Mauri Paavola
LAPPEENRANTA UNIVERSITY OF TECHNOLOGY
School of Business Finance
Helsinki, October 30th, 2007
Porvoonkatu 1 D 133
00510 Helsinki
+358 50 588 0826
ABSTRACT
This study investigates the relationship between different sorts of risk and return on six Finnish value-weighted portfolios from the year 1987 to 2004. Furthermore, we investigate if there is a large equity premium in Finnish markets. Our models are the CAPM, APT and CCAPM. For the CCAPM we concentrate on the parameters of the coefficient of the relative risk-aversion and the marginal rate of intertemporal substitution of consumption, whereas for the CAPM we estimate the market beta and for the APT we will select some macroeconomic factors a priori.
The main contribution of this study is the use of General Method of Moments (GMM). We implement it to all of our models. We conclude that the CAPM is still a robust model, but we find also support for the APT. In contradiction to majority of studies, we are able to get theoretically sound values for the CCAPM’s parameters. The risk-aversion parameters stay below two and the marginal rate of intertemporal substitution of consumption is close to one. The market beta is still the most dominant risk factor, but the CAPM and APT are as good in terms of explanatory power.
Key words:
Stochastic Discount Factor (SDF), Capital Asset Pricing Model (CAPM), Arbitrage Pricing Theory (APT), Consumption-based Capital Asset Pricing Model (CCAPM), Equity premium puzzle, General Method of Moments (GMM)
INTRODUCTION
The economic theory of capital asset pricing relies heavily on the principles of present value calculations and the hypothesis of efficient capital markets. The former tells us that the price of an asset is a function of the expected future yields discounted to the current date. This should apply to all assets, such as stocks, land, houses and durables, since they are alternative investment objects. (Takala & Pere, 1991) In particular, modern financial theory is founded on three central assumptions: markets are highly efficient, investors exploit arbitrage opportunities and investors are rational. (Dimson & Mussavian, 1999).
An important body of research in financial economics has been the behavior of asset returns and especially the forces that determine the prices of risky assets. There are also a number of competing theories of asset pricing. These include the original capital asset pricing models (hereafter CAPM) of Sharpe (1964), Lintner (1965) and Black (1972), the intertemporal models of Merton (1973), Long (1974), Rubinstein (1976) and Cox et al. (1985), the consumption-based asset pricing theory (hereafter CCAPM) of Breeden (1979); Lucas (1978) and the arbitrage pricing theory (hereafter APT) of Ross (1976).
Breeden (1979) and Lucas (1978) took a different approach in defining equilibrium in capital markets. They are able to show, under certain assumptions, that return on assets should be linearly related to the growth rate in aggregate consumption if the parameters of the linear relationship can be assumed to be constant over time (Elton et al., 2007). Breeden (1979) and Lucas (1978) models are so called “representative” agent models of asset returns in which per capita consumption is perfectly correlated with the consumption stream of a typical investor. In this type of models, a security’s risk can be measured using the covariance of its return with per capita consumption (Kocherlakota, 1996).
The CAPM is by far the most famous asset pricing model. It is widely used and examined both in literature and in practice. However, the CAPM is only a description of the reality. By this we mean that the CAPM does not help us understand what the ground factors are and how they affect the risky returns. If we want to go deeper and try to understand what the affecting forces are, how the investors define the returns for the risky assets, we have to start from the basic utility theory and try to find the solution from there.2 The intuitive model to examine is the CCAPM, where the return is given with the covariance of investor’s marginal utility. Moreover, in contrast to the CAPM, intertemporal general-equilibrium models identify clearly the economic forces that influence the risk-free real interest rate and the compensation that investors earn by accepting risk.3 (Carmichael, 1998).
Objectives and methodology
The purpose of this thesis is to find out what the affecting forces behind the stock returns are, and which of these risk factors are significant. We will test the traditional market beta of the CAPM and some other macro-economic risk factors employed in the APT. For the CAPM and APT our focus is on the risk factors (betas), whereas for the CCAPM we will focus on the risk-aversion and discount factor parameters, γ and β. Our purpose is to compare all of these models. We will also try to find reasonable values for the CCAPM’s parameters that have failed numerous times in empirical studies. Our focus will be on the CCAPM, because it is the least known from these asset pricing models. The CAPM and APT serve more as a benchmark models, although we are going to present them in detail. The results of testing the different models are quite inconclusive. CAPM is widely used and its functions are well documented. On the other hand, there is a big group of researchers5 that say that the CCAPM and its consumption beta should be preferable on theoretical grounds, although its empirical testing has failed numerous times.
