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I writing a paper and wanted to know the best way, method or theory to know if a portfolio is diversified. To give you some context, I wanted to know if whether putting Bitcoin into a portfolio with multi-asset class indexes will give the portfolio diversification benefits. I have two portfolios, a US Market portfolio and an international portfolio.

Although there might be an obvious answer to if Bitcoin does or does not offer diversification, I need to back it up with a method or theory or something. Any help will be appreciated.

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    $\begingroup$ No one simple metric is good alone. The most basic one is the correlation with US Equity and International equity. Perhaps Gold or other precious metal and commodity can also serve as a benchmark of comparison.Besides, diversification is a means not a goal, I think comparing Sharpe ratio of two different portfolio makes sense as well. Ultimately, unfortunately, BTC is really hot for not too long, less than a decade and I doubt if any meaningful interpretation can come out. $\endgroup$ – Preston Lui Apr 17 at 11:54
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    $\begingroup$ Informally, if including an asset X in a portfolio allows you to bring down the portfolio variance by a meaningful amount compared to a portfolio which does not include the asset, we can say that X helps with diversification. Formal statistical tests include the 'mean variance spanning test' of Huberman and Kandel JoF 1987, and subsequent work. $\endgroup$ – noob2 Apr 17 at 14:51

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