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)Assumetheinvestorsfindthattheresidualsofindividualriskysecuritiescalculatedusing

the single index model = + + are correlated. In other words, ( , )

0 for . They claim they still are able to reduce all firm-specific risk to zero by holding a well-diversified portfolio. (9 marks)