Lowest 250 vol stocks in S&P500
2008

2017


AvgVol 
60%

19%

AvgCorr 
0.48

0.14

Both total volatility and correlation were about 3 times higher in the crisis year of 2008. This is because the total market volatility was so much higher. One could say correlations rise in bad times, but one could also say that mathematically, given a 'onefactor' model (the market), if the market has higher volatility its assets will have a higher correlation.
The equation I presented last week calculates portfolio volatility as follows:
 Volatility (n assets, correlation c)=sqrt(avgVol^2/n + (n1)/n*c*avgVol^2)
Here c is the average correlation, so the average of the correlation matrix off the diagonal. Volatility and correlation are taken from the same period here, that in the years 2008 and 2017.
In the equation, most of this diversification benefit happens rather quickly, with 90% of it coming after n=15. Given many people look at multiple factors, not just the market factor, this could make this formula less relevant. So I took all those 250 stocks and created thousands random of subportfolios to get an estimate of the actual, or empirical, volatility.
Comparing this to the formula generated the data in the above chart: they are basically identical. You only see two lines because there are two sets of lines that overlap. In both scenarios, the 10 asset portfolio had insignificantly higher volatility than the 250 asset portfolio. While the correlations are quite different, generating different levels of diversification as a function of the number of assets, they both almost perfectly matched the simple formula.
Bottom line: 10 assets really is enough.
4 comments:
90% coming before n=15?
0.0 0.1 0.2 0.3 0.4 0.5
1 0% 0% 0% 0% 0% 0%
5 55% 69% 72% 74% 76% 77%
15 74% 88% 90% 91% 92% 92%
20 78% 91% 92% 93% 94% 94%
25 80% 92% 94% 94% 95% 95%
30 82% 94% 95% 95% 96% 96%
here's the percent by n and correlation
Thanks
And what about if you consider MSCI world ? How many assets to eliminate specific risk ?
Thanks for your great posts ...
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