Global Small Cap?

[GeoffF100]

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.

[Hariseldon58]

I agree in principle with a market weight whole heartedly...

Matter of interest, if you are a wholehearted believer in the principle of market weights, are you 60% in bonds and 40% equities? The global bond market is, I believe, about half again as big as the global equities market....

No is the answer, the balance between bonds and stocks is not one I choose to follow.... I have been rereading Peter Stanyers 4th edition of The Economist Guide to Investment Strategy ( each edition is worth reading) there are some interesting views on bonds, in particular those that are not of the highest government safety, comparing them to a safe bond with an attached option. Very interesting book, not often mentioned.

I have a strong bias to equity and whatever way we look at it , a market weighting of equity seems to work surprisingly well compared to other approaches

[EthicsGradient]

The mathematics to calculate beta is very simple, not even "O" Level:

https://www.wikihow.com/Calculate-Beta

Are you sure that article (by "Wikihow staff") has the faintest idea what it's talking about? Because that simple calculation has nothing at all to do with volatility; it just compares the rate of return with the return of the market. That sounds, to me, to be believing in the mythical "everything is perfectly priced in a market" claim, and then somehow saying there's even a direct ratio for rate of return and volatility.

In contrast, Investopedia has an article saying you need standard deviation, variance and covariance values: https://www.investopedia.com/ask/answer ... g-beta.asp

which means it is actually talking about volatility, not return (and notice your moneychimp article also says you use standard deviation to measure volatility, not just the rate of return). This gives it a lot more credibility. And I don't think standard O level maths included those.

[GeoffF100]

The mathematics to calculate beta is very simple, not even "O" Level:

https://www.wikihow.com/Calculate-Beta

Are you sure that article (by "Wikihow staff") has the faintest idea what it's talking about? Because that simple calculation has nothing at all to do with volatility; it just compares the rate of return with the return of the market. That sounds, to me, to be believing in the mythical "everything is perfectly priced in a market" claim, and then somehow saying there's even a direct ratio for rate of return and volatility.

In contrast, Investopedia has an article saying you need standard deviation, variance and covariance values: https://www.investopedia.com/ask/answer ... g-beta.asp

which means it is actually talking about volatility, not return (and notice your moneychimp article also says you use standard deviation to measure volatility, not just the rate of return). This gives it a lot more credibility. And I don't think standard O level maths included those.

We are talking about CAPM here. It is an assumption of CAPM that "everything is perfectly priced in a market". With CAPM the regression line passes through the origin. In practice, the regression line may not pass through the origin:

http://www.moneychimp.com/articles/risk/regression.htm

"Beta is the slope of this line. Alpha, the vertical intercept, tells you how much better the fund did than CAPM predicted (or maybe more typically, a negative alpha tells you how much worse it did, probably due to high management fees)."

[GeoffF100]

Wikihow and Money Chimp clearly describe the same regression. Stockopedia is making things more complicated than is necessary here.

[GeoffF100]

If anyone is interested in why the Wikihow and Stockopedia calculations are equivalent, here is the mathematics:

https://en.wikipedia.org/wiki/Simple_linear_regression

[EthicsGradient]

The problem is that Wikihow's calculation for beta does not involve multiple points - it is not a regression at all. It is, over some undefined period:

Beta = (stock's rate of return - risk-free rate) / (market rate of return - risk-free rate)

With their numbers,

risk-free rate=2%
stock's rate of return=7%
market rate of return=8%

Beta = (7-2)/(8-2) = 0.833...

If the market rate of return for that period happens to be equal to the risk-free rate, then beta is infinite. Not very useful, or reassuring for the calculation. If CAPM is claiming that the market rate of return will never drop to the risk-free rate, then it's bunk.

[GeoffF100]

The problem is that Wikihow's calculation for beta does not involve multiple points - it is not a regression at all.

You do not appear to have read the whole article. In "Part 3 Using Excel Graphs to Determine Beta", they clearly perform a linear regression:

Add a trendline to your scatter chart. You can do this either by selecting the trendline layout in newer versions of Excel or by finding it manually by clicking in Chart → Add Trendline. Make sure to display the equation on the chart, as well as the R2 value. Choose a linear trendline, not a polynomial or moving average.

As I have already said, it is the same regression as in Money Chimp.

If the market rate of return for that period happens to be equal to the risk-free rate, then beta is infinite. Not very useful, or reassuring for the calculation. If CAPM is claiming that the market rate of return will never drop to the risk-free rate, then it's bunk.

Yes, if the stock gives a non-zero rate of return over the risk free rate, and the index rate of return matches the risk free rate, beta is infinite, by definition. Within CAPM, the market rate of return can equal the risk free rate, or indeed be less than the risk free rate. CAPM was considered to be important enough to win the Nobel Prize for Economics.

[EthicsGradient]

You do not appear to have read the whole article. In "Part 3 Using Excel Graphs to Determine Beta", they clearly perform a linear regression:

An article in which they give two methods of finding a value, that have nothing to do with each other, is useless. It really does look like they didn't know what they were talking about. Nor do they know about writing, if they'll put one first, move on to Part 2 "how to use this", and then tell you a completely different definition in Part 3, without any hint that this would happen.

[mc2fool]

I agree in principle with a market weight whole heartedly...

Matter of interest, if you are a wholehearted believer in the principle of market weights, are you 60% in bonds and 40% equities? The global bond market is, I believe, about half again as big as the global equities market....

No is the answer, the balance between bonds and stocks is not one I choose to follow.... I have been rereading Peter Stanyers 4th edition of The Economist Guide to Investment Strategy ( each edition is worth reading) there are some interesting views on bonds, in particular those that are not of the highest government safety, comparing them to a safe bond with an attached option. Very interesting book, not often mentioned.

I have a strong bias to equity and whatever way we look at it , a market weighting of equity seems to work surprisingly well compared to other approaches

Ok, well I was just curious as to whether you did, and if not why not, but as my question seems to have sparked an ongoing detailed academic discussion on CAPM I'll just thank you for your brief answer above for now, and maybe revisit it with you on another occasion.

[GeoffF100]

You do not appear to have read the whole article. In "Part 3 Using Excel Graphs to Determine Beta", they clearly perform a linear regression:

An article in which they give two methods of finding a value, that have nothing to do with each other, is useless. It really does look like they didn't know what they were talking about. Nor do they know about writing, if they'll put one first, move on to Part 2 "how to use this", and then tell you a completely different definition in Part 3, without any hint that this would happen.

Wikihow usually does not explain concepts. It just shows how to accomplish practical tasks. The Money Chimp article is much better for understanding the concepts, which is why I posted that too.

There is just one definition of beta in the Wikihow article. Part 1 calculates beta from what are effectively two points on the regression line, and Part 2 shows how to fit a regression line to a scatter of points, but they do not explain that well. I posted the article in response to a claim that calculating beta required advanced mathematics. That clearly is not true. The Wikihow article gives a simple step by step algorithm for calculating beta.