A financial planner is examining the portfolios held by several of her clients. Which of the...

A financial planner is examining the portfolios held by several of her clients. Which of the following portfolios is likely to have the smallest standard deviation?

A portfolio containing Microsoft, Apple, and Google stock

A portfolio containing only Microsoft stock

A portfolio consisting of about three randomly selected stocks from different sectors

Portfolio managers pick stocks for their clients’ portfolios based on the investment objective of the portfolio and several other factors. One key consideration is each stock’s contribution to portfolio risk and its statistical relationship with the portfolio’s other stocks.

Based on your understanding of portfolio risk, identify whether each statement is true or false.

A portfolio’s risk is likely to be smaller than the average of all stocks’ standard deviations, because diversification lowers the portfolio’s risk.
Because of the effects of diversification, the portfolio’s risk is likely to be more than the average of all stocks’ standard deviations.
Portfolio risk will increase if more stocks that are negatively correlated with other stocks are added to the portfolio.
The unsystematic risk component of the total portfolio risk can be reduced by adding negatively correlated stocks to the portfolio.

Solutions

Expert Solution

To have the smallest standard deviation for a portfolio, the stocks must be uncorrelated such that losses from one stock is offset by the gains from another thus reducing the standard deviation. For this to happen, a portfolio consisting of three randomly selected stocks from different sectors would have the smallest standard deviation.

A portfolio’s risk is likely to be smaller than the average of all stocks’ standard deviations, because diversification lowers the portfolio’s risk. - True

Because of the effects of diversification, the portfolio’s risk is likely to be more than the average of all stocks’ standard deviations.- False

Portfolio risk will increase if more stocks that are negatively correlated with other stocks are added to the portfolio.- False

The unsystematic risk component of the total portfolio risk can be reduced by adding negatively correlated stocks to the portfolio.-True

jeff jeffy answered 2 years ago

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