The (revised) Hong Kong Polytechnic University Department of Applied Mathematics Investment Science AMA532 Semester 2, 2009/2010 Assignment One Hand in solutions of questions 1, 2, 3, 4 and 5 by 6:30pm, 9 February. This is worth 2.5% towards your nal course mark. Late submissions may not be marked, and if marked will receive reduced or zero credit. In the cases where applicable, present your results up to 4 decimal points. 1. During return: Year 1 2 3 4 5 the past 5 years, you owned two stocks that had the following annual rates of Stock T Stock B 0.19 0.08 0.08 0.03 0.12 0.09 0.03 0.02 0.15 0.04
a. Compute the arithmetic mean annual rate of return for each stock. Which stock is most desirable by this measure ? b. Compute the standard deviation of the annual rate of return for each stock. By this measure, which is the preferable stock ? c. Assume that the risk free interest rate rf = 2%. Compute the coecient of variation for each stock (or Shape ratio). By this relative measure of risk, which is preferable ? 2. (Sunk costs) A young couple has made a nonrefundable deposit of the rst months rent (equal to $1,000) on a 6-month apartment lease. The next day they nd a dierent apartment that they like just as well, but its monthly rent only is $900. They plan to be in the apartment only for 6 months. Should they switch to the new apartment? What if they plan to stay 1 year? Assume an interest rate of 1%. 3. (Conicting recommendations) Consider the two projects whose cash ows are shown in the table below. Find the IRRs of the two projects and the NPVs at 5%. Show that the IRR and NPV methods yield the same recommendation. 0 1 Project 1 110 35 Project 2 150 40 2 35 40 Years 3 4 35 35 40 40 1 5 35 40
4. Suppose that you can make a deposit at an annual interest rate at 20% with the certain amount of money in a Bank. However, you are required to buy certain stock with the same amount as you have deposited in the Bank. Suppose that, at the end of one year, the value of the stock has changed. If R is the total return of the stock, what is the total return on your investment? 5. (Two correlated assets) The correlation between assets A and B is .2, and other data are given in the table below. [Note: = AB /(A B ).] Asset r A 5.0% B 2.0% 15% 5%
(a) Find the proportions of A and (1 ) of B that dene a portfolio of A and B having minimum standard deviation. (b) What is the value of this minimum standard deviation? (c) What is the expected return of this portfolio?
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