ECON412JN-WE01 Advanced Financial Theory 2021
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ECON412JN-WE01
Advanced Financial Theory
2021
Part A
Question 1
Consider an economy in which the outcomes of investment are known with certainty. Assume that an investor has a production opportunity set given by the equation
C1 = 3 −
where C0 ≥ 0 and C1 ≥ 0 are the consumption quantities in the present and the future,
respectively. The preferences for consumption of the investor are given by the utility function U(C0, C1) = ln(C0) + ln(C1)
a) Assume that the investor has no access to a capital market and cannot borrow or lend. Determine the optimal consumption and investment plan of the investor and represent it in a diagram. Explain your approach. (30 marks)
b) Assume now that the investor has access to a capital market and can borrow and lend at interest rate r. Explain the Fisher Separation theorem using a diagram. Explain the conditions under which the Fisher separation theorem holds and the conditions under which it breaks down. Determine analytically and present graphically the optimal investment decision as a function of the interest rate. (30 marks)
c) Assume for the current example that the equilibrium interest rate is r = 50%. Calculate the optimal production and consumption plan of the investor and determine the amount that the investor is borrowing or lending in equilibrium. (30 marks)
d) Explain the concept of an equilibrium interest rate. Discuss the factors that have an impact on the equilibrium interest rate. (10 marks)
Question 2
Consider a decision-maker whose utility depends on wealth and is given by U() = W0.3
Assume that the decision-maker has to choose between the risky alternatives and that provide the following outcomes
Outcome |
Probability |
3 |
0.25 |
4 |
0.50 |
9 |
0.25 |
Outcome |
Probability |
2 |
0.2 |
5 |
0.6 |
8 |
0.2 |
a) Define risk aversion. Explain the concepts of “certainty equivalent wealth” and “Markowitz risk premium” . Determine the certainty equivalent wealth and the Markowitz risk premiums of the lotteries and . Determine whether the decision-maker would choose or . Explain your approach. (33 marks)
b) Represent the cumulative distribution functions of the lotteries and on a graph. Explain the concept of first-order and second-order stochastic dominance. Determine whether the lotteries and first-order or second-order stochastically dominate each other. Explain your calculations. (33 marks)
c) Determine the Arrow-Pratt measures of absolute and relative risk aversion for the given utility function. Explain the concepts of constant absolute risk aversion and constant relative risk aversion. Does the given utility function represent constant absolute or relative risk aversion? Explain. Determine the Arrow-Pratt risk premiums of the lotteries and . (34 marks)
Part B
Question 1
“The presence of rational investors should prevent the emergence of financial bubbles “ . Critically discuss, referring to the existing literature.
Question 2
Carefully introduce and discuss the concept of Style investing. What is the empirical evidence that this strategy is used? What are the costs and benefits of style investing?
2023-01-04