投资风险计量方法的优化研究 by xiaoshuogu

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									The Optimal Study on Econometric Measurements of Investment Risks
Haiying Wei MBA Education Center,Jinan University, 601,West Huangpu Road Guangzhou,510632,P.R.China tweihy@jnu.edu.cn Since Harry M. Markowitz put forward the Portfolio Theory half a century ago, people have been used to measuring investment risks in securities, conducting utility analysis of risks and returns, and deciding on investment portfolio with the mean-variance Model in statistics. Nevertheless, mean-variance model is directly generated from the error econometric measurement method in general statistics, which fails to take serious considerations of the important characteristics of investment risks. Directed by this innovative theory, the American fund managers have demonstrated embarrassingly poor performances in their investment activities. In the recent 50 years, 80 percent of the fund managers never overran the market trend. On the other hand, investors who do not take Markowitz Portfolio Theory seriously such as George Soros and Warren E Buffett have made unprecedented glorious achievements on the financial market. Therefore, the reform of investment risk measurement has been put forward after Markowitz published his Selection of Portfolio. This paper firstly analyzes four significant differences between investment risks and general statistical risks, which are the quality of the bias, expectancy feature of investment risk, time feature and capital feature of investment risk. Starting from the four significant differences, the authors first modified the definition of investment risk as possible loss in investment, which is more in accordance with the reality. Secondly, this paper reviews the development of investment risks measurement history and analyzes four reasons that semivariance method has always been ignored by investors. Thirdly, based on the other three characteristics ( especially the capital feature), the authors further optimized the generally used semivariance method by adding the factor of capital, utilizing modern computer technologies to match the calculation results of semivariance method to real investment practice, instead of being confined to the existing simple square values, thus constructing a more practical Expectation-Semivariance Model:

(1)

SV 



 U
m i 1

2 i

 2U i


RE -Ri, if RE≥Ri;

m

(2)

U = (RE - Ri)+ =

0, if RE<Ri. (RE: expected return rate. R: real return rate. m: investment time periods divided
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by a given time unit, such as twelve months or fifty transaction weeks in a one-year investment.) Finally, the authors measured the investment risks in Shenzhen Stock Market Index, in the time duration of 1995-2001, using variance method and semivariance method added with the capital factor. The comparisons of calculated possible weekly loss in Shenzhen Stock Market measured by the semivariance method added with capital factor and the variance method is showed in the following Table-1. Table 1. Comparison of calculated results by semivariance and variance methods
Shenzhen Possible weekly Stock Index loss SVvariation 0.003994 0.004789 0.002173 0.000626

1995 1996 1997 1998

0.021256 0.043719 0.013618 0.027667 0.016317 0.032848 0.013939 0.028619

above Table-1, the 1999 0.014924 0.030647 0.002062 coefficient of SV value and possible weekly loss 2000 0.008506 0.018138 0.0013 reaches 0.9986. It can be seen that it has an accurate 2001 0.013322 0.027902 0.00072 description of risk level. However, the coefficient 0.998627 0.482981 between coefficient possible weekly loss and variance is only 0.483, which reveals that the variance method can hardly describe possible weekly loss. This empirical test has proven that the new risk model in this paper is much more accurate in risk measurement than the mean-variance Model. REFERENCES William W. Hogan and James M. Warren (1974) Toward the development of , an equilibrium capita-market model based on semivariance, Journal of Financial and Quantitative Analysis, January 1974, P1. H. M. Markowitz(1959), Portfolio Selection. New York, John Wiley and Sons, Inc., 1959, P194. Bernell K. Stone(1973), A general class of three-parameter risk measures,

From the

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Journal of Finance, June 1973, P675.

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