Question 4.131

4.131 Perfectly negatively correlated investments.

CASE 4.3 Consider the following quote from an online site providing investment guidance: “Perfectly negatively correlated investments would provide 100% diversification, as they would form a portfolio with zero variance, which translates to zero risk.” Consider a portfolio based on two investments ( and ) with standard deviations of and . In line with the quote, assume that the two investments are perfectly negatively correlated .

  1. Suppose , and the portfolio mix is 70/30 of X to Y. What is the standard deviation of the portfolio? Does the portfolio have zero risk?
  2. Suppose , and the portfolio mix is 50/50. What is the standard deviation of the portfolio? Does the portfolio have zero risk?
  3. Suppose , and the portfolio mix is 50/50. What is the standard deviation of the portfolio? Does the portfolio have zero risk?
  4. Is the online quote a universally true statement? If not, how would you modify it so that it can be stated that the portfolio has zero risk?

4.131

(a) 2.2, no. (b) 1, no. (c) 0, yes. (d) No, “Perfectly negatively correlated investments with equal variance and equal mix….”