Suppose a portfolio is comprised of multiple stocks from within the S&P500. The standard deviation of the portfolio’s return is:Group of answer choicesalways lower than the standard deviation of the returns of each stock in the portfolioalways higher than the standard deviation of the S&P500’s returnalways lower than the average of the standard deviations of each stock’s return
Question
Suppose a portfolio is comprised of multiple stocks from within the S&P500. The standard deviation of the portfolio’s return is:Group of answer choicesalways lower than the standard deviation of the returns of each stock in the portfolioalways higher than the standard deviation of the S&P500’s returnalways lower than the average of the standard deviations of each stock’s return
Solution
The standard deviation of a portfolio's return is not always lower or higher than the standard deviation of the returns of each stock in the portfolio, the S&P500's return, or the average of the standard deviations of each stock's return.
The standard deviation of a portfolio's return depends on the weights of the stocks in the portfolio and the correlation of the returns of the stocks in the portfolio. If the stocks in the portfolio are perfectly positively correlated, the standard deviation of the portfolio's return will be the weighted average of the standard deviations of the returns of the stocks in the portfolio. If the stocks in the portfolio are not perfectly positively correlated, diversification will cause the standard deviation of the portfolio's return to be less than the weighted average of the standard deviations of the returns of the stocks in the portfolio.
Therefore, without knowing the weights of the stocks in the portfolio and the correlation of the returns of the stocks in the portfolio, we cannot determine whether the standard deviation of the portfolio's return is always lower or higher than the standard deviation of the returns of each stock in the portfolio, the S&P500's return, or the average of the standard deviations of each stock's return.
Similar Questions
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