Determinants of Cross Sectional Stock Returns Variation

Part 1 – Macroeconomic Factors

By Rodolfo Q. Aquino*

Abstract

This is the first part of a two-part study on the factors that influence cross variability in

stock returns, with particular attention to the role of macroeconomic fluctuations and

idiosyncratic risks. The study covered the listed firms represented in the Phisix for the period

1988-2000 and 1994-2000.

The first part of the study focuses on the role of macroeconomic fluctuations as risk

factors. It uses a multifactor asset pricing framework that is based on the inherent trade-off

between risk and return that has been a basic principle of investment theory since at least

Markowitz. Using factor analysis, seven macroeconomic factors are identified as potential

sources of significant risks to individual firms. Regression results indicate that fluctuations in

all of these macroeconomic factors have significant influence on individual stock returns.

An exact formulation of the multifactor asset pricing model, however, fails to price the

macroeconomic risk factors. Two possible explanations are offered for the poor results. The

first is that lack of market efficiency may result in excess profits that can be gained by

arbitrage, violating the major assumption of the exact form of the multifactor model. The

second is the presence of large idiosyncratic risks that are not fully diversified away by

investors. These do not necessarily invalidate the model but they can lead to large pricing

errors such that tests have little power to reject the null hypothesis that factor prices are zero.

Furthermore, incomplete arbitrage and lack of diversification also result in significant

idiosyncratic risks in investor portfolios . Thus, systematic risks due to macroeconomic

factors, while significant, may not by themselves be able to fully explain observed variation in

stock returns. The role of idiosyncratic risks, relative to systematic risks, is to be discussed in

the second part of the study.

* Professor of Accounting and Finance, College of Business Administration, University of the

Philippines.

1

1. Introduction

This is the first part of a two-part article, the main purpose of which is to determine the factors that influence cross sectional variation in stock returns, with particular attention to the role of macroeconomic fluctuations and idiosyncratic risks. The paper uses a multifactor asset pricing framework that is based on the inherent trade-off between risk and return that has been a basic principle of investment theory since at least Markowitz (1952). In the context of asset pricing, risk is defined to be the volatility of stock returns measured by the standard deviation or variance. Systematic risk represents that portion of volatility induced by unanticipated macroeconomic fluctuations and cannot be diversified away. Idiosyncratic risk is the difference between total volatility or risk and systematic risk. Based on standard investment theory, given enough assets in an investor's portfolio, idiosyncratic risks can be diversified away and can be ignored for pricing purposes. Thus, only systematic risk should matter in asset pricing.

However, the results of efficiency studies of the local stock market, for example Aquino (2002), indicate that the local bourse is at best only weak-form efficient. This suggest that excess profits can be made by trading on information indicating that arbitrage possibilities exist and some investors are prevented from holding their optimal portfolios. Anecdotal evidence also suggests the lack of diversification and the short-term orientation in individual and institutional investor portfolios. These suboptimal conditions imply that idiosyncratic risk could also be priced to compensate rational investors for their inability to hold their optimal portfolios (Malkiel and Xu, 2000).

With these considerations, the specific objectives of this study are:

o To test the standard multifactor asset pricing model based on the no-arbitrage condition to confirm the conjecture that idiosyncratic risk also matters in determining asset prices.

o To decompose total risk into its systematic and idiosyncratic components and determine their relative contributions to asset prices/stock returns.

o To determine the firm factors that affect the degree of the stock's exposure to systematic risk and the level of idiosyncratic risks.

The first objective is addressed in the first part of this paper. The second part will address the last two objectives.

There is nothing in the theoretical literature that determines how much market inefficiency and imperfect arbitrage conditions the standard multifactor model can tolerate before it breaks down. This is strictly an empirical issue. The first objective is important in the sense that if the model holds under testing, then only those macroeconomic factors that determine systematic risk should be priced by the market. Otherwise, idiosyncratic risk could also be priced by the market. Under the second objective, it is important for investors and analysts to understand the risk factors that generate returns and their underlying characteristics for purposes of portfolio formation and stock selection. To the extent that the stock market is considered important to the economy, it is also important for policy-makers to gain some insights as to the factors that affect stock returns and the role of idiosyncratic risk in asset pricing.

This part of the paper is organized as follows. The next section (section 2) discusses multifactor asset pricing models, the role of idiosyncratic risks and the associated theoretical and empirical issues. Section 3 discusses the data and methodology used in the paper. In Section 4, the impact of macroeconomic fluctuations on stock returns is studied. The hypothesis that the market prices the macroeconomic sources of systematic risk is also tested. Section 5 summarizes and concludes the first part of the paper.

2

2. Multifactor Models: Theoretical and Empirical Issues

Both the Arbitrage Pricing Theory (APT) introduced by Ross (1976) and the Intertemporal Capital Asset Pricing Model (ICAPM) introduced by Merton (1973) give a multifactor asset pricing model that, unlike the basic capital asset pricing model (CAPM) or the consumption-based CAPM, allows for factors other than market returns to explain cross sectional variation in individual asset returns. The main difference between APT and ICAPM is that the factors in APT originally are traded portfolios and the factors in ICAPM are state variables1. In current empirical practice, however, this distinction is often ignored. For an economy with N assets, the unconditional form of the model assumes that the asset return generating process can be expressed in matrix notation as (see Campbell, Lo and MacKinlay, 1997)

(1) BfaR exc

(2) 0][E

(3) ]'[E

where Rexc = R - Rf is the (N x 1) vector of asset excess returns over the risk-free rate, a is the (N x 1) intercept vector, B is an (N x K) beta matrix, f is a (K x 1) vector of common factor realizations, and is the (N x 1) vector of disturbances. It is assumed that the common factors account for the common variation in returns such that the disturbance term for large well-diversified portfolios disappears. Thus, the disturbance terms must be sufficiently uncorrelated across assets ( is not necessarily diagonal).

Given this structure, Ross (1976) shows that the absence of arbitrage implies that the following relation can approximate the expected returns for the N assets

(4) B]R[E exc ,

where E[Rexc] is the (N x 1) vector of expected asset excess returns and is the (K x 1) vector of factor risk premia. The risk premium of an individual factor is the compensation or additional price demanded by an investor for an extra unit of that risk factor associated with the asset. The beta of the asset for that factor represents the asset’s sensitivity to that factor. Thus, the expected return on an asset is equal to the return to a risk-free asset (or zero-beta asset) plus the sum of the individual factor premia weighted by the asset betas as shown in (4). In exact APT models, this relationship becomes an equality.

The difference between the left-hand-side and the right-hand-side in equation (4) for

finite N is the vector of pricing errors v = B]R[E exc . Ingersoll (Chapter 7, 1987) showed that even in the presence of idiosyncratic risks, the APT would hold and the pricing errors tend to zero as N goes to infinity. However, Ingersoll also showed that for a finite number of assets the pricing errors would be larger as idiosyncratic risks were larger.

Like the basic single-factor CAPM, the multifactor model has been subjected to an entire literature of testing. Huberman (1987), Campbell, Lo and MacKinlay (1997) and Cochrane (2001) cover various approaches to estimating and testing APT and multi-factor models as well as reviews of the econometric evidence in the U. S. market. Estimating and

testing multifactor models are generally based on the exact version, that is, B]R[E exc . It is extremely difficult to discuss the issues concerning the estimation and testing of multifactor models in limited space but the following points cover the essentials:

o There are two general modeling approaches. The first, based on the APT, assumes that the vector of factors f in equation (1) is unobservable (at least initially). These are identified

1 These refer to variables that describe the investment opportunity set such as macroeconomic

variables.

3

using multivariate statistical methods such as maximum likelihood or principal components factor analysis. The number of factors is also determined by the procedure used. The identities of the factors are subjectively determined by their factor loadings and given meanings usually in terms of the characteristics of the mimicking portfolios of stocks with similar statistical properties as the factors2. The second approach, in line with the ICAPM, predetermines the number and identities of the factors either based on theory or prior empirical evidence. Factors are usually macroeconomic variables or firm characteristics (e.g., size, book-to-market ratios, etc.). The approach in this paper is based on the second in the sense that macroeconomic variables are used as factors. However, factor analysis under the first approach is used to identify the factors.

o There are two general approaches in estimating the factor loading matrix B and the vector of risk premia . The first is the so-called two-pass procedure (Fama and MacBeth, 1973) where B is estimated row by row using ordinary least squares (OLS) in equation (1) using time series data and is estimated cross sectionally in equation (4). The second approach is to simultaneously estimate B and as a system of simultaneous equations. The latter approach is used in this essay.

o The testing procedures generally follow the estimation procedure used. In general, the procedures involve testing whether the intercept vector in a regression using equation (4) is zero or, if the gross returns are on the left-hand-side, whether the intercepts are uniformly equal to the risk-free interest rate. Then, the ’s are tested, jointly or individually, for significance. If they are significant, the factors are deemed priced by the market. Finally, additional factors are added, usually the individual stock’s own return volatility, to determine if the factors already included account for all observed variation in expected returns.

The results of testing the multifactor models in the U. S. have been inconclusive (Huberman, 1987 and Goyal and Santa-Clara, 2001) although the performance of multifactor models has been better than the CAPM. A typical conclusion by reviewers of empirical results is that of Haugen (1997) who states that “empirical testing of the APT is at an early stage of development, and there is no conclusive evidence either supporting or contradicting the model.” In the Philippines, mention must be made of Mangaran’s 1993 study where he tested the APT for the periods 1972-1981 and 1982-1991. His risk factors are four unobserved portfolios found significant in each period extracted using maximum likelihood factor analysis. The overall results are mixed with only a few of the extracted risk factors found significant or priced.

3 Data and Methodology

3.1 Sources of Data

Monthly data on stock prices and cash and stock dividends for 1988-2000 are from the Philippine Stock Exchange Let Pt denote end of month prices, Dt the cash dividends per beginning share, and SDVt the stock dividends as proportion of existing shareholdings, monthly simple returns for stock i are computed as follows:

1t

1ttttit P

PD)SDV1(PR

.

