Pricing and the return generating process

Beenstock and Chan (1988) state that the main limitation of the factor analytic approaches employed in the APT framework is that factors cannot be interpreted and therefore, it is impossible to determine whether factors derived using factor analysis represent systematic risk or idiosyncratic risk. Instead of focusing upon the cross-sectional implications of the APT model, the authors consider both the APT model and the return generating process by first establishing whether returns are linearly related to innovations in macroeconomics factors over time and then by establishing whether expected returns are linked to the estimated factor loadings. Two approaches to estimating factor loadings are applied, and in doing so, models of the relationship between macroeconomic factors and returns over time are estimated. In the first approach, innovations are generated and used to estimate factor

loadings over the first T observations whereas the remaining ₁ T observations are used to ₂ estimate the APT model. In the second approach, factor loadings are estimated from odd observations whereas the APT model is estimated using even observations. A set of eleven candidate risk factors is considered.⁴⁰ Using UK return data for the October 1977 to December 1983 period, Beenstock and Chan (1988) find that according to the first approach, returns on seventy-six portfolios are described by four factors over time. These are interest rates as measured by treasury bill rates, the broad measure of the money supply, fuel and material costs and retail prices. Under the second approach, results are almost identical in that returns on the portfolios are significantly related to innovations in the same four factors.

However, whereas under the first approach the relationship between the money supply and returns is negative, under the second approach it is positive.

Beenstock and Chan (1988) suggest that these findings imply a four-factor model to describe returns – this in essence representing a four-factor model of the return generating process derived within the APT framework. The number of positive and negative factor loading estimates is noted, and the authors ascribe economic meaning to these results in terms of the expected cash flow model employed by Chen et al. (1986). Factor loadings estimated under the two approaches are then used to estimate the cross-sectional APT model. Treasury bill rates, the money supply, fuel and material costs, and retail prices are priced under the first approach whereas treasury bill rates, the money supply and retail prices are priced under the second approach. The APT model explains over a third of cross-sectional variation in expected stock returns under both approaches. Unlike Chan et al. (1985), Chen et al. (1986) and Hamao (1988) who focus only upon the cross-sectional implications of the APT model, Beenstock and Chan (1988) directly consider the return generating process underlying the APT model and show that multiple factors drive returns. Furthermore, while it has been argued by Bower et al. (1984) and implied by Chen et al. (1986) and Hamao (1988) that the APT framework offers a systematic link between the APT model and the return generating process, none of the macroeconomic APT studies discussed so far have considered both the return generating process and the APT model together. Beenstock and Chan (1988) on the other hand show that factors that explain the time series behaviour of returns are also priced.

40 The UK treasury bill rate, broad money supply, fuel and material cost index, general index of retail prices, general index of wages, industrial stoppages, export and import volume indices, relative export prices, Gross Domestic Product (GDP), and total production in countries belonging to the Organization for Economic Co-operation and Development (OECD).

In doing so, a linkage between the macroeconomic APT model and the return generating process underlying the APT model is demonstrated. Notably, the authors identify a return generating process and APT model specification for UK stocks within the APT framework.

McElroy and Burmeister (1988) re-examine the APT framework as a multifactor non-linear regression with pre-specified factors and across-equation restrictions. Whereas the approach of pre-specifying factors is consistent with Chan et al. (1985), Chen et al. (1986) and Hamao (1988), the authors estimate the return generating process and APT model using NLSUR methods. As this approach yields joint estimates of factor sensitivities and risk premia, it permits insight into both aspects of the APT framework simultaneously. McElroy and Burmeister (1988) specify a five-factor model to describe returns on a sample of individual firms in the CRSP database over the January 1972 to December 1982 period. The factors incorporated into the model are the term structure of interest rates, the default spread, unexpected deflation, real final sales and the residual market factor where the residual market factor is a catch-all proxy representing variation in the return generating process not explained by the macroeconomic factors employed in the model (Burmeister & Wall, 1986).

In selecting these factors, reference is made to the expected cash flow model as discussed in Chan et al. (1985) and Chen et al. (1986). The residual market factor is constructed by regressing returns on the S&P Composite Index on the four remaining factors. This yields initial insight into the structure of the return generating process underlying returns as an aggregate. Returns on the S&P Composite Index are negatively and significantly related to changes in the default spread and final retail sales and positively and significantly related to changes in the term structure and unexpected deflation. Together, these four factors explain almost a quarter of the time series variation in S&P Composite Index returns.

The second set of results reported by McElroy and Burmeister (1988) shows the factor sensitivities of returns on individual stocks to the five factors. These results, in essence, provide insight into the return generating process underlying the returns on individual stocks in the sample. Together, these five factors explain between 30 percent and 50 percent of the variation in returns. The relationship between returns on individual stock and the default spread is found to be mostly significant and predominantly negative whereas the relationship between returns and changes in the term structure is mostly significant and predominantly

positive.⁴¹ The relationship between unexpected deflation and retail sales differs in direction and statistical significance across stocks. McElroy and Burmeister (1988) report that over 60 percent of the estimated factor sensitivities are statistically significant suggesting that macroeconomic factors that are widely used in asset pricing and are assumed to measure systematic risk, also feature in and explain the return generating process. In turn, all risk premia in the corresponding APT model are priced suggesting that the very factors that characterize the return generating process are also those that explain the cross-section of expected returns. In conclusion, the authors state that the proposed set of factors is not unique and suggest that further research should be undertaken into whether there are other factors that explain returns. Similarly to Beenstock and Chan (1988), McElroy and Burmeister’s (1988) results point towards a relationship between the APT model and the underlying return generating process. The role of the APT framework as a valid conceptual framework is demonstrated; it is successfully adapted for the purposes of identifying and modelling the return generating process as well as for asset pricing.