firm size effect is related to risk associated with a changing default spread (see Chan et al., 1985: Table 4). In a second test of the model, the business cycle indicator is substituted for the default spread factor. Results show that the indicator is priced implying that it can replace the default spread as an indicator of business conditions. In a third test, Chan et al. (1985) formally consider whether a size proxy has explanatory power in the cross-sectional context;

it is postulated that size is a proxy for unspecified risks. When size is the only factor in cross-sectional analysis, the risk premium on size is statistically significant. However, it is statistically insignificant when considered in combination with a set of macroeconomic factors which excludes market indices,²⁹ but includes the growth rate of industrial production, unexpected and expected inflation, the default spread and the term structure. In this version of the APT model, the default spread is statistically insignificant implying that that size and the other risk factors proxy for risk associated with the changing default spread. Chan et al.

(1985) conclude that the size effect is explained by a multifactor pricing model. The authors’

contribution is important in that pre-specified macroeconomic factors are used as proxies for systematic risk. Notably, these factors are correlated with returns over time suggesting that they explain the time series behaviour of returns. As a number of these risk factors are priced, it can be inferred that the APT framework can be used to not only explain expected returns, but to also model the time series variation in returns (Elton & Gruber, 1988).

Notwithstanding Chan et al.’s (1985) important contribution, Chen et al. (1986) are widely credited in the literature as being the first to utilize macroeconomic factors as proxies for unidentified APT risk factors. The influence of the APT framework on Chen et al. (1986) is evident; the authors, with reference to the work of Roll (1976), acknowledge that modern financial theory has focused upon the pervasive and systematic influences that affect stock prices. It is further argued that while it is accepted that individual stock prices are influenced by unexpected events, little is known about the identity of systematic factors that influence

29 See equation (vi) in Table 5 in Chan et al. (1985).

prices; although, the co-movement of stock prices points towards their existence. It is with this argument in mind and within the APT framework, that Chen et al. (1986: 384) refer to an

“embarrassing gap” between systematic factors and their identity. It is this gap that the authors seek to close by investigating the identity and nature of systematic risk factors.

The existence of systematic risk factors is suggested by observed co-movements of stock prices and implicit in the assumption that investors diversify. This suggests that only factors that are associated with the economic state have an impact upon the pricing of stock market aggregates. Although, Chan et al. (1985) allude to a theory upon which the identification and selection of factors can be based, Chen et al. (1986) formally identify and elaborate upon a theoretical model - the dividend discount model³⁰ - that aids the identification and selection of risk factors within the APT framework. It is hypothesized that any systematic factor that influences the expected stream of dividends, cash flows or/and the discount rate will impact stock prices. As current beliefs regarding potential and identified factors are assumed to be already incorporated into stock prices, it is only innovations in these factors that impact returns. While it is recognized that a failure to remove expected movements in the explanatory factors may introduce an errors-in-variables (EIV) problem, Chen et al. (1986) employ a simple rate of change methodology to represent (assumed) innovations³¹ in factors.

Their set of candidate risk factors incorporates the monthly and annual industrial production growth rates, the change in expected and unanticipated inflation, changes in the default spread, the term structure, consumption growth and changes in the oil price. Returns on the equally-weighted and value-weighted NYSE indices for the January 1953 to November 1983 period are used as a proxy for the market index. Factors considered, but not utilized, in the preliminary specification, are changes in real consumption and oil prices. As in Chan et al.