If cash dividends are declared after the payment of stock dividends (which did not apply to the data), the appropriate adjustments have to be made.

Philippine macroeconomic data are from NEDA, the Philippine Institute for Development Studies website and the Bangko Sentral ng Pilipinas Statistical Bulletins. U. S.

2 Please see the Appendix for a brief overview of factor analysis including the interpretation of factors.

Essentially, the factors are linear combinations of the original variables which in this case are returns. Thus, the factors can be interpreted as portfolios of stocks with given returns.

4

economic data are from the Federal Reserve Bank of St. Louis website.

3.2 Estimation and Testing Methodology

In estimating the systematic and idiosyncratic components of total risk, it is assumed that a fixed number of macroeconomic variables, with and without overall market risk, are the sources of systematic risks. Furthermore, market risk is proxied by the excess return on the market portfolio represented by the firms comprising the Philippine Stock Exchange index or the Phisix. The macroeconomic variables chosen as risk factors are identified by factor analysis and regression methods from a comprehensive list of candidate macroeconomic variables prepared based on availability of published statistics and the results of previous empirical investigations. The selection process is discussed in detail in the appropriate sections.

Given the macroeconomic risk factors, the factor sensitivity or factor loading matrix B in equation (1) is estimated using OLS. There is an important issue that must be settled at this point. The exact formulation of the multifactor model must be tested for applicability to the local stock market. If it is found that the model can adequately explain cross sectional variation in expected excess returns, then there is no need to go further. Instead of the two-pass procedure which although consistent is subject to the errors-in-variables problem, the approach of Ferson and Harvey (1994) is used where the factor prices in pricing equation (4) are estimated together with the betas in equation (1). Then the factor prices are tested for significance using a likelihood ratio test. The details of the testing procedure are discussed in the next section.

4. Systematic Macroeconomic Risks

This section has the following specific objectives:

o to identify the systematic risks attributable to firm exposure to macroeconomic fluctuations.

o to determine if these risk factors provide an exhaustive explanation of observed cross sectional variation in stock returns.

First, the macroeconomic variables that are likely sources of systematic risk are identified using factor analysis. A brief overview of factor analysis is provided in the Appendix. Then, a multifactor model using the identified macroeconomic variables is formulated and subjected to statistical testing. The significance of the betas, which can be interpreted as a measure of the risk exposure of individual stocks to specific macroeconomic factors, is tested. Then, under the second objective, the model in its exact interpretation is tested.

4.1 Macroeconomic Variables as Sources of Systematic Risks

4.1.1 Candidate Variables

A comprehensive list of candidate macroeconomic state variables is prepared here based on the results of previous investigations and availability of Philippine data. Table 1 lists down the macroeconomic variables used in selected papers. All of these studies covered the U. S. stock market except that of Ferson and Harvey (1994) which covered eighteen countries (16 OECD countries plus Singapore/Malaysia and Hong Kong). The list of candidate variables is later shortened as they are subjected to statistical analysis.

One of the earliest studies relating macroeconomic forces to stock market returns is by Chen, Roll and Ross (1986). They used a two-pass procedure originated by Fama and MacBeth (1973) to test the influence of macroeconomic variables on U. S. stock market returns from 1958-1984. The variables were selected based on past empirical studies by the authors and statistical analysis. The inclusion of consumption changes is to test the validity of the basic Consumption CAPM and the inclusion of oil prices is to test the popular notion that unanticipated movements in oil prices is a major source of risk in the financial markets.

5

In a previous study (Aquino, 2002), the significance of the exchange rate, real exchange rate, aggregate consumption, aggregate export, real money supply, real GDP, real domestic interest rate measured by the 90-day treasury bill rate, and real foreign interest rate measured by the LIBOR minus inflation rate as cointegrating variables with stock returns was noted. It is particularly problematic that aggregate consumption, GDP and exports are only available as quarterly series. However, these variables are highly correlated with combinations of the variables representing real money balances, nominal exchange rate, real exchange rate, and an index of industrial production.

Table 1 – Macroeconomic Variables Used in Selected Papers

Reference Macroeconomic Variables Used Chen, Roll and Ross, 1986 growth rate of an index of industrial production

change in a measure of expected inflation change in unexpected inflation default risk premium computed as the spread between the return on

high grade corporate bonds and long-term government bond shape of the term structure of interest rates measured by the spread

between the returns on long-term government bonds and that on a one-month treasury bill.

change in consumption change in oil prices

Burmeister and McElroy, 1988

default risk premium computed as the spread between the returns on corporate bonds and government bonds

time premium represented by the spread between the return on long-term government bonds and that on one-month U. S. treasury bills

unexpected inflation change in expected sales market return represented by the Standard and Poor composite index

Cutler, Poterba and Summers, 1989

unexpected changes in log dividends to a market portfolio proxy log industrial production log real money supply (M1) long-term corporate bond interest rate three-month U. S. Treasury bill rate consumer price index stock volatility

Ferson and Harvey, 1994 a global equity market index log first difference of the trade-weighted U.S. dollar exchange rate of

the currencies of ten industrialized countries a measure of unexpected inflation change in a measure of expected inflation change in the spread between the 90-day Eurodollar deposit rate and

the 90-day U.S. treasury bill rate real short term interest rate monthly change in the U.S. dollar price per barrel of oil industrial production growth rate

On the basis of the above and the available monthly macroeconomic data series, and after testing for stationarity, the following variables are selected for further analysis:

ibt - the interbank call loan rate

6

ut - a measure of unexpected inflation

spt – U. S. S&P 500 stock market index

rmt – monthly change in real money balances (M2).

ot – monthly change in the index of the value of industrial production

ftrs - spread between the 90-day LIBOR and the 91-day treasury bill

et – change in the end of month nominal exchange rate

rert – change in the end of month real exchange rate

dtr - monthly change in the 91-day treasury bill

dtrs - spread between the 364-day treasury bill and the 91-day treasury bill

opt – monthly change in the U.S. dollar price per barrel of crude oil

et - monthly change in a measure of expected inflation

o12t – change in the annual growth rate of the value of industrial production

The U. S. S&P 500 index is included for this first round because of the popular notion that Philippine stock returns are sensitive to movements in U. S. macroeconomic variables and the U. S. stock market. The difference between the 364-day treasury bill rate and the 91-day treasury bill rate is also included as the closest measure available for a term premium.

Expected inflation is obtained from a vector autoregression (VAR) of nine macroeconomic variables. The nine macroeconomic variables are actual inflation rate, index of industrial production, interbank call rate, exchange rate, real exchange rate, real money balances (M2), 364-day treasury bill rate, 91-day treasury bill rate, and 90-day LIBOR. Based on the Akaike Information Criterion and the Schwarz Criterion, only one lag is used. Unexpected inflation is obtained as the residual. Table 2 shows the correlation matrix of the macroeconomic variables selected. Except for the correlation of the monthly growth in the index of industrial production and its annual change, the correlation of the spread between LIBOR and the 91-day treasury bill rate with the U. S. S&P 500 index and the interbank call loan rate, and the negative correlation of monthly change in nominal exchange rate with that of the real exchange rate, the correlation coefficients are rather low. This makes the correlation matrix closer to orthogonality and tends to increase the precision of parameter estimates. Thus, it appears that multicollinearity should not pose any serious problem in estimation and, except for the variables just mentioned no one variable can be considered as close substitute for another.

4.1.2 Extraction of Factors

In this section, factor analysis3 is used to determine which of the macroeconomic variables selected have the most influence on the risk exposure of individual stocks.

The analysis considers an asset returns generating process embodied by the system described in equations (1) to (3) where the factors are unobserved factors that can only be extracted through factor analysis. The original test of the APT by Roll and Ross (1980) in the U. S. and that by Mangaran (1993) in the Philippines used this method. They then assigned economic or industry interpretations to the extracted factors. In this study, in view of the stated objectives, the factors extracted are further related to the candidate macroeconomic variable listed in the previous section.

3 Using SPSS

7

Factor analysis itself involves two stages. The first stage involves estimating the beta or factor sensitivity matrix or factor loading matrix B and the disturbance covariance matrix . Given K unobserved factors, where K is to be determined from the data, the covariance matrix of asset returns can be expressed as the sum of the variation due to the common factors and the residual variation, as follows:

(5) 'BB K ,

where K = E[ff’] and is a diagonal matrix. With unknown factors, B is identified only up to an orthogonal transformation and all transformations BG are equivalent for any (K x K) orthogonal (i.e., GG’ = I, the identity matrix) transformation. Thus, set K = I such that B is now unique. With this, equation (5) is restated as

(6) = BB’ + .

To apply these concepts, sample estimates of the covariance matrix of stock returns are computed. Two data sets are used. The first consists of the time series of returns on stocks from the Phisix which have had trading history way back to 1988. This turns out to consist only of seven stocks. The second set consists of data from stock with continuous trading history from 1994-2000. This consists of 18 stocks. The correlation matrices of the two sets of stock returns are shown in Tables 3 and 4. The acronyms in these tables (as well as in other subsequent tables) are the Philippine Stock Exchange codes for the listed stocks (see Table 2 in Aquino, 2002).

