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

Document Type : Original Article

Authors
Shapuor Mohammadi 1
Ahmad Nabizade 2
Reza Raei 3
Hassan Ghalibaf Asl 4
1 Associate Prof., Faculty of Management, University of Tehran, Tehran, Iran
2 Assistant Prof. Faculty of Management, Kharazmi University, Tehran, Iran (Corresponding Author)
3 Prof. Faculty of Management, University of Tehran, Tehran, Iran
4 Associate Prof. Faculty of Management, Alzahra University, Tehran, Iran
Abstract
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.
Keywords
High co-moments
Wavelet analysis
fractional pricing
Tehran Stock Exchange
*    اسلامی بیدگلی، غلامرضا و عبده تبریزی، حسین و محمدی، شاپور و شمس، شهاب الدین. (1388). بررسی زمان مقیاس مدل قیمتگذاری دارایی سرمایه ای از طریق تبدیل موجک. بررسیهای حسابداری و حسابرسی, 35-52.

*       محمدی، شاپور و  چیت سازان، هستی.(1390). بررسی حافظه بلند مدت بورس اوراق بهادار تهران. تحقیقات اقتصادی. شماره 97- 202-221

*       Capobiance, E. (2003). Empirical volatility analysis: Feature detection and signal extraction with function dictionaries. Physica, 495–518.
*       Cochrane, J. (2005). asset pricing. New jersey: Princeton University.
*       Daubechies, I. (1992). Ten lectures on wavelets. CBMS-NSF Regional Conference Series on. Philadelphia, PA: Vol. 61, SIAM.
*       fama, E & french, k. (1992). The Cross-Section of Expected Stock Returns. THE JOURNAL OF FINANCE, XlVII, No 2, 427-465.
*       Fama, E. and French, F. (1995). Size and Book-to-Market Factors in Earnings and Returns. Journal of Finance, 131–55.
*       Fama, E. and French, K. (1993). Common Risk Factors in the Returns on Stocks and Bonds. Journal of Financial Economics, 3–56.
*       Fama, E. and French, K. (1995). Size and Book-to-Market Factors in Earnings and Returns. Journal of Finance, 131–55.
*       Fama, E. and French, K. (1996). Multifactor Explanations of Asset Pricing Anomalies. Journal of Finance, 55–84.
*       Gencay, R & Selcuk, T & Whitcher, B. (2003). Systematic risk and timescales. quantitive finance, 108-116.
*       harrison, M. and Kreps, D. (1979). martingales and arbitrage in multiperiod security markets. journal of economic theory, 381-408.
*       Harvey, C. and Sediqque. (2000). Conditional skewness in asset pricing tests. Journal of, 55, 1263–1295.
*       Kim, S. and In, F. (2006). The relationship between Fama-French three risk factors, industry portfolio returns, and industrial production. Retrieved from SSRN: http://ssrn.com/.
*       Kostakis, A., Muhammad, K. and Siganos, A. (journal banking and finance). Higher co-moments and asset pricing on London Stock Exchange. 2012, 913-922.
*       Lee, J. and Y. Hong. (2001). Testing for serial correlation of unknown form using wavelet methods. Econometric Theory, 386–423.
*       Raei, R and Mohammadi, Shapour. (2008). Fractional return and fractional CAPM. Applied Financial Economics Letters, 269-275.
*       Smith, D. (2007). Conditional skewness and asset pricing. journal of empricial finance, 91-119.
*       Trimech, A., Kortas, H., Benammou, S. and Benammoum, S. (2009). Multiscale Fama-French model:application to the French market. The Journal of Risk Finance, 179-192.
*       Tsay, R. (2010). Analysis of Financial Time Series. Chicago: A JOHN WILEY & SONS, INC.