The Optimal Study on Econometric Measurements
of Investment Risks
MBA Education Center，Jinan University，
601,West Huangpu Road
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
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
(1) SV i 1
RE -Ri, if RE≥Ri;
(2) U = (RE - Ri)+ =
0, if RE<Ri.
（RE: expected return rate. R: real return rate. m: investment time periods divided
by a given time unit, such as twelve months or fifty transaction weeks in a
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. Comparison of calculated results by semivariance and variance methods
Shenzhen Possible weekly
Stock Index loss SV- variation
1995 0.021256 0.043719 0.003994
1996 0.013618 0.027667 0.004789
1997 0.016317 0.032848 0.002173
1998 0.013939 0.028619 0.000626
From the 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
possible coefficient 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.
（1974） Toward the development of
William W. Hogan and James M. Warren ,
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,
Journal of Finance, June 1973, P675.