4. Comment whether the following statements are true or false. Explain your argument. (1) If the single index model works, the total risk of a portfolio approaches zero as diversification increases. (8 marks) (2) Assume that stock market returns do not resemble a single-index structure. An investment fund analyses 40 stocks in order to construct a mean-variance efficient portfolio. They need to calculate 820 variance-covariance inputs. (8 marks) (3) Assume the investors find that the residuals of individual risky securities calculated using the single index model R; = ai + BiRM + ei are correlated. In other words, Cov(ei, e;) # O for i #j. They claim they still are able to reduce all firm-specific risk to zero by holding a well-diversified portfolio. (9 marks) 4. Comment whether the following statements are true or false. Explain your argument. (1) If the single index model works, the total risk of a portfolio approaches zero as diversification increases. (8 marks) (2) Assume that stock market returns do not resemble a single-index structure. An investment fund analyses 40 stocks in order to construct a mean-variance efficient portfolio. They need to calculate 820 variance-covariance inputs. (8 marks) (3) Assume the investors find that the residuals of individual risky securities calculated using the single index model R; = ai + BiRM + ei are correlated. In other words, Cov(ei, e;) # O for i #j. They claim they still are able to reduce all firm-specific risk to zero by holding a well-diversified portfolio. (9 marks)