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The Fractal Portfolio Selection Model with Transaction Costs

Author: WangYuXia
Tutor: ChenShengShuang
School: Wuhan University of Technology
Course: Applied Mathematics
Keywords: Fractal distribution Downside Risk Transaction costs
CLC: F224
Type: Master's thesis
Year: 2005
Downloads: 209
Quote: 1
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Abstract


The securities portfolio management process, including the assessment of the risks and benefits of each asset, portfolio optimization and portfolio performance measure. The risk and return of each asset valuation and portfolio optimization in these three processes has great theoretical significance, the core process of portfolio management study. However, the effectiveness of the market yield securities and risk-assessment methods and different. Therefore, to assess the risks and benefits of each asset, you should make on the effectiveness of the market test. Accurate measure of the capital markets as possible, under the premise of the establishment of efficient market hypothesis, various theoretical models have emerged. From modern portfolio theory of Markowitz, Sharpe, Lintner and Mossin assets balanced pricing theory as well as the Black-Scholes option pricing model and Ross' arbitrage pricing theory, are developed on the basis of the efficient market theory or closely related. However, as early as the efficient market theory is fully formed, it has been found that the yield of the financial capital market does not meet the normal distribution is assumed between the rate of return is not independent of each other, the efficient market theory there are obvious defects. In view of the defects of the EMH, the people began to introduce nonlinear science to study financial issues. Mandelbrot emphasized the Pareto studies based on the stylized facts of financial return series has a \shows a nonlinear stochastic process. So many scholars began to study the returns follow a fractal distribution of portfolio theory. Fractal distribution using the parameter lambda means that the degree of dispersion of the yield, Fama and Samuleson, people have to use this parameter description of the risks and tectonic portfolio. In the study assumes that all securities have the same spikes and thick tail characteristic parameter alpha, in order to write the portfolio risk with the risk of individual stocks and weighting factor form of expression. However, this is impractical because of the empirical study shows that different stocks exhibit different alpha values. Unfortunately, the equity portfolio with different fat tail multivariate extreme value distribution theory, so far still issues to be resolved. The same time, risk, there is still a similar problem with the variance measures the risk, that equal treatment of losses and earnings, which are contrary to the psychological feelings of investor risk parameter λ. The downside risk measure of the risk, and taking into account market factors of friction, with different characteristics index alpha portfolio model structure fractal distribution. With no short selling risk assets and lending of securities markets (such as China's securities market) risk-free asset, the model also takes into account does not allow short selling and borrowing.

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CLC: > Economic > Economic planning and management > Economic calculation, economic and mathematical methods > Economic and mathematical methods
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