请教金融问题 deviations from normality

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为什么 negatively skewed distribution 会低估 risk， 而 positively skewed 却会高估，书上的解释不清楚，哪位高人解释一下啊

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关键词：deviations Deviation normality normal tions

which book?

可能是指出现极端值的概率不一样的原因吧

Enthuse 发表于 2010-4-6 23:35
which book?

Investments by Zvi Bodie, Alex Kane, Alan J Marcus and Pitabas Mohanty

long4 发表于 2010-4-7 00:09
可能是指出现极端值的概率不一样的原因吧

书上的解释是 beacause extreme positive deviations from expectation( which are ot a source of concern to the investor) nevertheless increase the estimate of volatility.

但是我们判断risk的依据是standard deviation, 如果 positive skewed 的分布增加了risk，也就是SD的话， 那我怎么觉得negatively skewed 的分布也增加了SD啊（都是和Normal Distribution 比较而言的）， 为什么书上却说negatively skewed的分布低估了risk 呢？

That is because generally, an investor is only worried about downside risk.

Ask yourself. Do you prefer extremely positive returns, or extremely negative returns?

ectopic 发表于 2010-4-7 09:42
That is because generally, an investor is only worried about downside risk.

Ask yourself. Do you prefer extremely positive returns, or extremely negative returns?

Ok, let's say the distribution is positively skewed, which means that there is some probability of extremely positive returns. Are you tring to argue that the risk, under this scenario, is overestimated because risk here is meaning the "risk" of earning more returns rather than lost extra money which could happen in case of negatively skewed distribution. So here the so-called overestimated or underestimated risk has nothing to do with the standard deviation?

What I'm saying is standard deviation is an incomplete measure of risk.

When a buy and hold investor encounters a positively skewed distribution, and standard deviation is his only measure of risk, he is going to interpret the higher standard deviation as higher risk than normal. But the extra risk is biased to the upside, which is a good thing.

For a negative skew, the buy and hold investor would also intrepret the higher standard deviation as higher risk than normal. But in fact, it's even worse than he thinks, because the extra risk is biased to the downside.

ectopic 发表于 2010-4-7 16:18
What I'm saying is standard deviation is an incomplete measure of risk.

When a buy and hold investor encounters a positively skewed distribution, and standard deviation is his only measure of risk, he is going to interpret the higher standard deviation as higher risk than normal. But the extra risk is biased to the upside, which is a good thing.

For a negative skew, the buy and hold investor would also intrepret the higher standard deviation as higher risk than normal. But in fact, it's even worse than he thinks, because the extra risk is biased to the downside.

Ok now I got it. Really appreciate it!