(1985), time series relationships between returns on the two market aggregates and the macroeconomic factors are examined using a correlation matrix. Each of these factors is correlated with returns on the value and equally-weighted NYSE indices over the sample period (see Chen et al., 1986: Table 2, Panel A). The factors identified by Chen et al. (1986) are what Amenc and Le Sourd (2005: 153) term as “classic” factors suggesting wide usage in multifactor models employing pre-specified factors as proxies for systematic risk. The basic

30 Discussed in greater detail in Chapter 4.

31 As will become evident later, the rate of change methodology fails to generate true innovations.

multifactor specification³² describing the return generating process of individual stock returns proposed by Chen et al. (1986) is given by:

ε UTS is the change in the term structure. Equation (3.1), as stated in Chen et al. (1986: 394), represents an important acknowledgement that returns can be described by innovations in multiple macroeconomic factors representative of unspecified APT risk factors.³³ Most importantly, equation (3.1) represents the return generating process underlying the macroeconomic APT model which relates returns to innovations in macroeconomic factors over time. However, the authors do not use equation (3.1) to study the return generating process of US returns but rather to estimate factor loadings for use in the corresponding cross-sectional macroeconomic APT model. Factor loadings are estimated by regressing returns on size sorted portfolios onto innovations in macroeconomic factors.³⁴ Risk premia are estimated in the second stage by employing Fama-Macbeth regressions relating expected returns to factor exposures (Chen et al., 1986):

UTS explanatory factors in equation (3.2). The coefficients on the betas, λs, are interpreted as the risk premia – the price of risk - associated with a given macroeconomic factor. By taking

32 Chen et al. (1986) vary the model specification to investigate various aspects. The notation used by Chen et al. (1986) is retained for demonstrative purposes.

33 The separation of the APT into a time series model and a cross-sectional model employing factor loadings estimated in the time series model is explicitly acknowledged by Hamao (1988). Hamao (1988) specifies the time series model alongside its cross-sectional counterpart. Chen et al. (1986) specify the time series model but not its cross-sectional counterpart. The estimation of the cross-sectional regression using factor loadings estimated in the time series model can be seen as an implicit acknowledgement of a link between the two models.

34 Equation (3.1) is estimated as a time series model using size sorted portfolios to control for the EIV problem and to achieve a spread of expected returns required for cross-sectional tests.

equations (3.1) and (3.2) together, it then follows by implication that priced factors are risk factors that feature in the return generating process.

Results of the cross-sectional analysis over the entire sample period (1958-1984) indicate that the monthly industrial production growth rate, the unexpected inflation rate, the default spread and the term structure of interest rates are priced suggesting that these factors play an important role in explaining both the cross-section of expected returns and the time series behaviour of returns. This argument is strengthened by a finding that these factors that are also correlated with return aggregates over time (see Chen et al., 1986: Table 2, Panel A).

Risk premia on industrial production and the default spread are positive whereas the risk premia on unexpected inflation and the term structure are negative. Chen et al. (1986) hypothesize that the positive risk premium on industrial production reflects the benefit of insuring against real production risks whereas the positive risk premium on the default spread suggests that investors seek to hedge against unexpected increases in uncertainty. The negative risk premium on unexpected inflation is hypothesized to imply that assets are hedges against adverse influences on assets that are fixed in nominal terms. The sign of the risk premium on the term structure factor implies that stocks for which returns are negatively related to changes in the term structure are more valuable (Chen et al., 1986). In using pre-specified factors and ascribing meaning to estimated risk premia, Chen et al. (1986) address criticisms of the APT framework whereby it is not possible to ascribe meaning to the risk premia on statistically derived factors. In a second set of results, returns on equally and value-weighted indices compromising securities listed on the NYSE are incorporated into the model to test the pricing influence of the market indices and to gauge how the set of macroeconomic factors fares in comparison to market indices. Although Chen et al. (1986) note that the indices are the most statistically significant factors in unreported time series regressions, the equally and value-weighted market indices are not priced over the entire sample period and during any of the sub-periods. The macroeconomic factors however retain significance in the APT model suggesting that factors aside from market returns (extra-market factors) are priced in stock returns and therefore, are important in the return generating process (Chen et al., 1986).

