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As you randomly add stocks to a portfolio the expected return on the portfolio will tend to decline the sigma of the portfolio will tend

As you randomly add stocks to a portfolio

the expected return on the portfolio will tend to decline

the sigma of the portfolio will tend to decline but the beta will tend to increase

the beta of the portfolio will tend to decline

the sigma of the portfolio will tend to decline

the beta of the portfolio will tend to decline but the expected return will tend to increase

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