Question 1
You are given the following data about two securities. Security A standard deviation 80, expected rate of return security A = 26% Security B standard deviation 50, expected rate of return security B = 22%
WA is the weight in security A, WB is the weight in security B
WA WB Correl-1 Corre1=0.5 Correl=0 Correl= -0.5Correl= -1 Return
1 0
0.9 0.1
0.8 0.2
0.7 0.3
0.6 0.4
0.5 0.5
0.4 0.6
0.3 0.7
0.2 0.8
0.1 0.9
0 1
(i) Complete the above table for differing values of the correlation coefficient (correl) indicated above.
(ii) Plot the efficiency frontiers for all of the above values of the correlation coefficient using the excel chart function (all on the same chart).
(iii) When the correlation coefficient is equal to -I (minus 1 ) what weight between in security A and security B will create a risk free portfolio and what is the return associated with that risk free portfolio?
Question 2
You have the 1011(ming 7 years of data covering stocks A the market portfolio
Year Stock A Market Portfolio I 7% 8% 2 6% 2% 3 5% 15% 4 1% 5% 5 -2% -4% 6 6% 10% 7 7% 12%
(i) Calculate the yearly returns of a portfolio created by allocating your money equally between stock A and the market portfolio.
(ii) Calculate the expected return and standard deviation of stock A (use the population standard deviation n), the market and a portfolio made up of 40% the market and 60% investment in stock A.
Question 3
A market portfolio is made up entirely of the following 4 securities:
Total Value in Millions In millions Standard deviation A Correlation with BC D Security A $50 25% A 1.0 0 0 0 Security B $30 35% B 0 1.0 0 0 Security C $20 40% C 0 0 1.0 0 Security D $60 50% D 0 0 0 1.0
(i) Calculate the standard deviation of the market portfolio.
(ii) If the risk free rate of interest is 5% and the expected rate of return on the market portfolio is 10%. Draw a diagram to depict the relevant capital market line.
(iii) You have to advise someone seeking to obtain an expected rate of return of 15%. What investment strategy do you advise them to achieve this and what standard deviation can they expect?
Question 4
The risk free rate of interest is 6%. Alternatively, a risky portfolio is available that has an expected return of 1 1% for next year and a standard deviation of 20%.
(i) How could you combine the risk free with the risky portfolio to obtain an expected rate of return of 8.5%?
(ii) How could you combine these two portfolios to obtain a standard deviation of 15%?
(iii) How could you combine the two portfolios to obtain an expected return of 20%?
Question 5
The policy making committee of Bank ABC recently used reports from its securities analysts to develop the following efficient portfolios.
Portfolio Expected rate of return Standard deviation 1 8% 3% 2 10% 6% 3 13% 8% 4 I7% 13% 5 20% 18%
(i) If the risk free rate of interest is 6% which of the above portfolios 1 to 5 is best in the risk-return characteristics?
(ii) Assume that the policy making committee would like to earn an expected rate of return of 10% with a standard deviation of 4%, is this possible?
(iii) If a standard deviation of 12% was acceptable to the investment committee, what would be the expected return and how could it best be achieved?
(iv) Which if any, of the above portfolios can be described as a dominant portfolio?