7. Using historical data to measure portfolio risk and correlation coefficient Dai is an investor who believes that past variability of stocks is a reasonably good estimate of future risk associated with the stocks. Dai works on creating a new portfolio and has already purchased stock A. Now he considers two other stocks, B and C. Dai collected data on the historic rates of return for all three stocks, which are presented in the following table. Complete the table by calculating standard deviations for each stock: Year Stock A Stock B Stock C 2013 40% -5% 35% 2014 -10% 40% -5% 2015 35% -10% -10% 2016 -5% 35% 40% Average return Estimated standard deviation Suppose Dai can only afford to complement stock A by adding just one of the two other stocks, either stock B or stock C. Complete the following table by computing correlation coefficients between stocks A and B and between stocks A and C, and calculate average returns and standard deviation for the two potential portfolios, AB and AC: Suppose Dai can only afford to complement stock A by adding just one of the two other stocks, either stock B or stock C. Complete the following table by computing correlation coefficients between stocks A and B and between stocks A and C, and calculate average returns and standard deviation for the two potential portfolios, AB and AC: Stocks A and B Stocks A and C Correlation coefficient Average return Standard deviation Suppose Dai has to choose between two portfolios, AB and AC. Dai will be better off choosing Which of the following statements about portfolio diversifications are correct? Check all that apply. The risk of a portfolio declines as the number of stocks in the portfolio increases. Stocks with perfectly negatively correlated returns do not exist. By adding enough partially correlated stocks, risk can be completely eliminated. The higher the stocks' correlation coefficients, the lower the portfolio's risk