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Evaluate the following claims: a) If the correlation between securities is zero, as you add more and more securities the portfolio will variance eventually go

Evaluate the following claims: a) If the correlation between securities is zero, as you add more and more securities the portfolio will variance eventually go down to zero.

b) Efficient frontier calculated using the market model and Betas would lie below, towards the lower right corner to the efficient frontier calculated using the full covariance matrix.

Please first tell if these claims are right or wrong and then provide explanation

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