Out of curiosity, does the curriculum in the higher levels (II or III) delve into this?
That would be way too useful to make it into CFA text. Have to fill those pages with GIPS compliance rules, how to calculate options pricing by hand and the definition of heteroskedasticity. You know, stuff you use every day after the exam.
Haha, that was my inclination, though I was hoping it might show up somewhere! Talk about something that would be nice to cover… considering that asset returns seldom follow something so elegant as a normal distribution.
choked on my drink laughing. Every Econ major should know what heteroskedasticity means though.
I forget how CFA words the chapter, but mean variance optimization doesn’t assume normal distribution of returns. There might be some topics in CFA that are dependent on this distribution, but again, I don’t recall it.
I’m struggling with this one a little, Ohai. If you solely use the mean, variance, and covariance of two assets’ return samples, would you not be implicitly assuming that their joint distribution within a portfolio to be normally distributed? Meaning if you only depend on the mean and variance as a means of optimizing a portfolio then you must be implicitly accepting that the mean and variance completely describes the return profile of the individual assets, which would not be the case in the event the returns exhibit negative skew and, say, excess kurtosis? In any event, I’ll definitely need to research this some more! Was hoping this would be discussed somewhere within the CBOK!
That sentence hurt my brain, but mean, covariance and variance say nothing about skew or convexity. Mean is just the expected return, and variance describes the average move in asset prices. So, you are dealing with first and second moments. A process that does not address higher moments does not need to be specific to those higher moments. A return distribution can have any shape of skew or tails and still have the same mean or variance. You could, for instance, construct a set of assets with binomial distributions with any mean, variance and covariance. The optimization result might be different depending on the actual distribution. However, CFA never addresses how to actually perform the optimization. From their high level approach, you do not need to assume any particular distribution of returns.
There are many probability distributions for which the mean and variance uniquely describe the distribution. A uniform distribution, for example, is uniquely defined by its mean and variance.
Mean-variance optimization doesn’t assume zero skewness or zero excess kurtosis. It simply assumes that variance of returns is the appropriate measure of risk. If you want to use a different measure of risk, so be it: do your optimization based on that risk measure.
Thank you, Ohai and S2000! Your were of great help… my apologies on any brain hurting my question may have caused!
To be fair, heteroscedasticity is a pretty important part of regression analysis (by the way, word defines itself…see the etymology if you’re unsure). If you’re running regressions without considering it and investigating, you’re likely getting the wrong picture from the data.
Building off of this… say you wanted to optimize for conditional value at risk in place of variance. I’m loosely familiar with the process of estimating the conditional value at risk for a single asset via monte carlo simulations, but how could one go about estimating the conditional value at risk of a portfolio of assets? I understand this might be well out of the curriculum’s scope, but curious to see if anyone has a good online resource that they can point me to. Thanks in advance to all!