Table 2 – Correlation Matrix of Macroeconomic Variables

ibt ut spt rmt ot f

trs et rert dtr d

trs opt et o12t

ibt 1.000 -0.069 -0.193 0.042 -0.006 -0.419 0.023 -0.109 0.358 0.022 0.029 0.094 0.036

ut

-0.069 1.000 0.005 -0.378 0.027 0.041 0.001 0.156 -0.043 -0.005 0.102 0.133 -0.031

spt -0.193 0.005 1.000 0.144 0.006 0.437 0.083 -0.119 -0.062 -0.195 0.066 0.016 0.053

rmt 0.042 -0.378 0.144 1.000 -0.104 0.129 0.026 -0.063 0.032 0.011 -0.214 -0.066 0.108

ot -0.006 0.027 0.006 -0.104 1.000 0.072 -0.151 0.008 -0.019 -0.012 -0.032 -0.081 0.708

ftrs

-0.419 0.041 0.437 0.129 0.072 1.000 -0.025 0.038 -0.122 -0.251 0.019 -0.030 0.100

et 0.023 0.001 0.083 0.026 -0.151 -0.025 1.000 -0.606 0.146 0.039 0.057 -0.014 -0.091

rert -0.109 0.156 -0.119 -0.063 0.008 0.038 -0.606 1.000 -0.276 -0.041 -0.063 0.089 -0.036

dtr

0.358 -0.043 -0.062 0.032 -0.019 -0.122 0.146 -0.276 1.000 -0.115 0.124 0.147 -0.010

dtrs

0.022 -0.005 -0.195 0.011 -0.012 -0.251 0.039 -0.041 -0.115 1.000 0.036 -0.147 -0.062

opt -0.032 -0.121 0.042 0.068 -0.058 0.117 0.021 -0.227 0.164 -0.071 1.000 0.014 -0.028

et

0.094 0.133 0.016 -0.066 -0.081 -0.030 -0.014 0.089 0.147 -0.147 -0.027 1.000 0.021

o12t 0.036 -0.031 0.053 0.108 0.708 0.100 -0.091 -0.036 -0.010 -0.062 -0.079 0.021 1.000

8

The individual correlations for the 1988-2000 data set are all statistically significant, almost all at the 99% confidence level. For the 1994-2000 data set, all correlation coefficients are statistically significant mostly at the 95% and 99% confidence levels except for the correlation coefficient of the return on the B shares (unrestricted ownership) of the lone mining company to the returns on the B shares of the power company and the shares of a state-owned commercial bank. Thus, there seems to be a definite variance-covariance structure in the data that can be exploited in factor analysis.

Given the sample covariance matrix (or the equivalent sample correlation matrix), there are a number of methods to extract the factor sensitivity matrix and factor scores. The two most commonly used are the maximum likelihood and principal components methods. Asymptotically, the two methods mentioned are equivalent but choosing between the two in finite samples is still very much subjective. Since the objective at this point is to shortlist the candidate macroeconomic variables, both methods are employed.

For the 1988-2000 data set, both the maximum likelihood and principal component procedures identified two factors. To aid in identifying the factors, an orthogonal transformation of the factor loading or sensitivity measures (called factor rotation) using the Varimax method is performed4. The rotated factors/components for both factor analysis methods are shown in Table 5. The conclusions from both methods are the same. Factor 1 is heavy on all stocks (bold entries) except the mining company stock so that this factor can appropriately be termed the commercial-industrial factor. Factor 2, on the other hand, is heavy on the two share issues of the mining company so that it can be labeled as the mining factor.

For the 1994-2000 data set, the two factor analysis methods identified four factors. The rotated factors/components are shown in Table 6. The interpretation of the results is almost identical for both methods. Factor 1 is heavy (bold entries) on majority of the stocks except for those heavy on the other factors. This may be labeled as the catchall term commercial-industrial factor. Factor 2 is heavy on the stocks of the most dominant utility and manufacturing companies, which are among the longest-listed stocks in the bourse. This factor can be called the blue-chip factor. Factor 3 under the maximum likelihood method and factor 4 under the principal component method show identical results. They are heavy on the stocks of one of the oldest mining companies in the Philippines. Thus, this factor can be regarded as the mining factor. Factor 4 extracted under the maximum likelihood method is heavy on the stocks of the power company but so is factor 2. Thus, this factor is considered to have already been subsumed under factor 2. Factor 3 under the principal component methods is heavy on the banking stocks and the container terminal stock. Thus, since factor 1 also carries the container terminal stock, factor 3 can be labeled as the financial factor.

Other studies stopped at interpreting and labeling the extracted factors. However, the objective of this investigation is to study the levels of and changes in macroeconomic variables as risk factors. The following section proceeds with the shortlisting of the macro variables for further study.

4.1.3 Selection of Factors

This section deals with the selection of macroeconomic factors for the multifactor asset pricing model. Recall that the factors discussed in the previous section are unobserved or abstract factors extracted through statistical analysis. The factor scores or realizations of these factors are computed from the factor loadings and actual returns data. The factor scores thus recovered are then regressed against the realizations of the candidate macroeconomic variables. The macroeconomic variables that are highly correlated with the unobserved factors are then selected as the relevant macroeconomic factors to be used in subsequent analysis. Thus, the statistically generated factors are given macroeconomic significance.

4 Please see the Appendix for more details on factor rotation and interpretation.

9

Table 3 – Correlation Matrix of Monthly Stock Returns: 1988 - 2000

AC LC LCB MBT SMC SMCB TEL AC 1.000 0.275 0.286 0.423 0.370 0.391 0.440

LC 0.275 1.000 0.811 0.225 0.179 0.227 0.157 LCB 0.286 0.811 1.000 0.264 0.191 0.204 0.123 MBT 0.423 0.225 0.264 1.000 0.254 0.359 0.227 SMC 0.370 0.179 0.191 0.254 1.000 0.794 0.447 SMCB 0.391 0.227 0.204 0.359 0.794 1.000 0.553 TEL 0.440 0.157 0.123 0.227 0.447 0.553 1.000

Table 4 – Correlation Matrix of Monthly Stock Returns: 1994 - 2000

ABS AC ALI BPC FLI ICT JFC JGS LC LCB MBT MER MERB MPC PNB SMC SMCB TEL

ABS 1.000 0.483 0.550 0.446 0.538 0.542 0.501 0.535 0.149 0.214 0.338 0.406 0.421 0.457 0.348 0.228 0.240 0.221

AC 0.483 1.000 0.818 0.664 0.528 0.545 0.701 0.554 0.250 0.251 0.483 0.477 0.673 0.655 0.491 0.258 0.347 0.304

ALI 0.550 0.818 1.000 0.606 0.691 0.651 0.715 0.678 0.303 0.297 0.500 0.460 0.669 0.680 0.500 0.263 0.405 0.342

BPC 0.446 0.664 0.606 1.000 0.533 0.608 0.528 0.572 0.270 0.191 0.391 0.372 0.515 0.565 0.435 0.267 0.251 0.326

FLI 0.538 0.528 0.691 0.533 1.000 0.715 0.537 0.657 0.236 0.294 0.451 0.256 0.413 0.644 0.399 0.141 0.276 0.300

ICT 0.542 0.545 0.651 0.608 0.715 1.000 0.506 0.676 0.257 0.263 0.579 0.242 0.498 0.522 0.493 0.243 0.391 0.346

JFC 0.501 0.701 0.715 0.528 0.537 0.506 1.000 0.551 0.121 0.147 0.333 0.368 0.548 0.606 0.415 0.191 0.216 0.224

JGS 0.535 0.554 0.678 0.572 0.657 0.676 0.551 1.000 0.230 0.190 0.532 0.336 0.485 0.686 0.418 0.224 0.268 0.317

LC 0.149 0.250 0.303 0.270 0.236 0.257 0.121 0.230 1.000 0.837 0.327 0.168 0.192 0.341 0.135 0.178 0.247 0.136

LCB 0.214 0.251 0.297 0.191 0.294 0.263 0.147 0.190 0.837 1.000 0.332 0.075 0.120 0.353 0.173 0.207 0.226 0.062

MBT 0.338 0.483 0.500 0.391 0.451 0.579 0.333 0.532 0.327 0.332 1.000 0.232 0.440 0.360 0.600 0.159 0.407 0.257

MER 0.406 0.477 0.460 0.372 0.256 0.242 0.368 0.336 0.168 0.075 0.232 1.000 0.814 0.342 0.296 0.461 0.511 0.461

MERB 0.421 0.673 0.669 0.515 0.413 0.498 0.548 0.485 0.192 0.120 0.440 0.814 1.000 0.478 0.488 0.476 0.601 0.528

MPC 0.457 0.655 0.680 0.565 0.644 0.522 0.606 0.686 0.341 0.353 0.360 0.342 0.478 1.000 0.447 0.066 0.171 0.216

PNB 0.348 0.491 0.500 0.435 0.399 0.493 0.415 0.418 0.135 0.173 0.600 0.296 0.488 0.447 1.000 0.167 0.273 0.276

SMC 0.228 0.258 0.263 0.267 0.141 0.243 0.191 0.224 0.178 0.207 0.159 0.461 0.476 0.066 0.167 1.000 0.698 0.359

SMCB 0.240 0.347 0.405 0.251 0.276 0.391 0.216 0.268 0.247 0.226 0.407 0.511 0.601 0.171 0.273 0.698 1.000 0.522

TEL 0.221 0.304 0.342 0.326 0.300 0.346 0.224 0.317 0.136 0.062 0.257 0.461 0.528 0.216 0.276 0.359 0.522 1.000

10

Table 5 – Rotated Factor/Component Sensitivity Matrix: 1988-2000 Set

Factor Component 1 2 1 2 AC 0.412695 0.253769 0.616186 0.315424 LC 0.150912 0.834131 0.112927 0.923809 LCB 0.120862 0.950358 0.106038 0.934536 MBT 0.351348 0.232603 0.470783 0.330098 SMC 0.821191 0.090385 0.833915 0.050729 SMCB 0.950474 0.094467 0.883938 0.088558 TEL 0.576647 0.065085 0.751292 0.025809

