顶啊，不要沉！

up up up!

ding a

同问阿，有大仙来解答吗

好老的问题被顶上来了。我看看能不能回答。

Q： 想问一下，谁能帮我详细解释一下，为什么在分析股票期货的return distribution时要引入stochastic dominance 和 modified beta 两种方法，两种方法的长处和短处又有什么？

A:  ``In order to obtain reliable conclusions regarding the relative performance of portfolios
including options, it is necessary to resort to tools that go beyond the mean-variance
framework.'' 加入了short call的投资组合，收益率分布不再是高斯的。其实不加option, 收益率也不是高斯的。所以光是平均值和方差不足以完全评价投资组合的效果。``For example, most investors have a preference for positively skewed returns''

两种方法的比较: ``Both approaches share the desirable property of going beyond the mean-variance
framework but when returns are normally distributed they give exactly the same
results as mean-variance analysis. The main differences is that stochastic dominance
makes a few general assumptions on the utility functions of investors, and that it
compares the whole distribution of returns which makes it very sensitive to any
outlier. The modified beta approach makes reasonable but more restrictive
assumptions on the behavior of investors 􏰀utility functions and intertemporal
optimization), and it also assumes that markets are complete.'
就是说他们的assumptions是不同的。到底哪个更接近事实就见仁见智了。

Q: 另外还想问一下(i.e., they consider moments of higher order, not only mean and variance)中的moments of higher order具体是指什么？

A: higher order就是3阶以上的，比如skewness 和 kurtosis. 加了option的portfolios 的收益率分布不是对称的，需要高阶的moment描述它的扭曲度，峰的陡峭度等等。
'