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## Über dieses Buch

In the mid-eighties Mehra and Prescott showed that the risk premium earned by American stocks cannot reasonably be explained by conventional capital market models. Using time additive utility, the observed risk pre­ mium can only be explained by unrealistically high risk aversion parameters. This phenomenon is well known as the equity premium puzzle. Shortly aft­ erwards it was also observed that the risk-free rate is too low relative to the observed risk premium. This essay is the first one to analyze these puzzles in the German capital market. It starts with a thorough discussion of the available theoretical mod­ els and then goes on to perform various empirical studies on the German capital market. After discussing natural properties of the pricing kernel by which future cash flows are translated into securities prices, various multi­ period equilibrium models are investigated for their implied pricing kernels. The starting point is a representative investor who optimizes his invest­ ment and consumption policy over time. One important implication of time additive utility is the identity of relative risk aversion and the inverse in­ tertemporal elasticity of substitution. Since this identity is at odds with reality, the essay goes on to discuss recursive preferences which violate the expected utility principle but allow to separate relative risk aversion and intertemporal elasticity of substitution.

## Inhaltsverzeichnis

### Chapter 1. Introduction

Abstract
Investors are concerned with the choice between risky and risk-free investments. It is consensus among economists that investors demand a reward for bearing the risks of risky investments such as stocks as compared to investments free of risk. The quantification of this tradeoff between risk and expected return is one of the central problems of financial economics and has been the focus of theoretical and empirical research for many decades. But the question of how to measure risk and how to calculate the market reward for bearing a given amount of risk is not fully answered.
Bernd Meyer

### Chapter 2. The Market Pricing Kernel Approach

Abstract
In a frictionless market1 it follows from the Law of One Price2 that a market pricing kernel3 $$\tilde \varphi _{t + 1}$$ exists for each date t such that the ex-dividend price $$P_t^i$$ of any asset i can be calculated from the equation
$$P_t^i = E_t \left\{ {\tilde \varphi _{t + 1} \cdot \left( {\tilde P_{t + 1}^i + \tilde D_{t + 1}^i } \right)} \right\}.$$
(2.1)
Bernd Meyer

### Chapter 3. Implications of Asset Prices for the Market Pricing Kernel

Abstract
A vital interest in financial research is to derive information about the distribution of the market pricing kernel, about the state price density or, equivalently, about the risk-neutral probability distribution and the risk-free rate. As shown in the previous chapter this knowledge would enable the pricing of any asset. The traditional approach to gain insights into the properties of the market pricing kernel is to start by choosing a functional form for the pricing kernel and then test equation (2.1) empirically. Recently, more suggestive approaches attempt to reveal properties of the market pricing kernel without assuming an explicit functional form. These approaches first examine asset returns or asset prices and then analyze which properties the market pricing kernel must exhibit to be consistent with these data. One can distinguish theoretical and empirical approaches. The theoretical approaches make assumptions about the distribution or the stochastic process of asset returns or prices, whereas the empirical approaches use observed data. The first part of this chapter briefly surveys one of the theoretical approaches. Then, two empirical approaches, one employing cross-sectional data and one employing time series data, are compared. The approach that employs time series data to place restrictions on the moments of the unconditional distribution of the market pricing kernel is applied in chapter 7 and is therefore described in greater detail.
Bernd Meyer

### Chapter 4. Parametric Models of the Market Pricing Kernel

Abstract
This chapter is concerned with the derivation of parametric models of the market pricing kernel, i.e. the specification of intertemporal asset pricing models. For this purpose the consumption-based equilibrium asset pricing approach is applied, which relates asset prices to aggregate consumption. Within this approach the market pricing kernel is derived from the optimal intertemporal consumption and investment choice of a representative agent. Alternative approaches attempt to generalize one-period models — in particular the Capital Asset Pricing Model (CAPM) — that usually relate asset prices to aggregate wealth, to the intertemporal context. These attempts suffer from problems that arise because in a multiperiod world aggregate wealth may not deterministically determine aggregate consumption, except for the last period. Although there exist theoretically founded generalizations they are of no practical use because they do not specify the relevant pricing factors. Therefore, the factors in the recently suggested Conditional CAPMs, which can be interpreted as linear multifactor models in the spirit of the theoretically founded generalizations, are more or less arbitrarily chosen. Moreover, in contrast to the consumption-based equilibrium asset pricing approach the conditional asset pricing approach takes the risk-free rate and the risk premia on the market portfolio and on a set of “factors” as exogenously given instead of determining them. This, however, is an important goal of the present analysis. This study therefore applies the consumption-based equilibrium asset pricing approach.
Bernd Meyer