Table 6 – Rotated Factor/Component Sensitivity Matrix: 1994-2000 Set

Factor Component 1 2 3 4 1 2 3 4 ABS 0.588884 0.181471 0.100296 0.103008 0.632532 0.170365 0.194108 0.052391 AC 0.719242 0.204233 0.118805 0.406852 0.791384 0.282599 0.166763 0.102425 ALI 0.805887 0.237271 0.145552 0.275416 0.801196 0.265280 0.272664 0.147406 BPC 0.677000 0.191290 0.061910 0.161196 0.677500 0.206049 0.254106 0.093239 FLI 0.793207 0.126788 0.146836 -0.074070 0.666864 0.042031 0.442308 0.145809 ICT 0.793331 0.307451 0.098927 -0.201368 0.546855 0.162793 0.636573 0.113033 JFC 0.703468 0.079247 0.023921 0.333520 0.820484 0.141886 0.081130 -0.021407 JGS 0.786982 0.171644 0.040286 0.019966 0.683236 0.118333 0.436170 0.071358 LC 0.170865 0.134787 0.813689 0.049075 0.150763 0.123027 0.080404 0.923353 LCB 0.176044 0.073166 0.980995 -0.017419 0.147538 0.053836 0.122180 0.936403 MBT 0.540705 0.316637 0.216400 -0.093003 0.252041 0.183719 0.787606 0.214025 MER 0.231592 0.607340 -0.000176 0.578804 0.437344 0.742794 -0.127229 -0.018927 MERB 0.476247 0.644769 -0.002333 0.502055 0.556709 0.707794 0.143874 -0.023453 MPC 0.741761 -0.014331 0.232825 0.274793 0.812261 0.005805 0.158891 0.244696 PNB 0.534291 0.239652 0.064164 0.098012 0.369978 0.186501 0.637746 -0.019267 SMC 0.068941 0.695111 0.147113 0.049061 0.038630 0.793043 0.043382 0.160712 SMCB 0.187659 0.816884 0.136217 -0.001918 0.048609 0.825255 0.299008 0.169005 TEL 0.252238 0.561740 -0.022272 0.083411 0.153623 0.642017 0.270579 -0.046539

11

The results for the 1988-2000 data set are shown in Table 7. Under the maximum likelihood method, there are no statistically significant variables for both factors 1 and 2. Under the principal components method, the monthly change in crude oil prices is significant for factor 1. The monthly change in the nominal exchange rate and the spread between the 364-day and the 91-day treasury bill rates are statistically significant for factor 2. The monthly change in industrial production is also marginally significant.

The results for the 1994-2000 data set are shown in Table 8. Under both methods, factor 1 regression is significant on the monthly change in nominal exchange rate and factor 2 is significant on the spread between the 90-day LIBOR and the 91-day treasury bill rate and monthly change in real money balances. In addition, under the maximum likelihood method, factor 1 is significant on the monthly change in real money balances and nominal exchange rate. However, no variable is significant on the factor 3 and factor 4 regressions. Under the principal components method, factor 3 is significant on the monthly change in nominal exchange rate and the monthly change in expected inflation. There are no significant variables for factor 4.

On the basis of the aforementioned analysis, the following macroeconomic variables are included in the multifactor model:

et – change in the end of month nominal exchange rate

et - monthly change in a measure of expected inflation

ot – monthly change in the index of the value of industrial production

opt – monthly change in the U.S. dollar price per barrel of crude oil

dtrs - spread between the 364-day treasury bill and the 91-day treasury bill

ftrs - spread between the 90-day LIBOR and the 91-day treasury bill

rmt – monthly change in real money balances (M2).

12

Table 7 – Regression of Factors Against Macroeconomic Variables: 1988-2000

Maximum Likelihood Method Factor1 Factor2 Coefficients p-value Coefficients p-value ibt 0.00867 0.68160 0.00867 0.68160 u

t 0.00131 0.92000 0.00131 0.92000

spt -0.00002 0.83060 -0.00002 0.83060 rmt 0.13411 0.21620 0.13411 0.21620 ot -0.00073 0.85440 -0.00073 0.85440 f

trs -0.00348 0.88780 -0.00348 0.88780

et -0.12031 0.20450 -0.12031 0.20450 rert 0.00536 0.92170 0.00536 0.92170 d

tr -0.06587 0.30410 -0.06587 0.30410

dtrs 0.01513 0.87150 0.01513 0.87150

opt -0.07687 0.10950 -0.07687 0.10950 e

t -0.00130 0.97070 -0.00130 0.97070

o12t -0.00012 0.97360 -0.00012 0.97360 Principal Components Method Factor1 Factor2 Coefficients p-value Coefficients p-value ibt 0.01643 0.44740 -0.02793 0.20110 u

t 0.00977 0.46470 -0.00010 0.99390

spt -0.00003 0.67960 -0.00003 0.69470 rmt 0.17537 0.11440 0.00576 0.95880 ot -0.00158 0.69620 0.00658 0.10940 f

trs -0.00774 0.75860 -0.00772 0.76120

et -0.14092 0.14650 -0.16812 0.08620 rert -0.00571 0.91850 -0.02589 0.64550 d

tr -0.09120 0.16480 0.01887 0.77480

dtrs -0.00973 0.91900 -0.17626 0.06920

opt -0.08411 0.08700 -0.03413 0.48900 e

t 0.00231 0.94920 0.01706 0.64080

o12t 0.00108 0.76220 -0.00531 0.14020

13

Table 8 – Regression of Factors Against Macroeconomic Variables: 1994-2000

Maximum Likelihood Method Factor1 Factor2 Factor3 Factor4 Coefficients p-value Coefficients p-value Coefficients p-value Coefficients p-value

ibt -0.01357 0.6879 -0.04796 0.1778 -0.03157 0.4396 -0.03107 0.3751ut 0.02971 0.0592 0.00628 0.6998 -0.00396 0.8331 -0.00430 0.7892

spt 0.00010 0.3280 0.00004 0.6636 -0.00005 0.6837 -0.00011 0.2698rmt 0.19635 0.0882 0.27191 0.0253 -0.05184 0.7065 0.06870 0.5607ot 0.00116 0.7601 0.00162 0.6841 0.00536 0.2449 0.00066 0.8659

ftrs -0.03957 0.3937 -0.13102 0.0084 -0.00379 0.9459 -0.00932 0.8458

et -0.34716 0.0004 -0.05542 0.5713 -0.05368 0.6341 -0.07877 0.4159rert -0.03199 0.6268 -0.06238 0.3665 0.00796 0.9202 -0.10851 0.1140

dtr -0.07125 0.4838 -0.08280 0.5155 0.04791 0.6962 0.08401 0.4252

dtrs 0.00515 0.9662 -0.02806 0.7921 -0.17708 0.2293 -0.03786 0.7631

opt 0.02711 0.6751 0.08056 0.2366 -0.03104 0.6910 -0.06882 0.3055

et 0.04288 0.3253 0.08439 0.0670 -0.03043 0.5624 0.01687 0.7077

o12t -0.00464 0.1706 0.00003 0.9936 -0.00410 0.3154 -0.00244 0.4847Principal Components Method

Factor1 Factor2 Factor3 Factor4 Coefficients p-value Coefficients p-value Coefficients p-value Coefficients p-value

ibt -0.03172 0.3983 -0.06110 0.1169 0.02487 0.4924 -0.04686 0.2487ut 0.02458 0.1571 0.00544 0.7598 0.01838 0.2717 -0.01037 0.5778

spt 0.00004 0.7052 0.00003 0.7785 0.00014 0.1857 -0.00007 0.5758rmt 0.19852 0.1197 0.29675 0.0254 0.02547 0.8348 -0.05408 0.6921ot 0.00209 0.6206 0.00128 0.7686 -0.00247 0.5435 0.00715 0.1193

ftrs -0.02411 0.6389 -0.13394 0.0134 -0.04743 0.3403 -0.01604 0.7724

et -0.32305 0.0026 -0.02024 0.8497 -0.16629 0.0996 -0.09042 0.4198rert -0.07172 0.3273 -0.09674 0.2011 0.06499 0.3577 -0.00694 0.9298

dtr -0.00404 0.9714 -0.00966 0.9337 -0.12976 0.2355 0.04174 0.7316

dtrs -0.03895 0.7725 -0.10805 0.4375 0.00565 0.9653 -0.08534 0.5576

opt -0.02496 0.7280 0.06501 0.3808 0.11479 0.1007 -0.01648 0.8315

et -0.00158 0.9739 0.07650 0.1271 0.10398 0.0281 -0.02537 0.6263

o12t -0.00603 0.1095 0.00048 0.9014 0.00083 0.8173 -0.00500 0.2176

14

4.2 Macroeconomic Variables as Risk Factors

Macroeconomic variables as sources of systematic risks can potentially affect stock returns in two ways. First, individual stock returns can be affected by macroeconomic fluctuations, e.g., an increase in interest rates may lead to lower stock prices and hence reduced returns. Secondly, mere exposure of a stock to a systematic risk induced by potential macroeconomic fluctuations may require an increase (premium) or decrease (decrease) in the stock’s expected returns. The premium or discount is the price of the risk factor, which is constant for all stocks, multiplied by the beta of the stock for that risk factor. The effects of macroeconomic fluctuations will be examined first. Then, the pricing of the risk factors will be examined.

4.2.1 Effects of Macroeconomic Fluctuations

To evaluate the effects of macroeconomic fluctuations on stock returns, OLS regression is run on equation (1) which is restated below in terms of demeaned

macroeconomic factors fff~

:

(7) f~

BaR exc

Table 9 shows the results. The top entries in each row are the estimated coefficients and the bottom entries are the p-values. The bold entries signify that the coefficients are significant at least at the 90% confidence level. The last column shows the coefficients of determination R2

which indicate the proportion of the stock return variation accounted for by macroeconomic fluctuations. To put this into perspective, Goyal and Santa-Clara (2001) found that for the U. S. from 1926-1999, systematic risk, with market returns as one of the factors, accounted for 15-20% of total stock return variation. Other results are summarized below:

All of the macro variables are statistically significant for at least one stock.

Except for the stocks of the mining company, at least one beta corresponding to a macroeconomic variable is statistically significant.

