Problem 1 (10 marks). Assume the annual fixed term deposit rate is 3.4% in a New Zealand bank. Mary has $10,000 and plans to deposit into the bank for two years. She also wants the bank to reinvest her interests. The bank gives her the option to choose payment frequency in each year from 1, 2, and 4. The frequency tells how many times the bank pays her the interests. Suppose there is no interest tax a) How much Mary will get when the deposit matures after two years, when the interest payment frequencies per year are 1, 2, and 4 times, respectively? Which option is best for Mary? (5 marks) b) Former Chief Economist, John McDermott, in the Reserve Bank of New Zealand, says that inflation is a thief in your wallet. Suppose the inflation rate in New Zealand in the coming a few years is 2%. What are the real rates of returns of the annual bank deposit rate under the approximation rule, and in the exact relationship, respectively. [5 marks) Problem 2 (10 marks). In the past four years, the annual returns of one company's stock are 12%, 18%, and -14%, and 7%. a) What is the geometric average return? [3 marks) b) What is the arithmetic average of the returns? [3 marks) c) According to an economist' forecast on the Year 2020, the probabilities of repeating the performances of the former four years are 30%, 30%, 20%, and 20%, respectively. What is the expected return of the stock in the Year 2020? [4 marks) Problem 3 (15 marks). Stocks offer an expected rate of return of 18%, with a standard deviation of 22%. Gold offers an expected return of 10% with a standard deviation of 30%. a) In light of the apparent inferiority of gold with respect to both mean return and volatil- ity, would anyone hold gold? If so, demonstrate graphically why one would do so. 17 marks) b) Given the data above, reanswer a) with the additional assumption that the correlation coefficient between gold and stocks equals 1. Draw a graph illustrating why one would or would not hold gold in one's portfolio. Could this set of assumptions for expected returns, standard deviations, and correlation represent an equilibrium for the security marlot? 18 marke Problem 1 (10 marlos). Assume the annual fixed term deposit rate is 3.4% in a New Zealand bank. Mary has $10,000 and plans to deposit into the bank for two years. She also wants the bank to reinvest her interests. The bank gives her the option to choose payment frequency in each year from 1, 2 and 4. The frequency tells how many times the bank pays her the interests. Suppose there is no interest tax a) How much Mary will get when the deposit matures after two years, when the interest payment frequencies per year are 1, 2, and 4 times, respectively? Which option is best for Mary? 15 mars b) Former Chief Economist, John McDermott, in the Reserve Bank of New Zealand, says that inflation is a thief in your wallet. Suppose the inflation rate in New Zealand in the coming a few years is 2%. What are the real rates of returns of the annual bank deposit rate under the approximation rule, and in the exact relationship, respectively 15 marks Problem 2 (10 marks). In the past four years, the annual returns of one company's stock are 12%, 18%, and -14%, and 7%. a) What is the geometrie average return 3 mars b) What is the arithmetic average of the returns? 3 mars c) According to an economist' forecast on the Year 2020, the probabilities of repeating the performances of the former four years are 30%, 30%, 20%, and 20%, respectively. What is the expected return of the stock in the Year 2020? Problem 3 (15 marks). Stocks offer an expected rate of return of 18%, with a standard deviation of 22%. Gold offers an expected return of 10% with a standard deviation of 30%. a) In light of the apparent inferiority of gold with respect to both mean return and volatil- ity, would anyone hold gold? If so, demonstrate graphically why one would do so. 17 mars b) Given the data above, reanswer a) with the additional assumption that the correlation coefficient between gold and stocks equals 1. Draw a graph illustrating why one would or would not hold gold in one's portfolio Could this set of assumptions for expected returns, standard deviations, and correlation represent an equilibrium for the security 8 marlo Problem 4 (15 marks). Consider the following information about a risky portfolio that you manage, and a risk-free aset: E[r) = 11%, p = 15%,r= 5%. a) Your client wants to invest a proportion of her total investment budget in your risky fund to provide an expected rate of return on her overall or complete portfolio equal to 8%. What proportion should she invest in the risky portfolio, P, and what proportion in the risk-free wet? 5 marks) b) What will be the standard deviation of the rate of return on her portfolio? (5 marks c) Another client wants the highest return possible subject to the constraint that you limit his standard deviation to be no more than 12%. Which client is more risk averse
