Diversification
I was interested in calculating what the portfolio volatility would be for a portfolio given various correlation assumptions, and also the number of assets. So I took two portfolio of the S&P500 in two very different years: 2008 and 2017. The VIX had one of its highest average levels in 2008, at 31.5, while its lowest in 2017, at 11.0. Because I’m interested in low vol portfolios, I took the stocks with below-average volatility from the prior year. The statistics on these 250 stocks were as follows:
Lowest 250 vol stocks in S&P500
2008 | 2017 | |
AvgVol | 60% | 19% |
AvgCorr | 0.14 | 0.48 |
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 ‘one-factor’ model (the market), if the market has higher volatility its assets will have a higher correlation.
- Volatility (n assets, correlation c)=sqrt(avgVol^2/n + (n-1)/n*c*avgVol^2)
Source: http://falkenblog.blogspot.com/2020/01/diversification.html
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