The coefficient of the monthly change in the nominal exchange rate et is significant for 12 of the 18 stocks and the signs of the coefficients are all negative, implying that exchange rate depreciation has an adverse impact on stock returns.

The coefficient of the monthly change in anticipated inflation is significant in the two banking stocks and the utility company stocks. In all these cases, the signs are positive, implying that anticipated inflation has a favorable effect on stock returns. Noting that real returns are already adjusted for actual inflation, this result is probably because anticipated inflation, unlike unanticipated inflation, can be factored into future pricing and operating decisions.

The coefficients of the spread between the 90-day LIBOR and the 91-day treasury bill are significant in five of the stocks covered. In all cases, the signs are negative. This implies that an increase in the difference between foreign and domestic interest rates has a negative effect on the returns on these stocks, suggesting that higher returns abroad may draw away funds from local investments.

Changes in real money balances for the most part have a positive effect on stock returns but the coefficients are only significant for the stocks of the Philippine largest manufacturing firm and the power company.

The coefficients for the monthly change in industrial production and the monthly change in the price of crude oil are significant only in the returns to one banking stock.

15

Table 9 – Regression of Stock Returns Against Macroeconomic Risk factors: 1994-2000

Stock Intercept et et ot opt rmt d

trs ftrs R2

ABS 0.013167 -0.02283 -0.00273 0.00010 0.01209 0.01047 -0.01674 0.00039 0.13835 0.2799 0.0162 0.6109 0.7760 0.1332 0.4318 0.2666 0.9294

AC 0.019223 -0.05859 0.01061 -0.00077 -0.00654 0.03472 0.02560 -0.00455 0.16173 0.4135 0.0014 0.3052 0.2594 0.6736 0.1766 0.3786 0.5870

ALI 0.006153 -0.05252 0.00757 -0.00048 -0.00252 0.02399 0.02540 -0.00738 0.16513 0.7547 0.0006 0.3824 0.4025 0.8465 0.2651 0.2969 0.2932

BPC -0.01042 -0.04437 0.00347 -0.00066 0.00128 0.01021 -0.01558 -0.00119 0.20691 0.489 0.0002 0.6012 0.1332 0.8980 0.5350 0.4025 0.8242

FLI 0.075922 -0.19181 0.01405 -0.00114 -0.00344 -0.01845 0.14557 -0.03155 0.23523 0.1616 0.0000 0.5562 0.4694 0.9236 0.7556 0.0300 0.1029

ICT 0.001075 -0.07768 0.01431 -0.00009 0.01070 0.02422 0.01912 -0.01497 0.22939 0.9636 0.0000 0.1686 0.9001 0.4927 0.3476 0.5123 0.0754

JFC 0.007197 -0.02480 -0.00058 -0.00031 -0.00065 0.01939 0.01333 -0.00461 0.07581 0.6512 0.0455 0.9341 0.5036 0.9506 0.2651 0.4981 0.4173

JGS 0.000351 -0.06212 0.01240 -0.00036 0.00101 0.01277 0.01507 -0.00575 0.15924 0.9877 0.0004 0.2146 0.5837 0.9463 0.6063 0.5911 0.4775

LC 0.010648 -0.01958 -0.00382 0.00054 -0.00393 -0.00992 -0.01227 0.00114 0.04741 0.5664 0.1757 0.6403 0.3175 0.7485 0.6252 0.5932 0.8629

LCB 0.017066 -0.02689 -0.00791 0.00043 -0.01599 -0.01518 -0.03621 0.00214 0.07794 0.4418 0.1196 0.4180 0.5012 0.2755 0.5315 0.1870 0.7872

MBT 0.00838 -0.04325 0.01798 -0.00017 0.00656 -0.00083 0.00713 -0.01183 0.25318 0.5781 0.0002 0.0068 0.6935 0.5097 0.9601 0.7020 0.0278

MER -0.01125 -0.00853 0.00265 -0.00019 0.00257 0.01340 -0.00586 -0.00655 0.11237 0.2088 0.2209 0.5017 0.4611 0.6636 0.1706 0.5966 0.0401

MERB -0.00770 -0.02113 0.00845 -0.00008 0.00114 0.02398 -0.00071 -0.00857 0.17183 0.507 0.0194 0.0985 0.814 0.8814 0.0589 0.9604 0.0387

MPC 0.017103 -0.12668 0.00136 -0.00058 -0.01799 -0.02402 0.05861 -0.00475 0.26267 0.5782 0.0000 0.9200 0.5177 0.3762 0.4751 0.1235 0.6649

PNB 0.010197 -0.06193 0.02307 -0.00192 0.03050 -0.01518 -0.01623 -0.00541 0.25969 0.6845 0.0016 0.0370 0.0086 0.0660 0.5800 0.6010 0.5455

SMC -0.00093 -0.00374 0.00069 -0.00016 0.00327 0.01965 -0.01196 -0.00589 0.10448 0.9217 0.6113 0.8682 0.5649 0.6008 0.0570 0.3055 0.0803

SMCB 0.001256 -0.01493 0.00741 0.00008 0.00667 0.02372 0.01666 -0.00937 0.10999 0.9217 0.1334 0.1882 0.8356 0.4295 0.0895 0.2917 0.0398

TEL -0.00359 0.00577 0.00935 0.00055 0.01041 0.01423 -0.00094 -0.00433 0.09355 0.7396 0.492 0.0492 0.082 0.1442 0.2276 0.9436 0.2599

H0:ik=0 15.6419 91.8248 19.7962 34.0964 19.4634 23.5285 38.7185 28.9746 0.5493 0.0000 0.3444 0.0123 0.3638 0.1711 0.0031 0.0487

H0:ik=jk 16.2737 90.7935 19.7506 33.8392 17.6758 21.7437 35.3412 24.3522 0.5735 0.0000 0.2872 0.0088 0.4096 0.1948 0.0056 0.1102

16

Finally, the coefficient for the spread between the 364-day treasury bill and the 91-day treasury bill is significant only in one service company stock.

The second to the last row of the table shows the Wald test statistics for the hypotheses that the intercepts i= 0 and the betas ik = 0 for all i. The figures underneath the chi-square statistics are the corresponding p-values. It is seen that the hypothesis that ik = 0 is rejected for all macro variables except expected inflation and the monthly changes in crude oil prices and real money balances. The last row shows the Wald test statistics and the corresponding p-values for the hypothesis i = j that ik = jk for all i j. The hypothesis that ik = jk for all i j is accepted for most variables except the change in end-of-month nominal exchange rate, monthly change in industrial production and the spread between the 364-day treasury bill and the 91-day treasury bill. Thus, it can be concluded that macroeconomic variables, in particular the nominal exchange rate, the rate of industrial production, the spread between the longer-term and the short-term treasury bills, and the spread between foreign and domestic interest rates, have significant effects on stock returns.

To see whether there are influences that are not captured by the set of macroeconomic variables, the market excess return is included in equation (7) as a risk factor to proxy for these unobserved influences. The inclusion of market excess return results in a model that is more in line with the ICAPM of Merton (1973). The results are in Table 10. R2 has increased significantly for all stocks. Other results are summarized below:

Each macro variables is statistically significant for at least one stock. Except for the stocks of the mining company and the country’s largest manufacturing company, at least one beta corresponding to a macroeconomic variable other than excess market return is statistically significant.

The coefficient of the excess market return is significant at at least the 90% confidence level in all but one stock. Out of these, the coefficient is significant at at least the 99% confidence level in all but one stock.

The coefficient of the monthly change in the nominal exchange rate et which is significant for ten of the 18 stocks and the signs of the coefficients are mostly negative, implying that exchange rate depreciation has an adverse impact on stock returns.

The coefficient for the spread between foreign and domestic interest rates is significant in four stocks while the coefficients for the spread between the 364-day and 91-day treasury bill rates and the monthly change in a measure of expected inflation are significant in three stocks.

All the other coefficients are significant in only one or two stocks.

The second to the last row of the table shows the Wald test statistics for the hypothesis that the betas ik = 0 for all i. The figures underneath the chi-square statistics are the corresponding p-values. It is seen that, as before, this hypothesis is rejected for all macro variables except expected inflation and the monthly changes in crude oil prices and real money balances. The last row shows the Wald test statistics and the corresponding p-values for the hypothesis that ik = jk for all i j. This is also rejected for all variables except those just mentioned and the spread between foreign and domestic interest rates. Note that in Table 9 where excess market return is excluded from the set of macro variables, the same coefficients are found statistically significant. Thus, the results are quite robust.