Chen et al. (1986) acknowledge that the set of factors employed in the study is not exhaustive and that the identification of other potential factors should not be abandoned. Based upon the preceding findings, the authors state that stock returns are responsive to systematic news and

priced according to their exposure to factors describing macroeconomic conditions. Similarly to Chan et al. (1985), little consideration is given to the time series relationships between returns and macroeconomic factors, and the validity of the underlying return generating process. However, explicit recognition is given to the form and composition of the return generating process. Furthermore, the results of the macroeconomic APT model suggest that macroeconomic factors are also important in the time series context. This, together with a more detailed exposition of a theory dealing with the identification of factors, points towards the APT’s role as a framework for identifying and employing pre-specified systematic risk factors to explain the return generating process.

Hamao (1988) seeks to confirm the robustness of Chen et al.’s (1986) results by performing a parallel analysis on the Japanese market. The macroeconomic factors identified by Chen et al. (1986) are interpreted as proxies for underlying risk factors that drive stock returns. It is acknowledged that the advantage of using pre-specified macroeconomic factors lies in that economic meaning can be ascribed to these factors. The specification of the return generating process and the cross-sectional macroeconomic APT model is identical to that of Chen et al.

(1986) in that the same factors are incorporated into the base model (equation (3.1)).

Similarly to Chen et al. (1986), Hamao (1988) directly acknowledges the multifactor return generating process underlying the macroeconomic APT model although, its role is again limited to that of a time series regression run to estimate inputs for the cross-sectional APT model. The growth in oil prices is also considered in addition to two factors hypothesized to be relevant in the Japanese context; namely, unexpected changes in the foreign exchange rate and changes in the terms of trade.³⁵ The inclusion and consideration of these factors represents an early acknowledgement that there may be other relevant risk factors aside from those suggested by Chen et al. (1986) and that these factors may be specific to a given market. Moreover, this also suggests that a given set of factors should not be considered as

“fixed” and is in line with Chen et al.’s (1986) argument that there are other influential systematic risk factors. Equally and value-weighted market indices are constructed using returns on the Tokyo Stock Exchange (section I) (TSE) Index.

To gain preliminary insight into the time series relationships between the macroeconomic factors and the return aggregates, the correlation between returns on the market indices and

35 Hamao (1988: 52) refers to the constructed exchange rate factor as an “innovation variable for the exchange rate change.” This reflects the APT framework’s emphasis on the use of innovations.

the macroeconomic factors is investigated. To obtain factor loadings, size sorted portfolios are formed and time series regressions of returns on these portfolios on the five Chen et al.

(1986) factors are conducted. Estimated factor loadings are used as independent factors in cross-sectional regressions over the same period that is used to estimate factor loadings in time series regressions (January 1975 - December 1984). Results are similar to those of Chen et al. (1986); over the entire sample period, changes in industrial production, changes in unanticipated inflation, the default spread and the term structure explain expected returns. In contrast to Chen et al. (1986) and in addition to these four factors, changes in expected inflation are also priced (Hamao, 1988: Table 5, Part 1). Changes in the terms of trade are not priced and the reason cited for this is the presence of serial correlation in the time series related to this factor (Hamao, 1988: Table 5, Part 3). A second set of tests is conducted by using factor loadings estimated over the first part of the sample (January 1975-December 1979) to explain expected returns in the second part of the sample (January 1980-December 1984). Hamao (1988) finds that factors with consistent explanatory power for expected returns are changes in expected inflation, changes in the default spread and to a (much) lesser extent changes in the term structure. These factors are also notably correlated with returns on the value and equally-weighted TSE indices over time. The foreign exchange rate, terms of trade and the oil price have no impact upon expected returns and the value and equally-weighted market indices are not associated with statistically significant risk premia in the same APT model specification. This implies that market indices are not associated with missing factors and confirms the cross-sectional explanatory power of extra-market factors (Hamao, 1988). The estimation of market betas together with factor loadings requires a specification of the return generating process which combines market factors and extra-market factors representative of systematic risk. This yields a multifactor model of the return generating process.

In a final test, Hamao (1988) estimates the market beta using the value-weighted market

In a final test, Hamao (1988) estimates the market beta using the value-weighted market