Design and explanation of fractional multiresoloution capital asset pricing model with higher co-moments on Tehran stock exchange

The purpose of this study is to provide an appropriate pricing model and also addressing the common deficiencies in other valuation models. To this goal, a sample of 82 companies is selected. (Financial companies, companies with fiscal year different from end of 29th of isfand, companies which their stocks were not traded in past 3 month and those which listed after 1389 are excluded). Then portfolios based on the third and fourth moments are formed by the sampled companies. We used three pricing models including CAPM, Fama- French 3 factor model and Carhart Model for each portfolio. Results show that estimating these models accounting third and fourth moment lead to increase of significance of these models. But the insignificance of the interception of difference between two portfolios showed that third and fourth moment premium are not priced which can be due to assuming homogeneous investment horizon for investors. For this, using wavelet analysis, we analyzed three portfolios with in two horizon levels including level 1 (2 to 4 month) and level 2 (4 to 8 month). Results interestingly showed the improvement in significance and also in R^2.
Using GPH estimator, we showed that there is long term memory in studied time series. In order to making these series stationary, we used recent method by calculating fractional data and again we estimated the models. Results showed that models estimation significantly improved for all three portfolios. But except CAPM for the two first portfolios, in other models the risk premium is not priced. Comparing fractional models with those obtained by wavelet models strongly indicates the superiority of the latter. Comparing all models, we concluded that best model for pricing, based on the third moment, is fama- French 3 factor model in level 2 daubeechies4 and by regarding the fourth moment, CAPM is optimal one for the level 2 symlts8.