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3

The motivation of the Cornish-Fisher expansion is to approximate quantiles when the data is not normally distributed. It may help to think about parameters of a probability distribution and the resulting variance of the probability distribution. For instance, a normal distribution has two parameters, a location and a scale. It turns out that the maximum ...

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Given a set of returns, say 500 days, and a fixed portfolio construction, you can derive the 500 daily portfolio valuation changes. You can easily measure the mean and variance of these valuation changes. Since this is a sample you are interested in the confidence of your estimators (i.e. the mean and variance). One method that is often used is a resampling ...

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It is not clear that this allocation would be useful or even possible. Suppose you had a portfolio of two assets and that the optimal weights you had derived, based on a mean-variance approach were 0.4, 0.6. These are independent of the 3rd and 4th moments, suggesting that whatever the 3rd and 4th moments were in these assets the 0.4/0.6 weights would be ...

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Yes, they can/do. But you have to drink the proverbial Kool-Aid(or taking the blue pill is probably the more relevant metaphor these days ;-), and approach this as a Bayesian inference problem. So instead of mu, you have a normally distributed probability distribution of mu, depending on mu-of-mu and variance-of-mu. And the same for variance (mu-of-var, and ...

0

In the limit, the distribution of the mean of samples taken from an independent identically distribution is always normally distributed according to the Central limit theorem. So the empirical distribution for the portfolio mean should be normally distributed according to the Central limit theorem. But is the question then, how to calculate the mean and ...

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