g. Explain correlation to your client. Calculate the estimated correlation between Blandy and Gourmange. Does this explain why the portfolio standard deviation was less than standard deviation? Blandy’s Answer: Loosely speaking, the correlation coefficient measures the tendency of two (ρ) variables to move together. The formula, shown below, is complicated, but it is easy to use Excel to calculate the correlation. Estimated = R = ρi,j Using Excel, the correlation between Blandy (B) and Gourmange (G) is: = 0.11 Est. ρB,G A correlation coefficient of +1 means that the stocks always move together; a correlation coefficient of means that the stocks always move oppositely to one −1 another. A correlation coefficient of 0 means that there is no relationship between the movements. The correlation coefficient of 0.11 means that sometime when stocks’ Blandy is up, Gourmange is down, and vice versa. This makes the total risk of the portfolio less than the risk of holding either stock by itself. h. Suppose an investor starts with a portfolio consisting of one randomly selected stock. As more and more randomly selected stocks are added to the portfolio, what happens to the risk? portfolio’s Answer: The standard deviation gets smaller as more stocks are combined in the portfolio, while rp (the return) remains constant. Thus, by adding stocks to your portfolio’s portfolio, which initially started as a 1-stock portfolio, risk has been reduced.
g. Explain correlation to your client. Calculate the estimated correlation between Blandy and Gourmange. Does this explain why the portfolio standard deviation was less than Blandy’s standard deviation? Answer: Loosely speaking, the correlation (ρ) coefficient measures the tendency of two variables to move together. The formula, shown below, is complicated, but it is easy to use Excel to calculate the correlation. Estimated ρi,j = R = Using Excel, the correlation between Blandy (B) and Gourmange (G) is: Est. ρB,G = 0.11 A correlation coefficient of +1 means that the stocks always move together; a correlation coefficient of −1 means that the stocks always move oppositely to one another. A correlation coefficient of 0 means that there is no relationship between the stocks’ movements. The correlation coefficient of 0.11 means that sometime when Blandy is up, Gourmange is down, and vice versa. This makes the total risk of the portfolio less than the risk of holding either stock by itself. h. Suppose an investor starts with a portfolio consisting of one randomly selected stock. As more and more randomly selected stocks are added to the portfolio, what happens to the portfolio’s risk? Answer: The standard deviation gets smaller as more stocks are combined in the portfolio, while rp (the portfolio’s return) remains constant. Thus, by adding stocks to your portfolio, which initially started as a 1-stock portfolio, risk has been reduced.