17

Table 10 – Regression of Stock Returns Against Macroeconomic Risk Factors

with Market Returns: 1994-2000

Market Stock et e

t ot opt rmt dtrs f

trs Return R2

ABS -0.00899 -0.00715 0.00022 0.01246 -0.00099 -0.01921 0.00284 0.61863 0.35137 0.2970 0.1307 0.4812 0.0746 0.9328 0.1421 0.4539 0.0000

AC -0.01785 -0.00238 -0.00043 -0.00546 0.00100 0.01834 0.00269 1.82079 0.66454 0.1410 0.7202 0.3226 0.5786 0.9519 0.3190 0.6151 0.0000

ALI -0.01758 -0.00357 -0.00019 -0.00159 -0.00494 0.01917 -0.00117 1.56181 0.69618 0.0697 0.5012 0.5915 0.8397 0.7081 0.1922 0.7834 0.0000

BPC -0.02058 -0.00412 -0.00046 0.00191 -0.00949 -0.01982 0.00304 1.06325 0.60315 0.0179 0.3865 0.1404 0.7862 0.4227 0.1326 0.4276 0.0000

FLI -0.14125 -0.00208 -0.00072 -0.00209 -0.06031 0.13655 -0.02257 2.26000 0.35197 0.0005 0.9258 0.6226 0.9495 0.2769 0.0271 0.2083 0.0000

ICT -0.04618 0.00426 0.00018 0.01154 -0.00186 0.01351 -0.00937 1.40781 0.50724 0.0027 0.6135 0.7456 0.3549 0.9295 0.5629 0.1668 0.0000

JFC 0.00011 -0.00853 -0.00010 0.00001 -0.00124 0.00889 -0.00018 1.11354 0.53170 0.9902 0.0925 0.7614 0.9988 0.9217 0.5259 0.9652 0.0000

JGS -0.03003 0.00216 -0.00009 0.00186 -0.01379 0.00935 -0.00004 1.43416 0.49976 0.0354 0.7823 0.8571 0.8719 0.4781 0.6658 0.9945 0.0000

LC -0.01050 -0.00672 0.00062 -0.00369 -0.01743 -0.01389 0.00276 0.40570 0.08972 0.4780 0.4080 0.2444 0.7582 0.3876 0.5365 0.6725 0.0395

LCB -0.01901 -0.01043 0.00050 -0.01578 -0.02170 -0.03762 0.00354 0.35249 0.09502 0.2890 0.2887 0.4350 0.2774 0.3743 0.1668 0.6542 0.1393

MBT -0.03112 0.01411 -0.00007 0.00689 -0.01087 0.00497 -0.00967 0.54235 0.34848 0.0068 0.0251 0.8631 0.4589 0.4869 0.7755 0.0558 0.0004

MER 0.00298 -0.00102 -0.00010 0.00288 0.00388 -0.00791 -0.00451 0.51413 0.39262 0.6216 0.7573 0.6592 0.5563 0.6371 0.3880 0.0901 0.0000

MERB -0.00171 0.00225 0.00008 0.00166 0.00790 -0.00418 -0.00511 0.86807 0.63677 0.7851 0.5122 0.7085 0.7436 0.3552 0.6607 0.0642 0.0000

MPC -0.07904 -0.01384 -0.00018 -0.01672 -0.06345 0.05012 0.00371 2.12921 0.61775 0.0000 0.1625 0.7822 0.2533 0.0100 0.0676 0.6408 0.0000

PNB -0.03135 0.01332 -0.00166 0.03131 -0.04050 -0.02168 0.00002 1.36680 0.48070 0.0675 0.1566 0.0067 0.0243 0.0831 0.4045 0.9975 0.0000

SMC 0.00218 -0.00120 -0.00011 0.00342 0.01476 -0.01302 -0.00484 0.26431 0.17548 0.7680 0.7676 0.6816 0.5676 0.1428 0.2455 0.1370 0.0072

SMCB -0.00407 0.00394 0.00017 0.00696 0.01473 0.01472 -0.00744 0.48542 0.24003 0.6726 0.4554 0.6248 0.3724 0.2616 0.3135 0.0794 0.0002

TEL 0.019082 0.0051 0.0007 0.0108 0.0032 -0.0033 -0.0020 0.5950 0.37180 0.0092 0.2039 0.0121 0.0698 0.7480 0.7653 0.5416 0.0000

H0:ik=0 76.2654 17.4785 33.5589 23.2495 20.1447 38.3423 27.2869 568.718 0.0000 0.4905 0.0143 0.1812 0.3247 0.0035 0.0738 0.0000

H0:ik=jk 75.8684 17.0626 33.3224 17.5187 20.0514 35.9956 24.4543 116.393 0.0000 0.4501 0.0103 0.4198 0.2716 0.0046 0.1076 0.0000

18

Given that 0)f~

(E in equation (7), the non-rejection of the null hypotheses that the

intercepts i= 0 for all i and i = j for all i j in Table 9 implies that the expected excess returns may be uniformly zero for all stocks. This result is not supportive of the hypothesis that the market systematically prices the macro risk factors. The next subsection examines this issue further.

4.2.2 Pricing of Risk Factors

The exact formulation of the multifactor model implies that the systematic risk factors should be priced uniformly by the market and the variation in individual stock returns due to these factors can be explained by difference in their exposure to these factors as measured by the betas. In this subsection, following Ferson and Harvey (1994), the factor prices in pricing equation (4) are estimated together with the betas in equation (1) using a seemingly unrelated

regression or SUR model. Again, let fff~

be the demeaned factors, then the model implies

(8) u)f~

(BR exc

where B is the (N x K) matrix of betas and is the (K x 1) vector of factor prices. If the factors are not priced, then k = 0 for all k. This suggests a likelihood ratio test like that in the Macro Rational Expectations model of Mishkin (1983). The restricted model (restricting k = 0) is

(9) uf~

BR exc .

The likelihood ratio test statistic is

U

RLnT)k(LR

which is distributed as a 2 with k degrees of freedom. The values UR and are the

determinants of the residual covariance matrices of the restricted and unrestricted equations, respectively, T is the number of usable observations, and k is the number of restrictions.

The regressions for both the restricted and unrestricted models are run. The null hypothesis that k = 0 for all k is not rejected. The likelihood statistic with 84 usable observations is 10.34 and there are seven restrictions yielding a p-value of 0.170 for the chi-square test. Thus, the evidence narrowly rejects the hypothesis that the macroeconomic risk factors are jointly priced. Individually, however, two of the macro factors are priced. Table 11 shows the results for individual stocks. The top figures are the coefficients and the bottom figures are the p-values. Most of the betas that are significant in the restricted regression remain significant. The last column in Table 11 shows the R2 for individual stocks which are not significantly different from the R2 in Table 9. This provides additional, more intuitive evidence for the observation that the factors are not priced.

The last line in Table 11 shows the estimated prices or risk premia for the risk factors. Individually, most of the risk factors are not statistically significant except for and the spread

between the 364-day treasury bill and the 91-day treasury bill ( dtrs ) and the spread between

foreign interest rate and domestic rate ( ftrs ). The estimated factor prices for d

trs and ftrs are

44.85% and 265.65% per month per unit of beta exposure, respectively. To put things into

perspective, the beta for dtrs ranges from –0.02686 to 0.0567 indicating a risk premium

(discount) ranging from –1.2% to 2.27% for individual stocks. For ftrs , beta ranges from

19

Table 11 – Pricing of Macroeconomic Risk Factors

Stock et et ot opt rmt d

trs ftrs R2

ABS -0.02324 -0.00260 0.00010 0.01231 0.01089 -0.01589 0.00073 0.13809 0.0132 0.6263 0.7859 0.1248 0.4107 0.2816 0.8601 AC -0.05651 0.00997 -0.00075 -0.00763 0.03261 0.02132 -0.00631 0.16001 0.0017 0.3334 0.2739 0.6212 0.2009 0.4507 0.4238 ALI -0.05043 0.00693 -0.00046 -0.00361 0.02186 0.02111 -0.00915 0.16269 0.0008 0.4215 0.4257 0.7797 0.3045 0.3675 0.1565 BPC -0.04125 0.00251 -0.00062 -0.00036 0.00704 -0.02199 -0.00383 0.19804 0.0003 0.7050 0.1566 0.9712 0.6668 0.2216 0.4400 FLI -0.19539 0.01515 -0.00118 -0.00156 -0.01482 0.15290 -0.02853 0.23437 0.0000 0.5233 0.4532 0.9649 0.8005 0.0181 0.1105 ICT -0.07572 0.01371 -0.00006 0.00967 0.02223 0.01510 -0.01663 0.22801 0.0000 0.1854 0.9255 0.5328 0.3848 0.5945 0.0360 JFC -0.02447 -0.00068 -0.00031 -0.00083 0.01905 0.01265 -0.00489 0.07570 0.0423 0.9219 0.5077 0.9368 0.2666 0.5000 0.3398 JGS -0.05892 0.01141 -0.00033 -0.00067 0.00952 0.00850 -0.00845 0.15488 0.0006 0.2507 0.6218 0.9643 0.6976 0.7517 0.2505 LC -0.02135 -0.00328 0.00052 -0.00301 -0.00812 -0.00863 0.00264 0.04515 0.1273 0.6860 0.3349 0.8043 0.6845 0.6910 0.6522 LCB -0.03145 -0.00651 0.00038 -0.01360 -0.01055 -0.02686 0.00599 0.06782 0.0624 0.5037 0.5542 0.3509 0.6606 0.3063 0.4023 MBT -0.04495 0.01850 -0.00019 0.00746 0.00091 0.01063 -0.01039 0.25070 0.0001 0.0052 0.6615 0.4521 0.9559 0.5593 0.0421 MER -0.00836 0.00260 -0.00019 0.00248 0.01323 -0.00620 -0.00670 0.11228 0.218 0.5069 0.4645 0.6715 0.1703 0.5575 0.0210 MERB -0.02058 0.00828 -0.00007 0.00086 0.02342 -0.00184 -0.00903 0.17135 0.0202 0.1034 0.828 0.9104 0.0622 0.8944 0.019 MPC -0.12281 0.00017 -0.00054 -0.02002 -0.02795 0.05067 -0.00802 0.25964 0.0000 0.9898 0.5497 0.3218 0.4014 0.1674 0.4288 PNB -0.06075 0.02271 -0.00191 0.02988 -0.01638 -0.01865 -0.00641 0.25926 0.0017 0.0393 0.0090 0.0704 0.5477 0.5388 0.4530 SMC -0.00511 0.00111 -0.00017 0.00399 0.02105 -0.00914 -0.00473 0.09953 0.4776 0.7882 0.5277 0.5204 0.0396 0.4164 0.1272 SMCB -0.01489 0.00739 0.00008 0.00665 0.02368 0.01658 -0.00941 0.10999 0.1255 0.1860 0.8343 0.4269 0.0862 0.2750 0.0248 TEL 0.00596 0.00929 0.00055 0.01031 0.01403 -0.00133 -0.00449 0.09348 0.4676 0.0491 0.0802 0.1445 0.2283 0.9173 0.2036 Factor -0.37074 0.2982 -1.1058 0.4513 0.3501 0.4485 2.6565 Prices 0.2984 0.7636 0.9154 0.4553 0.3993 0.0744 0.0512

20

-0.02853 to 0.00599 indicating a risk premium (discount) of –7.58% to 1.59% for individual stocks. For the remaining variables, positive factor prices are indicated for monthly changes in expected inflation, crude oil prices and real money balances. The opposite goes for changes in the monthly change in nominal exchange rate and the index of industrial production. Of course, the signs of the factor prices must be related to the signs of the betas. To evaluate the reasonableness of the factor prices, the pricing errors indicated in equation (4) are computed

assuming that the factors representing dtrs and f

trs are priced. The results are quite large, in some cases the pricing errors are even larger that the computed expected returns. As in the previous analysis, the addition of market excess returns as one of the factors raises significant the R2 for individual stocks (last column).

