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If an investor can hold a portfolio of almost infinite number of assets, is there a certain type of risk of the portfolio that matters

If an investor can hold a portfolio of almost infinite number of assets, is there a certain type of risk of the portfolio that matters the most to the investor (assuming all the assets are equal-weighted in the portfolio)

Average volatility of each asset

The relative importance of volatility and covariance risks depends on the average return of each asset

Covariance between assets

Both volatility of each asset and the covariance between assets are equally important

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