CAPM and not normal distributed assets (Feasibility)

[Alex Theo]

Hello there. I'm new on this forum here. I'll try my best to explain my problem.

One of the biggest assumptions in Finance is that Assets are normal distributed. There are a lot of statistical tests (JB-Test, QQ-Plotting, KS-Test...) which say that given timeseries (Assets) are not normal distributed.

Lets say we have 4 Assets. BMW, Pfizer, AIG and General Motors. I create a 4-Asset Portfolio with its return and risk given by the deviation. The deviation of the normaldistribution is known.

- If the tests say as result, that given timeseries are not normal distributed is it possible to make a, let's call it, a best fit?
- Which of given distribution is the most suitable for my timeseries?
- If there is a way to fit an other distribution on my timeseries, is this result significant?
- Is it possible to reconstruct a portfolio with the new deviation given by the new probability distribution?

The big question ist, is this process feasible?

My aim ist to compare the traditional way of building a portfolio with a modified one which its deviation is not normal distributed.

I hope I can get some answers. I'm gonna start my Masters degree in a while and I have already some topics I want to write about but I need some advice about my ideas.

Thanks

Alex

 

[BlackMamba]

I've looked into this myself. While I haven't arrived at the proper methodology, you may want to read more on plotting optimal portfolios where as opposed to minimizing variance for any given level of return you minimize modified VaR which incorporates the historical higher order moments (i.e., skew and kurtosis) of the data set.

 

[vertigo]

everything is feasible, you just need to be clever. try shifted lognormal/normal, mixture of lognormal/normal, this will introduce skew. try skewed T, too, for heavy tails.

"one of the biggest assumptions in finance is that assets are normally distributed" is bullshit. it is not true. try working in a bank and saying that, you will get laughed at. i suppose you mean 'returns are normally distributed', because thats what it says in the books. guess what, people will still laugh at you, because even that statement is bullshit. nobody takes the normal distribution seriously when pricing derivatives nor for portfolio theory. everything is implied in nature. forget using parametric models