Table 12 shows the results when market excess return is included as a risk factor to proxy for unobserved macroeconomic influences. Again, the joint hypothesis that k = 0 for all k is not rejected. The likelihood statistic with 84 usable observations is 10.78 and now there are eight restrictions yielding a p-value of 0.215 for the chi-square test. Thus, the evidence cannot support a hypothesis that the macroeconomic risk factors, even with the market return as a catchall factor, are jointly priced. Note that the risk premia for two macro

factors that are found statistically significant in the preceding discussion, dtrs and f

trs , are no longer so when market return is included in the factor set. The p-values of these factors

increased somewhat to 0.2545 for dtrs and 0.1684 for f

trs , indicating that aggregate market return also captures the effect of these factors on individual stock returns.

Thus, the overall finding is that the macroeconomic factors affect the level and movement of stock returns. The regression results in the previous section are supportive of this finding. However, the mere exposure of individual stocks to the macro risk factors (in varying degrees as reflected by the betas) does not appear to merit additional rewards. One of the possible reasons for this is that macroeconomic risks appear to be diversifiable. If so, they are not sources of systematic risks but rather idiosyncratic risks to individual companies. An indication of this is that the betas of all macro factors, except that of excess market return, in either Table 11 or Table 12 have both positive and negative signs across all stocks. This means that a zero-beta portfolio of stocks can theoretically be formed such that all risks emanating from the macroeconomic variables can be arbitraged away even without short selling or purchase of derivative securities5. Note that this is not so with the market return factor. As earlier noted, all the betas associated with this factor are positive. In the absence of derivative securities and limitations of short sale transactions, this risk factor cannot be diversified away. Thus, the explanation for the poor performance of the multifactor model that the macro risk factors, with the market return factor, do not represent diversifiable idiosyncratic risks is not plausible.

5 The question of whether risks associated with all macro factors can all be arbitraged away with the

proper choice of nonnegative portfolio weights is a more complicated matter. A basic result in linear algebra is that the homogeneous system of equations Bx = 0 where B is n x k with rank k n has a nontrivial solution. A sufficient condition for the systems Bx = 0, where x 0, to have a solution is for the nonhomogeneous system Bx = b, x 0, to have a bounded feasible solution (see Gass, 1969, Chapter 9, Problem 19). This can be shown using the duality theory of linear programming. For the system to be bounded, it is necessary that for the ith entry such that xi 0 not all the entries in the ith column of B have the same sign.

21

Table 12 – Pricing of Macroeconomic Risk Factors and Excess Market Returns

Market Stock et e

t ot opt rmt dtrs f

trs Return R2

ABS -0.00907 -0.00712 0.00022 0.012564 -0.00071 -0.01897 0.002978 0.624898 0.36852 0.2695 0.1222 0.4730 0.0661 0.9484 0.1349 0.4125 0.0000 AC -0.01698 -0.00267 -0.00043 -0.00568 -0.00024 0.01767 0.00250 1.83742 0.67752 0.1292 0.6756 0.3166 0.5497 0.9872 0.3134 0.6147 0.0000 ALI -0.01743 -0.00362 -0.00018 -0.00159 -0.00507 0.01914 -0.00115 1.56809 0.70031 0.0496 0.4801 0.5913 0.8357 0.6581 0.1733 0.7707 0.0000 BPC -0.01825 -0.00491 -0.00046 0.00094 -0.01354 -0.02236 0.00204 1.07458 0.60260 0.0246 0.2913 0.1428 0.8917 0.2004 0.0800 0.5726 0.0000 FLI -0.14529 -0.00071 -0.00071 -0.00006 -0.05254 0.14168 -0.02034 2.27233 0.37395 0.0001 0.9738 0.6174 0.9985 0.2882 0.0165 0.2243 0.0000 ICT -0.04269 0.00309 0.00018 0.01017 -0.00776 0.00987 -0.01077 1.43153 0.50643 0.0031 0.7078 0.7389 0.4082 0.6806 0.6631 0.0933 0.0000 JFC -0.00217 -0.00776 -0.00010 0.00099 0.00280 0.01144 0.00084 1.10498 0.53568 0.7997 0.1148 0.7558 0.8930 0.8019 0.3969 0.8250 0.0000 JGS -0.02767 0.00137 -0.00009 0.00095 -0.01777 0.00691 -0.00097 1.45088 0.49969 0.0341 0.8563 0.8624 0.9334 0.2889 0.7393 0.8671 0.0000 LC -0.01409 -0.00551 0.00061 -0.00219 -0.01117 -0.00996 0.00432 0.38963 0.09092 0.3010 0.4840 0.2468 0.8521 0.5249 0.6446 0.4770 0.0447 LCB -0.02582 -0.00814 0.00049 -0.01295 -0.00985 -0.03020 0.00647 0.31985 0.09349 0.1230 0.3963 0.4420 0.3652 0.6514 0.2517 0.3848 0.1749 MBT -0.03225 0.01449 -0.00007 0.00739 -0.00883 0.00627 -0.00914 0.54016 0.35242 0.0035 0.0193 0.8615 0.4212 0.5477 0.7131 0.0613 0.0004 MER 0.00175 -0.00061 -0.00010 0.00333 0.00590 -0.00669 -0.00406 0.50292 0.40216 0.7545 0.8486 0.6490 0.4856 0.4179 0.4470 0.1024 0.0000 MERB -0.00207 0.00237 0.00008 0.00179 0.00847 -0.00383 -0.00499 0.86420 0.63793 0.7218 0.4778 0.7106 0.7201 0.2608 0.6757 0.0534 0.0000 MPC -0.07953 -0.01366 -0.00018 -0.01640 -0.06235 0.05091 0.00409 2.13733 0.623981 0.0000 0.1577 0.7821 0.2538 0.0062 0.0560 0.5907 0.0000 PNB -0.03253 0.01371 -0.00166 0.03186 -0.03832 -0.02027 0.00061 1.36656 0.484033 0.0508 0.1395 0.0065 0.0207 0.0862 0.4284 0.9335 0.0000 SMC 0.00117 -0.00086 -0.00011 0.00383 0.01648 -0.01195 -0.00443 0.25840 0.174459 0.8664 0.8285 0.6783 0.5171 0.0718 0.2734 0.1528 0.0080 SMCB -0.00310 0.00362 0.00017 0.00659 0.01311 0.01373 -0.00782 0.49257 0.240264 0.7299 0.4824 0.6216 0.3909 0.2629 0.3315 0.0504 0.0001 TEL 0.01747 0.00564 0.00066 0.01141 0.00596 -0.00161 -0.00131 0.58493 0.369911 0.0123 0.1530 0.0125 0.0521 0.5172 0.8820 0.6718 0.0000 Factor -1.03867 0.712504 1.16428 0.763773 1.167762 0.452769 3.591454 Prices 0.2544 0.6449 0.9411 0.3698 0.2824 0.2357 0.1487

22

The other possible explanations are already hinted at in previous discussions. The first is that market efficiencies may result in excess profits that can be gained by arbitrage, violating the major assumption of the exact formulation of the multifactor model. The second is the presence of large idiosyncratic risks that are not diversified away by investors. This does not necessarily invalidate the model but leads to large pricing errors such that tests have little power to reject the null hypothesis that factor prices are zero.

4.7 Concluding Remarks

This two-part study set out to examine the various factors that may explain cross sectional variation in individual stock returns in the context of a multifactor asset pricing model. In this first part of the study, seven macroeconomic factors are identified as potential sources of risks to individual firms. Regression results indicate that fluctuations in all of these macroeconomic factors have significant influence on individual stock returns. However, an exact formulation of a multifactor asset pricing model fails to price these risk factors. There are two possible explanations for the poor results. The first is that lack of market efficiency may result in excess profits that can be gained by arbitrage, violating the major assumption of the exact formulation of the multifactor model. The second is the presence of large idiosyncratic risks that are not diversified away by investors. These do not necessarily invalidate the model but they can lead to large pricing errors such that tests have little power to reject the null hypothesis that factor prices are zero. Furthermore, incomplete arbitrage and lack of diversification on the part of investors also result in significant idiosyncratic risks in investor portfolios. Thus, systematic risks due to macroeconomic factors, while significant, may not by themselves be able to fully explain observed variation in stock returns.

The role of idiosyncratic risks is discussed further in the second part of this study.

23

Appendix

Factor Analysis

Introduction

This appendix will cover a brief introduction to factor analysis in the context of the multi-factor returns model.6 Note that the factor in factor analysis is an unobserved construct. In the study, the interest in on real factors, i.e., the macroeconomic variables that influence stock returns. Thus, factor analysis is used in this study for data reduction and identification of observable factors (the macroeconomic variables) to:

extract the unobserved latent factors generating the observed excess returns of stock.

measure the realization of these factors during the sample period by computing the factors score.

interpret these factors and provide them with a meaningful label in the context of the multi-factor model.

use the factor scores to identify real macroeconomic variables for subsequent statistical analysis.

Recall that in this model, for an economy with N assets, the unconditional form of the model assumes that the asset return generating process can be expressed in matrix notation as:

(1) BfaR exc

(2) 0][E

(3) ]'[E

where Rexc = R - Rf is the (N x 1) vector of asset excess returns over the risk-free rate, a is the (N x 1) intercept vector, B is an (N x K) beta matrix, f is a (K x 1) vector of common factor realizations, and is the (N x 1) vector of disturbances. It is assumed that the factors account for the common variation in returns such that the disturbance term for large well-diversified portfolios disappears. Thus, the disturbance terms must be sufficiently uncorrelated across assets.

