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The Risk Measurement of the Portfolio Under Environment of Fractional Brownian Motion

Author: HuXiangFei
Tutor: YangShanChao
School: Guangxi Normal University
Course: Probability Theory and Mathematical Statistics
Keywords: Fractional Brownian motion CVaR VaR ratio Sharpe ratio
CLC: F830.59
Type: Master's thesis
Year: 2010
Downloads: 86
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Abstract

In recent years, with the rapid development of the economy, the investment has become a common phenomenon in people's lives. Then how to choose investment assets? Various combinations of assets should be determined how? Every investor concern is to solve this problem, many scholars at home and abroad on the portfolio risk measure .1952 years of Markowitz (1952, [1]) mean - variance model, the model of a single-term investment strategy portfolio selection theory On this basis, in the mid-1960s, SharpeW.F et al proposed the famous capital asset pricing model, the linear model reveals the expected rate of return of the assets of each risk and market risk of the portfolio return the relationship between these two results are due to the huge contribution to economics was awarded the Nobel Prize in economics since the 1990s, VaR model and CVaR model has become a major tool for risk management on CVaR model is correct VaR model proposed on the basis that it takes into account the losses in excess of VaR, is a more risk-averse, risk measurement tool. fractional Brownian motion is the promotion of the standard Brownian motion, and a large number of empirical studies have shown that fractional Brownian motion characterize the market price behavior model than the standard Brownian motion, Levy processes more realistic price movement characteristics. [49] in the standard Brownian motion environment a detailed comparison of the Sharpe ratio, VaR ratio, STARR ratio and the the Rachev ratio in the measure of portfolio risk. This article is intended to promote the text of these four ratios to fractional Brownian motion environment, to discuss the application of these four ratios measure of portfolio risk that the fractional Brownian motion environment main duties include: The first chapter is the full text the preamble gives the background to the study, the basic theory of the fractional Brownian motion environment portfolio research status and needs in this article for the fractional Brownian motion, and then outlines the structure of this article. discussed in the second chapter of fractional Brownian motion environment under a single asset CVaR CVaR optimal portfolio. Firstly, the theory of the two results, then were analyzed by numerical simulation of its basic nature. obtained by analyzing, in the holding period and confidence under the conditions of the same level, a single asset CVaR With the increase of the Hurst exponent decreases; When the Hurst exponent certain, CVaR value decreases gradually with the increase of the holding period; portfolio CVaR With the holding period of growth and gradually decreases the single asset CVaR trend is the opposite. Finally, the simulation results were verified through empirical analysis. third chapter focuses on the fractional Brownian motion environment portfolio risk measure several ratios. Firstly, the theoretical results of the Sharpe ratio, VaR ratio, STARR ratio and Rachev ratio, then different risk-free rate, the empirical analysis of these four ratios were compared in the same holding period, Sharpe Ratio the same level of interest rates, Sharpe ratio as the holding period of growth gradually larger. decrease as interest rates rise; under the same risk-free rate and the same confidence level, VaR ratio, STARR ratio With holding period of growth and gradually increase; same holding period and the same confidence level, VaR ratio, STARR ratio with the risk-free rate increases gradually decreases: in the same period and the same holds no risk-free rate, VaR ratio, STARR ratio as the confidence level increases and decreases. Rachev ratio better than α = β when α = β = 0.95 when investment optimal combination to determine the optimal portfolio. Finally, the four common ratio Sharpe ratio, V aR99% ratio STARR95% ratio and Rachevα = β = 95% ratio are compared by comparison, the following conclusions: Rachevα = β = 95% ratio is poor, V aR99% ratio of the second., STARR ratio when the risk-free rate is smaller than the Sharpe ratio advantage is more obvious: With the risk-free interest rate increases, the the STARR ratio and the Sharpe ratio value is close so when the risk-free rate is relatively large when you use the the STARR ratio of utility and measure portfolio risk using the Sharpe ratio is consistent Chapter Conclusions and Outlook section, which summarizes the main content of this paper, given some of the problems to be studied further.

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