Multivariate kointegrationsanalyser: En analyse af risikopræmien på det danske aktiemarked

Abstract

This thesis presents an attempt to resolve the problems emerging from the assumptions concerning the risk premium on the stock markets. The main concern is the calculation of the historical risk premium, which until now has been based on the assumption that the risk premium can be assumed constant, if the sample period is long enough. Since the risk premium for a specific stock market has different size depending on the period, the risk premium might not be constant after all. This thesis presents calculations of a timevariant risk premium and discusses the relevance for investors. The thesis firstly reviews the original risk premium theory from 1985, presenting the definition of the risk premium, the calculation methods and the main assumptions. In the continuation of this, the next part of the thesis presents the appropriate series to represent both the Danish stock market and a Danish riskfree asset, with a prior disscusion of the theoretical relevance of the alternatives. The thesis proceeds to review the cointegration theory. The variation of the VAR-representation of multiple series is presented with the main focus on the effects from cointegration between the series. Especially the split into the long run parameters a, b and the short run parameters i G are relevant, because it shows the different information within the series. Afterwards, both the univarate and the multivariate cointegration theory are described, with the center of attention on the consequences following choices concerning the parameters indicated by testresults. The empirical part of the thesis shows how the theoretical arguments are put to work on the Danish stock market. Extensive attention is payed to the specification of the unrestricted VAR-model to ensure that the assumption of multivariate normality in the residuals is obtained. The final restricted model consists of one cointegration that describes the long run dynamic and respectively an AR(2)- process for the risk free asset and an AR(3)-process for the stock market to describe the short run dynamic. It is shown that the timevariante risk premium can be calculated from a statistical method and a financial method using the estimated parameters, but both methods are in some areas inconsistent with the known financial forces and the statistical definitions concerning the series. The risk premium is calculated under the assumption of concistency, so that the result can be used as benchmark. Both timevariate calculation methods and the concistency method show that an investor can expect an annual risk premium of about 5% on a long investment. But the assumption of concistency during the periode is shown to be unacceptable, since the spread of the annual timevariant riskpremium is -28% to 38%. The timing of a shorter investment is therfor crucial for the size of the risk premium.