To simplify notation and subsequent discussion, let R = Rexc – a, i.e., the demeaned excess return. Then, equation (1) becomes

(4) R = Bf + .

In the factor analysis stage, f is the set of latent variables to be extracted. In subsequent stage, f will be the set of macroeconomic variables that will used to estimate systematic risk.

Some Key Terms

Factor - a linear combination of the original variables in factor analysis. Factors represent the underlying dimensions or constructs that summarize or account for the original set of variables.

Factor analysis - class of multivariate statistical techniques whose primary purpose is data reduction, summarization and interpretation. It addresses the problem of analyzing the interrelationships among a large number of variables (e.g., returns of a number of company stocks) and then explaining these variables in terms of their common underlying dimensions or factors.

Factor loadings – correlation between the original variables and the factors. In the context of a

6 References are Campbell, Lo and MacKinlay (1997), Johnson and Wichern (1992) and Hair,

Anderson, Tatham, and Black (1998).

24

multi-factor asset pricing model, this also called the set of betas as measures of the systematic risk exposure of a particular financial asset. Squared factor loadings indicate what percentage of the variance in an original variable is explained by a factor.

Factor loading matrix – the matrix of factor loadings (B above). In asset pricing context, also referred to the beta or factor sensitivity matrix.

Factor rotation - the process of changing the reference axes of the factors to achieve a simpler and easier to interpret factor solution. The most popular factor rotation method is Varimax (see below).

Factor score - factor analysis reduces the original set of variables (e.g. Individual stock returns) to a smaller set of variables or factors. These latent or unobservable factors can be given a measure or score computed as a linear combination of the original variables. The relative weights of the variables are a product of factor analysis.

Maximum likelihood – in factor analysis, this method assumes the multivariate normal distribution and estimates the factor loadings from the sample covariance matrix that maximizes the likelihood function. In statistical analysis for descriptive purposes, the multivariate normality assumption is not critical. In the limit, the factors estimated using this approach is the same as the principal components obtained using the principal components approach (see below).

Multi-factor model - in the context of asset pricing, the return on an asset is expressed as the sum of influences by various observable economic, industry or company factors or by latent factors. Also called multi-index model. When there is only one factor, it is referred to as a single-factor or single-index model.

Principal components – is factor analysis technique to reduce the number of variables studied without losing too much information in the covariance matrix. The first principal component is the normalized linear combination of the original variables (e.g., asset returns) with minimum variance. The nth principal component is the linear combination of the original variables with maximum variance orthogonal to the first n-1 principal components. In the limit, the principal components estimated using this approach is the same as the factors obtained using the maximum likelihood approach (see above).

Varimax - a factor rotation method that maximizes the sum of the normalized variances of required loadings of the factor matrix. With the rotation, there will tend to be some high loadings (i.e., close to one in absolute value) and some loadings close to zero which arguably facilitates interpretation.

Factor Extraction

The first stage involves estimating the factor loading matrix B and the disturbance covariance matrix . Given K factors, where K is to be determined from the data, the covariance matrix of asset returns can be expressed as the sum of the variation due to the common factors and the residual variation, as follows:

'BB K ,

where k = E[ff’] and is a diagonal matrix. With unknown factors, B is identified only up to an orthogonal transformation and all transformations BG are equivalent for any (K x K) orthogonal (i.e., GG’ = I, the identity matrix) transformation. Thus, set k = I and B is unique. With this, equation (5) is restated as

= BB’ + .

To apply these concepts, sample estimates ̂ of the covariance matrix of stock returns are obtained.

25

There are two main extraction methods used: principal components method and maximum likelihood method. Principal components will be described first.

As mentioned earlier, principal components is a factor analysis technique that aims to reduce the number of variables studied without losing too much information in the covariance matrix. The first principal component is the normalized linear combination of the original variables (e.g., asset returns) with maximum variance. Let the first principal component be

Rx*1 where the (N x 1) vector *

1x is the solution to the optimization problem

.1xx

tosubject

xˆ x

1'1

1'1Max

1x

The solution *1x is the eigenvector associated with the largest eigenvalue 1 of ̂ since

11'1111

'11

'1 xxxxxˆx

The second principal component is the linear combination of the original variables with maximum variance orthogonal to the first principal component. It solves the above

problem with 2x in place of 1x with the additional restriction 0xx 2*'1 . The succeeding

principal components are obtained in similar fashion. The factor loading vector for the kth factor is given by the square root of the kth largest eigenvalue multiplied by the associated eigenvector. The number of principal components (factors) is usually determined by a stopping rule such as the eigenvalues must be at least one, meaning that the additional principal component must at least contribute one unit of the average normalized variance to the factor structure.

In the limit, the principal components estimated using this approach is the same as the factors obtained using the maximum likelihood approach. In finite samples, however, it has the advantage over the other method in that for the same number of factors, it extracts those with the higher cumulative variance.

Under the maximum likelihood method, the common factors f and disturbances are assumed to be normally distributed. Then, for each K, the likelihood function L(R, ) is

maximized with the uniqueness condition 1' , a diagonal matrix, imposed. The number of factors K can be predetermined, if a priori knowledge is available, or the rule that the eigenvalues must be at least one can be used as the stopping rule in an iterative procedure. The this study, the eigenvalue rule is used, supplemented by a visual test (i.e., the Scree test - see

either of the last two references in the footnote).

Rotation and Interpretation of Factors

The factors extracted can be interpreted and labeled. However, especially when the number of factor exceed two in number, this can be a very difficult process. As an aid in interpretation, an orthogonal factor rotation is often employed. The new factor loadings obtained from an orthogonal transformation of the original factor loadings have the same ability to reproduce the original covariance structure. An orthogonal transformation can be

visualized as a rigid rotation of the coordinate axes. If B̂ is the initial (K x N) estimated factor loading matrix, then given (N x N) matrix T such that T’T = I (the identity matrix) is the new matrix of “rotated” loadings. The Varimax factor rotation method used in this study is the most popular rotation method. Essentially, it maximizes the sum of the normalized variances of required loadings of the factor matrix. With the rotation, there will tend to be some high loadings (i.e., close to one in absolute value) of the original variable and some

26

loadings close to zero for each factor. This arguably facilitates interpretation. Nevertheless, the interpretation is still very much a subjective process.

Computation of Factor Scores

Recall that each factor is a construct representing a linear combination of the original variables (e.g., returns). The factors are also orthogonal to each other. Given that in the present context the original variables are returns, this has an important financial application. If short sales are allowed (or, if not, the weights of each variable are constrained to be non-negative), with the weights normalized to sum up to one, each factor can be interpreted as a portfolio of stocks. These portfolios are also called tracking or mimicking portfolios, in the sense that their returns can track or mimic the underlying factor realizations or scores.

The factor scores can be computed through various methods. The simplest one is as indicated by the principal components methods discussed above. The eigenvector associated with the factor, normalized so that all its elements sum up to one, can be used as the weights. One popular method, which is the one used in this study, is the regression method. This has the advantage of obtaining factor score estimates that maximizes the variance accounted for by the common factors. Given the estimated factor loading matrix, equation (4) is restated below

fB̂R .

The estimated factor score (K x 1) vector for sample period t is given by

t1

t Rˆ'B̂f̂ .

The computed factor scores thus obtained are used in subsequent statistical analysis. Note that

the ((K x N) matrix 1ˆ'B̂ with each elements in each column normalized such that they sum up to one can be used as the portfolio weights for a tracking or mimicking portfolio.

27

References

Aquino, R. Q. (2002). “Informational Efficiency Characteristics of the Philippine Stock Market,” Unpublished Working Paper.

Campbell, J. Y., M. Lettau, B. G. Malkiel, and Y. Xu. (2001). “Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk,” Journal of Finance 56 1.

Campbell, John Y., Andrew W. Lo and A. Craig MacKinlay (1997). The Econometrics of Financial Markets, New Jersey: Princeton University Press.

Dybvig, P. H. and S. A. Ross (1989), “Arbitrage,” in John Eatwell, Murray Milgate and Peter Newman, eds , New Palgrave Dictionary of Money and Finance, New York: W. W. Norton.

Fama, E. F. and J. MacBeth (1973). “Risk, Return and Equilibrium: Empirical Tests,” Journal of Political Economy 71: 607-636.

Goyal, A. and Santa-Clara, P. (2001). “Idiosyncratic Risks Matter!” NBER Working Paper (November).

Hair, J. F. Jr., R. E. Anderson, R. L. Tatham, and W. C. Black (1998). Multivariate Data Analysis, 5th ed., New Jersey: Prentice-Hall.

Haugen, R. A. (1997). Modern Investment Theory, 4th ed., New Jersey: Prentice-Hall.

Huberman, G. (1989), “Arbitrage Pricing Theory,” in John Eatwell, Murray Milgate and Peter Newman, eds , New Palgrave Dictionary of Money and Finance, New York: W. W. Norton.

Ingersoll, J. E. (1987). Theory of Financial Decision Making, New Jersey: Rowan and Littlefield.

Mangaran, Pablo F. Jr. (1993). The Arbitrage Pricing Theory and Common Stock Returns, unpublished DBA dissertation, College of Business Administration, University of the Philippines, Quezon City, Philippines.

Markowitz, H. M. (1952). “Portfolio Selection,” Journal of Finance 7 1: 77-91.

Merton, Robert C. (1973). “An Intertemporal Capital Asset Pricing Model,” Econometrica 41: 867-887.

Mishkin, F. (1983), A Rational Expectations Approach to Macroeconometrics: Testing Policy Ineffectiveness and Efficient-Markets Models, National Bureau of Economic Research.