On the Empirical Importance of the Conditional Skewness Assumption in Modelling the Relationship between Risk and Return

M. Pipień Department of Econometrics, Cracow University of Economics, Rakowicka 27, 31-510 Kraków, Poland

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Received: 22 11 2007;

We present the results of an application of Bayesian inference in testing the relation between risk and return on the financial instruments. On the basis of the Intertemporal Capital Asset Pricing Model, proposed by Merton we built a general sampling distribution suitable in analysing this relationship. The most important feature of our assumptions is that the skewness of the conditional distribution of returns is used as an alternative source of relation between risk and return. This general specification relates to Skewed Generalized Autoregressive Conditionally Heteroscedastic-in-Mean model. In order to make conditional distribution of financial returns skewed we considered the unified approach based on the inverse probability integral transformation. In particular, we applied hidden truncation mechanism, inverse scale factors, order statistics concept, Beta and Bernstein distribution transformations and also a constructive method. Based on the daily excess returns on the Warsaw Stock Exchange Index we checked the empirical importance of the conditional skewness assumption on the relation between risk and return on the Warsaw Stock Market. We present posterior probabilities of all competing specifications as well as the posterior analysis of the positive sign of the tested relationship.

DOI: 10.12693/APhysPolA.114.517 PACS numbers: 89.65.Gh, 05.10.Gg