Question

Which of the following statements is FALSE?

A. The volatility of a portfolio depends on the correlation between the securities in the portfolio.

B. The volatility declines as the number of stocks in a portfolio grows.

C. We say a portfolio is an efficient portfolio whenever it is possible to find another portfolio that is better in terms of both expected return and volatility.

D. An investor seeking high returns and low volatility should only invest in an efficient portfolio.

Answer 1

A. The volatility of a portfolio depends on the correlation between the securities in the portfolio is true because generally, a lower correlation between securities in a portfolio results in a lower portfolio variance. And a higher correlation between securities in a portfolio results in a higher portfolio variance.

B. Volatility of portfolio depend on the correlation between stocks and individual stock variance. Lower the correlation between stocks lower the portfolio variance. If the stocks with higher correlation are added to existing portfolio, then it will lead to increase in portfolio variance. Hence, the statement that the volatility declines as the number of stocks in a portfolio grows is only partially true because an investor can have diversification benefit only when he adds stocks that have very low or negative correlation with each other.

C. We say a portfolio is an efficient portfolio whenever it is possible to find another portfolio that is better in terms of both expected return and volatility. This statement is false because a portfolio is an efficient portfolio whenever it is not possible to find another portfolio that is better in terms of both expected return and volatility.

D. An investor seeking high returns and low volatility should only invest in an efficient portfolio is true because an efficient portfolio is either a portfolio that offers the highest expected return for a given level of risk, or one with the lowest level of risk for a given expected return.