A portfolio manager adds a new stock that has the same standard deviation of returns as the existing portfolio but has a correlation coefficient with the existing portfolio that is less than +1. Adding this stock will have what effect on the standard deviation of the revised portfolio’s returns? The standard deviation will: A) increase. B) decrease only if the correlation is negative. C) decrease. Please explain with an example, if possible.
C Diversification benefits, decreasing unsystematic risk, arise from adding a security that has a correlation of less than 1. When you diversify across assets that are not perfectly correlated, the portfolio’s risk is less than the weighted sum of the risks of the individual securities in the portfolio. Look around in the texts i.e. CFAI, Stalla, or Schweser. There should be a good visual of what happens upon the addition of more securities to a portfolio. Unsystematic risk will decrease but Systematic risk will remain the same.
C. Adding assets that are less than perfectly correlated to a portfolio will reduce that portfolios volatility. That’s the fundamental basis for diversification. Looking at the formula for portfolio standard deviation should make this clear.