Assume that an investor can invest (long or short) in only two assets, the characteristics of which are summarised in the following table: Asset Expected rate of return (p.a.) Standard deviation (p.a.) A 7% 15% B 5% 4% The correlation between the returns on A and B is 0.5. Assume that the random returns on these assets have normal distributions. Assume that the investment horizon is one year and that no adjustment is possible to any portfolio during the year. i) Determine the overall minimum variance portfolio. (05 marks) Assume now that the investor has to pay a random sum of money (the liability) to a creditor at the end of the year which can be written as R20,000(1 + X), where X is a normal random variable with mean 6% and standard deviation 12%. X has a correlation of 0.7 with the return on A and 0.2 with the return on B. Surplus is defined as the value of the portfolio less the liability at the end of the year. 3 ii) Assume the investor has R20,000 at the start of the year. Determine the portfolio that will result in the lowest standard deviation of surplus. (05 marks) iii) Assume that the investor has R21,000 at the start of the year and that she wishes to construct a portfolio (the "least risk portfolio") that minimises the probability that the surplus is negative. (05 marks)