If portfolio weights are positive: 1) Can the return on a portfolio ever be less than the smallest return on an individual security in the portfolio? 2) Can the variance of a portfolio ever be less than the smallest variance of an individual security in the portfolio? A) 1) yes; 2) no B) 1) no; 2) yes C) 1) no; 2) no D) 1) maybe; 2) no E) 1) yes; 2) yes

Based on the information given, the correct option will be B. 1) no; 2) yes

It should be noted that the return on a portfolio when the portfolio weights are positive will be calculated as the value that is between the highest return and the lowest return.

In such a case, the return on a portfolio can never be less than the smallest return on the individual security in the portfolio. Also, the variance of a portfolio can be less than the smallest variance of the individual security in the portfolio.

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B) 1) no; 2) yes

Explanation:

The return on a portfolio when the portfolio weights are positive will be between the highest return and the lowest return. It cannot exceed these limits.

With Variance however, the variance of a portfolio can be less than the smallest variance of an individual security in the portfolio because in the calculation of portfolio variance, the correlation is used in the calculation (refer to formula below). As a result, if the securities are negatively correlated, it could lead to a lower value than the smallest variance in the portfolio.

Variance of Portfolio = (w(1)^2 * o(1)^2) + (w(2)^2 * o(2)^2) + (2 * (w(1)*o(1)*w(2)*o(2)*q(1,2)))

Highlighted portion is the correlation. If this is negative, Portfolio variance will reduce to a point lower than the lowest individual variance.

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