Andrei Semenov

Testing the random walk hypothesis through robust estimation of correlation

This paper uses Monte Carlo simulations to examine the properties of the conventional Pearson and some of the most well-known robust to outliers estimators of correlation in the presence of general heteroskedasticity. We show that the tests of a random walk based on the Pearson autocorrelation coefficient, including the Lo and MacKinlay [1988. Stock market prices do not follow random walks: evidence from a simple specification test. Rev. Financial Studies 1, 41-66] robust form of the variance-ratio test, can be unreliable in the presence of some forms of conditional heteroskedasticity. As an alternative to the Pearson autocorrelation coefficient, we propose the median coefficient of autocorrelation. Our simulation results show that, in contrast to the Pearson autocorrelation coefficient, the median coefficient of autocorrelation is robust to conditional heteroskedasticity. When applied to exchange rate returns, the variance-ratio test based on the median autocorrelation coefficient provides stronger evidence against the random walk hypothesis compared with the Lo and MacKinlay [1988. Stock market prices do not follow random walks: evidence from a simple specification test. Rev. Financial Studies 1, 41-66] robust variance-ratio test.

The measure of relative risk aversion in the consumption CAPM with power utility

The study shows that in the consumption CAPM with power utility the Arrow–Pratt measure of relative risk aversion differs from the utility curvature parameter when the lottery an individual faces is not actuarially neutral. This implies that the measure of relative risk aversion in the CCAPM with power utility may be different for different individuals and may change over time even when the agents are assumed to have homogeneous preferences which are presented by the power utility function with the time-invariant curvature parameter. Another implication is that the elasticity of intertemporal substitution deviates from the reciprocal of the relative risk aversion coefficient unless the lottery is actuarially neutral. The study also shows the importance of the result obtained for assessing the empirical performance of the CCAPM with power utility.

Historical simulation approach to the estimation of stochastic discount factor models

We propose an approach to the estimation of the parameters of stochastic discount factor (SDF) models which is based on the idea that the next period joint distribution of the variables in a SDF and asset returns can be well approximated by their joint historical distribution. The estimates of the SDF parameters may therefore be found as the values of the parameters at which the mean of the historical distribution of the product of the SDF with an asset return equals one. Each time period, the estimates are updated using the most recent periods of data and hence can change over time. This method can be viewed as an alternative to the approaches that specify a particular functional form relating the SDF parameters to proxies for the state of the world.