colin wrote:Not only is the mathmatics used to calculate beta advanced it has been demonstrated to be irelevant to investors because as I have already stated the Eugene Fama and Kenneth French study published in 1992 found no evidence that the predictions of the CAPM were true.
The mathematics to calculate beta is very simple, not even "O" Level:
https://www.wikihow.com/Calculate-Beta
Here is a simple introduction to Modern Portfolio Theory, with no complicated mathematics:
http://www.moneychimp.com/articles/risk/riskintro.htm
The mathematics required to prove the result that I quoted is beyond the scope of that article. That mathematics is not at all advanced, but it is complicated.
Whether or not CAPM fits the US data accurately is not relevant to the point I was making. People do not always behave as Sharpe thought they should. All I was trying to do was show the motivation for market weighting, and explain where had I decided that it was reasonable to deviate from market weighting.
Farma and French's 3 factor model fits the US data well. but does not fit the data from other markets well. Various other factors were later identified, and there are Vanguard funds for harvesting several of them. There are people who believe, as Farma and French did, that there is a persistent small cap premium that is compensation for the extra risk of investing in small cap stocks. Despite selling a small cap fund, Vanguard does not include it in their packaged portfolios. Their committee evidently believes that even a market weighting of small cap stocks is not worthwhile.