Evidence for state and time nonseparable preferences: the case of Finland

Abstract

Preferential modifications to the standard state and time separable power utility are studied for the Finnish equity and bond returns. The reported ambivalence of the high equity premium and low Sharpe ratio makes the Finnish market an important case study. The estimations of the Epstein and Zin (1991) recursive utility and the Campbell and Cochrane (1999) habit formation preferences show that Finnish risk premia are time-varying across samples. Moreover, the results demonstrate that stronger time preferences improve the explanation of asset returns for the modified preferences more so than assuming tighter time preference and higher risk aversion (RA). We conclude that the Campbell–Cochrane-based pricing kernel outperforms the competing models in generating plausible model parameters and suppressing specification errors. The study supports the US evidence relative to the conclusions drawn from the European economies in comparable studies.

Keywords:

• power utility
• iterated GMM
• risk premia
• habit aggregation
• risk factor
• specification errors

JEL Classification:

• G32
• G12
• G15

Notes

¹   The standard CCAPM assumes the von Neumann–Morgenstern utility, that is, separable in time and states.

²  Agents’ smoothing consumption across various states of nature under the CRRA preferences also smooths consumption across periods; that is, they dislike growth. The coefficient of RRA is the reciprocal of the elasticity of inter-temporal substitution (EIS) under the standard CCAPM. The conventional time additive and state separable von Neumann–Morgenstern inter-temporal utility function, under no a priori economic justification, relates investors’ risk preferences with investors’ consumption variations over time, specifically as reciprocals of one another.

³  Other European markets that have market capitalization-to-GDP ratio more than 50% are Belgium, Denmark, France, Greece, Iceland, Ireland, Luxembourg, Montenegro, the Netherlands, Spain and Sweden. If we drop this threshold to 40%, Cyprus, Greece and Norway are also included in the subset of capital markets in-line to the Finnish stock market.

⁴   The sample period starts from 1990 instead of from 1975:01 because of the nonavailability of aggregate dividend data that restricts the estimation of the Campbell and Cochrane (1999) external habit model. Furthermore, the model estimations are also reported for the sample, excluding the recession period – that is, from 1995:01 through 2009:02 – and are referred to as stable or recovery periods in the text.

⁵   The spectral density matrix is the Newey and West (1987) heteroscedasticity and autocorrelation consistent (HAC) estimator. Bartlett kernel is used to downgrade the auto-covariance structure for the positive semi-definiteness of the S. The bandwidth algorithm is set to the Newey–West (1994) nonparametric method based on a truncated weighted sum of the estimated cross-moments, which control the number of auto-covariances in the HAC estimator and are important for consistent finite sample properties of S. The statistically optimal (most efficient) weighting matrix is obtained as the inverse of the covariance matrix of the sample orthogonality conditions – that is, S⁻¹. It provides the smallest possible SEs whereas any suboptimal matrix may produce inconsistent estimates.

⁶   The reported annual yields are converted to quarterly returns using the price difference approach in Vaihekoski (2009).

⁷   The size (Small-minus-Big, SMB) and value (High-minus-Low, HML) return series are constructed from all the available stocks in the Finnish market during the sample years. We divide all the stocks in two groups of small and big firms using end of June median market capitalization break point for subsequent four quarters. Similarly, we make three partitions with respect to yearly BM ratio break points. The generated percentiles include the bottom 30% (L, growth), middle 40% (M) and top 30% (H, value) of the BM stock returns from the quarter beginning from July in the current until the fourth quarter ending in June in the following year. The partitions for size and BM for the whole sample period are rebalanced each year at the end of June. The independent intersection of two size quartiles with growth, middle and value BM percentiles produces six portfolios: SL, SM, SH, BL, BM and BH, respectively. The SMB risk factor is generated from the average of the small stock portfolios (SL, SM and SH) minus the average big stock portfolios (BL, BM and BH) each quarter. The value-growth factor return, HML, is the difference of the average of the two value portfolios (SH, BH) and the average of the two growth portfolios (SL, BL); HML is calculated each quarter.

⁸  Similar observations are also noted for the Finnish consumption growth in Oikarinen and Kahra (2002), Viitanen (2004) and Virk (2012b).

⁹   The construction constraint of the EZ (1991) model SDF factually limits the model comparison between the recursive utility specification and the habit persistence models for using different HJ-weighting matrices. This structural limitation of the EZ (1991) preferences perturbs the constancy of weighting matrix.

¹⁰   In theory, the risk under the consumption-based models has more encompassing implications for assigning pay-offs to the stocks. First, it incorporates the agents’ decision-making preferences across periods. Second, the measure governing investor portfolio decision-making in different states of the world implicitly incorporates additional sources of wealth compared to the wealth from only the equity market.

¹¹   For example, we take the log of the consumption-based model IMRS such that the standard power utility based SDF, that is, is transformed to . The exogenous variables for log linearization are reported in lower case. Moreover, in this context signifies both the substitution effect and investor RA. Similar transformations are also employed for EZ (1991) and CC (1999) model SDFs. The EZ (1991) model IMRS is aggregated across expected utility and nonexpected utility components for with in consideration to the available results in Table 2 for Finnish market. The results for the robustness checks are not reported to conserve space and are available upon request.