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oli · 2021年11月05日

老师上课的时候说如果correlation=-1, 组合方差是可能等于0的,有道题也是说correlation=1,有zero variance, 为什么本题中b是错误的呢?

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问题如下:

Some statements about covariance and correlation are listed below, the least accurate is:

选项:

A.

The covariance between two assets is zero, which means there is no linear relationship between the returns of the two assets.

B.

If two assets are perfect negatively correlated, the variance of return for a portfolio that is constructed by these two asset equals to zero.

C.

The covariance of a two stock portfolio is equal to the correlation coefficient multiples the standard deviations of each stock's returns.

解释:

B is correct.

If two assets are perfect negatively correlated,  the correlation is -1, then the set of portfolio risk/return combinations becomes two straight lines. The portfolio of these two assets will have a positive return variance, unless the weight of the portfolio is the combination of those that minimize the combinatorial variance.

The covariance is equal to the correlation coefficient times the standard deviation of the returns of two stocks in the two-stock portfolio.

If the covariance is zero, the correlation coefficient is zero, which means there is no linear relationship between the returns of the two stocks.

老师上课的时候说如果correlation=-1, 组合方差是可能等于0的,有道题也是说correlation=1,有zero variance, 为什么本题中b是错误的呢?

1 个答案

Kiko_品职助教 · 2021年11月05日

嗨,努力学习的PZer你好:


“老师上课的时候说如果correlation=-1, 组合方差是可能等于0的”这句话没问题。


这张图可以很好的解释,correlation=-1,组合可以形成一条折线,只有一个点variance=0,那就是折现的拐点。B想表达的就是所有variance=0,所以B是错的。

“有道题也是说correlation=1,有zero variance”这句话不对。你应该是记错了。看图也可以找到答案。


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