Economics 422 Midterm Exam 1 - Optimal Consumption and Investment - Prof. Eric Zivot, Exams of Economics

Download Economics 422 Midterm Exam 1 - Optimal Consumption and Investment - Prof. Eric Zivot and more Exams Economics in PDF only on Docsity! NAME:_____________________________ ECONOMICS 422 MIDTERM EXAM 1 R. W. Parks Autumn 1994 Answer all questions on the examination sheets. Weights are given in parentheses. In general you should try to show your work. If you only present a numerical answer and it is wrong, then you get no credit. If you show what you are doing and you make a numerical error you will receive some credit for a correct approach. 1.(30) Pandora lives in a two period Fisherian world. Her utility function for consumption streams can be written as U c c c c( , )0 1 0 2 1= , hence her marginal rate of substitution is MRS c c= −2 1 0/ . Her endowment of present and future resources is (20,000,144,200). She can borrow or lend at a market real interest rate of 3 percent. a. What is her wealth? b. What is her optimal consumption in the present and in the future? b. What financial transactions are required to attain the optimal consumption stream? Indicate both the transaction and the amount involved. 2. (35) In a two period Fisher model assume that a person has • an initial endowment that consists entirely of present resources • an investment function that gives the relationship between amounts invested in the present and the corresponding returns to be received in the future. • preferences regarding time dated consumption streams a. Initially assume that there are no capital markets. In a well labeled diagram show the elements listed above and indicate the person's optimal investment and consumption decisions. b. Now assume that the person can borrow or lend at a real rate of interest r>0. Using a new diagram indicate the optimal investment and consumption decisions. c. Is the person better off under a. or b.? Explain. d. What happens to amount of real investment selected in part b if the real interest rate falls? Explain using a diagram. 2. (16) Your company is considering a project which requires the building of a warehouse. Warehouse A costs $120,000 to build and lasts five years. It requires maintenance expenditures of $4000 per year. An alternative, Warehouse B, costs $180,000 to build, lasts 8 years, and requires maintenance expenditures of $2200 per year. Both warehouses would provide the same stream of services in the context of the project. Neither has a scrap value at the end of its life. Assuming that the opportunity cost of capital is 10 percent, which warehouse would you choose? Explain and show your work. 3. (24) A person whose utility of wealth function is U(W)=loge(W), i.e. the person's utility associated with any given level of wealth is equal to the natural log of the wealth level. If the person chooses occupation A his or her wealth is given by the following wealth distribution: Wealth: 1,000,000 2,000,000 Probability: 0.8 0.2 If the person chooses occupation B his or her wealth is given by the following wealth distribution: Wealth: 1,100,000 1,300,000 Probability: 0.5 0.5 a. Which occupation will the person choose and why? Or will the person be indifferent to the alternatives? Explain. b. Compute the certainty equivalent wealth for occupation A. 4. (24) A stock currently sells for $80 per share. The distribution of its price in one year is: Price: 76 80 84 88 Probability: .10 .20 .50 .20 a. What is the probability distribution of the stock's rate of return? b. Compute the expected value of the rate of return over the next year. c. Compute the variance of the rate of return. 5. (20) Two companies have stock for which the expected returns and standard deviations of return are forecast as: Company: A B Expected Return: 0.2 0.2 Standard Deviation of Return 0.3 0.3 The correlation coefficient between the two rates of return is 0. a. What are the expected return and variance of returns for a portfolio made up, half of A and half of B? b. Since the two stocks' returns and standard deviations are the same, does it make any sense to combine them in a portfolio, or would you be just as well off holding either one of the stocks separately? Explain. 422au94.me2 Name:___________________________________ ECONOMICS 422 FINAL EXAMINATION R. W. Parks Autumn 1994 Two hours. Answer all questions on these exam sheets. Question weights (total=120) are given in parentheses. In general you should try to show your work for the problems i.e. the non-multiple-choice questions. If you only present a numerical answer and it is wrong, then you get no credit. If you show what you are doing and you make a numerical error you will receive some credit for a correct approach. 1. (20) Provide brief definitions of the following: a. The Fisher separation theorem. b. The distribution of a random variable. c. The expected utility hypothesis. d. The duration of a bond e. The yield to maturity of a bond. 7. (25) Employee Options. Young companies often pay salaries that are relatively low but which are supplemented with stock options. Suppose that an employee of Imagioco is granted 500 American call options. Their exercise price is $25, which is equal to the price of Imagioco's stock on the day of the grant. The options expire in ten years. Imagioco pays no dividends and the standard deviation of the rate of return on its stock is 0.347851. The yield on a ten year stripped Treasury bond is 5.75571 percent. a.) Use the Black-Scholes option pricing formula to estimate the value of the option grant. b.) What are the advantages and disadvantages to the company and to the employee of this form of compensation? c.) Employee options usually are not marketable and they become exerciseable according to a vesting schedule e.g. 20 percent of the options become exerciseable on the first through fifth anniversaries of the option grant. Would you expect these features to increase or decrease the value of the options relative to the value computed in part a above? Explain. d.) It has been observed that employees often exercise their options according to the vesting schedule when they are in the money even though by doing so they give up some of the options' value. What factors might explain this choice by the employees? 8. (5) The closing price on the 100 ounce gold futures contract for April (treat this as 0.333 years from now) was $383.20 per ounce. The closing spot price of gold was $378.20 per ounce. The April T-bill has a yield of 6.06 percent. If the convenience yield for gold is negligible and if the present value of the cost of storing an ounce of gold for four months is positive, are the spot and futures prices consistent? Explain. If you find that the prices are not consistent, explain how you could take advantage of the situation. 422au94.exm