7. Your analyst informs you that shares in the eight companies that you are considering investing in each have an expected return of 10 per cent per annum and a standard deviation of returns of 15 per cent per annum. Further, the correlation coefficients of returns between each of the seven companies are all 0.4.

(a) Explain what proportion of wealth should be invested in each of the eight companies.

(b) Suppose that one of the eight companies is a company that is involved in slavery and that you now decide not to invest any of your wealth in that company. Explain what proportion of wealth should be invested in each of the seven remaining eight companies. Will the Sharpe ratio of this portfolio be higher than when the portfolio comprised eight companies?

(c) Suppose now that your analyst informs you that most of the above information is still the same. The seven companies (named A, B, C, D, E, F and G) that you are considering investing in each have an expected return of 10 per cent and a standard deviation of returns of 15 per cent. Further, all except one of the correlation coefficients of returns between each of the seven companies is 0.4. However, the returns of Company A and Company B are perfectly positively correlated. Explain what proportion of wealth should be invested in each of these seven companies.