The analytical method also called the variance-covariance method makes use of knowledge of the input values and any pricing models along with assumptions of normal distribution to analyze risk. The historical returns of two investments A and B for a given period in time are summarized in the table below showing percentage rates of return and probability occurrences

Probability Investment A % Investment B %

0.2 12 19

0.1 10 20

0.4 14 17

0.3 18 10

Required:

i. Determine the optimum risk of a portfolio consisting of A and B (5 Marks)

ii. Given that the value of the investment portfolio is sh.1.5 Million determine the Value at risk of this portfolio at 95% confidence (2 Marks)

iii. Discuss the Strategies that the investor will use to minimize the risk exposure in (ii) above (8 marks)