We will employ Lucas (1978) study for testing the CCAPM with the standard Constant Relative Risk-aversion (hereafter CRRA) power utility function. We will examine a developed stock market of Finland and try to explain the differences in the returns of value-weighted portfolios. The other purpose of this thesis is to examine the equity-premium puzzle emerged from the fact that the consumption tends to be too smooth. Mehra & Prescott (1985) presented the equity-premium puzzle and this rock solid evidence against the CCAPM is still unsolved.
These differences in our value-weighted portfolio returns should be explained only by the different risk factors and the sensitivities of returns to the risk factors according to the theory. In the CAPM the expected equity premium (excess return) is proportional to market beta. The APT relates the expected rate of return on a sequence of primitive securities to their factor sensitivities, suggesting that factor risk is of critical importance in asset pricing. In comparison, the standard CCAPM measures the risk of a security by the covariance of its return with per capita consumption. (Elton et al., 2007)
Most of the empirical tests of these models have been conducted for developed markets, e.g., U.S. and Germany. This study will examine the stock market of Finland. To the best of our knowledge, the Finnish stock market has not been examined this way. There are tests of the CCAPM and of course of the CAPM and APT, but no comparisons of these models in the same data set. We will compare the realized asset returns within these models to see which model provides the best results of explaining the time-series variation of value-weighted stock portfolios.
One of the main contributions of this thesis is the use of the Generalized Method of Moments (hereafter GMM) method. Again, to the best of our knowledge, this method has not been used in this way for the Finnish data, i.e., comparing these asset pricing models in the same data set. We will employ the GMM to all of our empirical tests and make comprehensive conclusions of the asset pricing models’ ability to explain the portfolio returns. The GMM is a general statistical method for obtaining estimates of parameters of statistical models and it is widely used in the finance literature. All the empirical tests are done with Matlab.
Limitations and motivations
This study is performed from the European investor’s point of view so that the currency used in this study is euro and also risk-free rate is quarterly Euribor. In selecting the factors for our different models we will choose them a priori, as in Chen et al. (1986). The data used in this study is gathered from ETLA, Research Institute of the Finnish Economy, and Data- stream. The research period will be from the beginning of the year 1987 to the end of year 2004.
We will test the asset pricing models in their purest form. This means that, e.g., the CCAPM is tested as it was presented in Lucas (1978). Thus, we will not use any other implications of the CCAPM that are, e.g., the habit formation of Constantinides (1990), the “non-expected utility” preferences of Epstein and Zin (1989) or the investment-based asset pricing model of Cochrane (1996), to name a few. However, these studies are important because they had had some success in solving the problems of the CCAPM and the key results are presented in this thesis. We are well aware that doing this thesis in this way, without any further assumptions or modifications of the CCAPM, may lead to a rejection of the CCAPM. This is probably the case, because we know that Finnish stock market has a relatively high equity premium, especially in our research period.9 How- ever, we also know that other models that we presented above have not had success in solving the equity premium puzzle, at least not in different markets, data sets, etc. Thus, right now we do not have an explicit solution to the equity premium puzzle, which we will show in further chapters.
Structure
The thesis is structured as follows. The next chapter introduces the basics of the utility theory and the concept of Stochastic Discount Factors (SDF). The third and fourth chapter presents the different asset pricing models in great detail and also one of the biggest debate issues in earlier studies, the determination of relevant factors, is represented. We will separate the discussion between the CAPM/APT and the CCAPM, because our main focus in on the less known CCAPM. Furthermore, the CAPM and APT are quite alike models, but the CCAPM comes from totally different grounds. In the fifth chapter we will go through some of the basic problems associated with the asset pricing models and go through an extensive amount of previous empirical studies. The sixth chapter describes the data for our purposes. We will especially concentrate on the research methodology, because we have found out that there are a lot of different methods to choose from. Furthermore, the GMM is explained in a difficult way and also quite irrationally in many parts of the literature, although it is a quite simple and effective method. The seventh chapter reports the empirical results and findings. The final chapter is for conclusions and suggestions for further research.
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