Department of Economics, SUFFOLK UNIVERSITY

Jonathan Haughton

Fall 2014

ECONOMICS 826: Financial Economics

ASSIGNMENT 6

Answers to this assignment are due back by Wednesday, October 15, 2014.

Question 1: Quick concept checkers

Answer questions 1, 2, 4, 6, 11, 16 on pages 86-88 of the Hens and Rieger book. Note that for some of the questions there is more than one correct answer.

Question 2: Portfolios (again)

This is a modification of exercise 3.1 in the Hens and Rieger textbook. There are two risky assets, k = 1,2, and one risk-free asset that yields 2%. Short selling is not allowed. The expected returns on the risky assets are μ1=6% and μ2=9% respectively. The covariance matrix is:

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  1. Calculate the minimum-variance portfolio. [Hint: Either use solver in Excel, or minimize the variance of the portfolio subject to the shares summing to 1 (i.e. s.t. λ1+λ2=1). This is equivalent to minimizing L’ COV L, where L is a column vector with λ1 and 1-λ1.]
  2. Calculate the Tangent portfolio. [Hint: Apply equation 3.3. from the book; in effect we need L = COV-1 (μ – rf1) where μ is a vector of returns and 1 a column of ones. You will then need to normalize the L so that they add up to 1 – an application of two-fund separation.]
  3. Assume the market portfolio has shares λM = (0.4, 0.6). Compute the betas for each asset. [Hint: Find the covariance of asset returns with the market portfolio; and the variance of the market portfolio. It may help to note that , where r1 are the returns on asset 1, etc.]
  4. Determine the expected returns of the two risky assets (assuming that CAPM applies). Are either of the assets mispriced? Explain.

Question 3: Discounting

It is the first week of October, 2011 (t=1). You are an avid rugby fan, but you also have mid-term exams coming up. You face the following dilemma: you will miss seeing one of two rugby games that you would love to see. Either you will miss the game between Ireland and Wales in the second week (t=2), or between Australia and New Zealand in the third week (t=3). These options yield the following instantaneous utilities:

Ireland vs. Wales (t=2): u1=0, u2=4, u3=0

Australia vs. New Zealand (t=3): u1=0, u2=0, u3=10.

  1. If you discount future utilities exponentially with a discount factor δ=0.5, which game do you prefer to watch when asked in the first week of October? Is your preference ordering the same when asked in the second week of October? [Explain.]
  2. Now you yearn for instant gratification, and are a hyperbolic discounter. Actually, you follow quasi-hyperbolic discounting, where the discount factor is 1 for the present, and for future time periods. [This is sometimes called a beta-delta preference.] Assume δ=0.5 and β=0.7. Now which game do you prefer to watch when asked in the first week of October? Is your preference ordering the same when asked in the second week of October? [Explain.]
  3. How do -preferences give rise to preference reversals and reflect self-control problems?

Question 4: Instant Gratification

Attached to this assignment is a fascinating PowerPoint presentation on discounting by David Laibson. Read it first to make sense of the key ideas. Then dig up one of the articles that he references, and provide a short summary of the article’s main findings. [One page maximum.]

[Time needed: 5 hours]1 | Page