### Chapter 5. The Calibration Approach for Empirically Investigating Parametric Models of the Market Pricing Kernel

Abstract
Section 5.1 introduces the calibration approach and compares it with the more common estimation approach for the empirical investigation of parametric models of the market pricing kernel. Both approaches have strengths and weaknesses as has been discussed in the literature. This discussion is briefly surveyed and the use of the calibration approach for the present analysis is motivated. Section 5.2 illustrates the calibration approach for a simple model economy with i.i.d. production growth, using both the parametric model of the market pricing kernel derived from time-additive expected utility with constant relative risk aversion and that derived from recursive non-expected utility in turns. Section 5.3 reviews studies applying the calibration approach. A summary ends the chapter.
Bernd Meyer

### Chapter 6. Overview and Description of Data

Abstract
This section provides an overview of the empirical analysis. The analysis proceeds in two steps. The first step (chapter 7) is to apply the variance bound approach in order to analyze the information content of different asset return data sets for intertemporal asset pricing and to compare the potential of the parametric models of the market pricing kernel derived in section 4.2 to be consistent with these returns. Variance bounds are calculated from German stock, bond and money market returns in the period 1968 to 19941. The second step is to apply the calibration approach (chapter 8) and to evaluate calibrated models using simulation techniques (chapter 9) in order to analyze whether the parametric models of the market pricing kernel can explain specific properties of the German one-period risk-free rate and the German equity premium observed in the period 1960 to 19942.
Bernd Meyer

### Chapter 7. Analyzing Variance Bounds of the Market Pricing Kernel

Abstract
The empirical analysis of the variance bounds for the market pricing kernel, i.e. of the bounds for the relationship between the first and the second unconditional moment of the market pricing kernel, covers the period 1968 to 1994 and proceeds in two steps. First, in section 7.1 the variance bounds are estimated employing different time series of asset returns. The sensitivity of the bounds with respect to changes in (1) the underlying set of assets, (2) the method of return calculation, (3) the taxation scenario applied, and (4) the length of the time intervals is analyzed. These analyses provide insights into the information content of different asset return data sets for testing parametric models of the market pricing kernel. Second, in section 7.2 different parametric models of the market pricing kernel are evaluated using the estimated variance bounds, i.e. the implications of the estimated variance bounds for the parameters of the parametric models of the market pricing kernel are analyzed. The investigated parametric models are those derived from the consumption-based asset pricing model alternatively assuming time-additive expected utility with constant relative risk aversion, time-additive expected logarithmic utility and recursive non-expected utility. Notice that the purpose of this analysis is to visualize the models’ capability to jointly price different assets and to illustrate how this capability is affected by changes in the models’ parameters but not to formally test the parametric models of the market pricing kernel. For formal tests sampling errors in the variance bounds and the means and standard deviations of the parametrized market pricing kernel must be considered in addition. But, as discussed in section 3.3.3, even then the variance bound approach is an unsatisfactory tool for formally testing parametrized market pricing kernels.
Bernd Meyer

### Chapter 8. Applying the Calibration Approach

Abstract
The application of the variance bound approach in the previous chapter has given a first impression of the capability of the different parametric models of the market pricing kernel to jointly price different assets. Now, the calibration approach described in chapter 5 is applied to quarterly German data for the period 1960 to 1994. The goal is to analyze, whether the parametric models of the market pricing kernel derived from time-additive expected utility and, alternatively, derived from recursive non-expected utility can be calibrated to match the first and second moments of the empirically observed risk-free rate and equity premium. The “benchmark returns” that are to be matched are those calculated for the four taxation scenarios (see table 6.8). Different modifications of the original approach of Mehra and Prescott (1985) discussed in section 5.3 are investigated.
Bernd Meyer

### Chapter 9. Evaluating the Calibrated Equilibrium Models

Abstract
This chapter is concerned with a further assessment of the calibrated equilibrium models. Recall that within this study a calibrated model is a model that exactly implies the empirically observed average one-period risk-free rate and average equity premium. In the previous chapter it has already been shown that calibrated equilibrium models are able to imply the empirically observed correlation between the risk-free rate and the equity premium but that they are not able to generate the empirically observed standard deviations. While the primary focus has been on the unconditional first and second moments of the one-period risk-free rate and the equity premium in the previous chapter, the performance of the calibrated equilibrium models is now measured along other dimensions.
Bernd Meyer

### Chapter 10. Conclusion

Abstract
The purpose of this study was to explain both the average levels and the co-movement of the German risk-free interest rate and the German equity premium over the 35 years from 1960 to 1994. In particular, the study analyzed whether intertemporal equilibrium asset pricing models can explain the empirically observed risk-free rates and equity premia in Germany, maintaining the assumptions of complete and frictionless markets and rational investors. The study contributes to the rapidly growing literature on the Equity Premium Puzzle and the Risk-free Rate Puzzle initiated by Mehra and Prescott (1985).
Bernd Meyer

### Backmatter

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