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ECN6105

Modern Finance

SECTION A

Answer ALL THREE questions from this section

1. Consider a market portfolio containing two risky assets. Consider the problem of deriving the security market line for this portfolio.

a. Write down the Lagrangian for this problem. [5 marks]

b. Demonstrate that λ = Rf /σm , where λ is a Lagrange multiplier, Rf is the return on the riskless asset, and σm is the standard deviation of the market portfolio. [15 marks]

c. Using your answer in (b), derive the security market line. [5 marks]

2. Suppose the market portfolio contains two assets, A and B, held with respective value weights wA and wB . Beginning from the security market line, show that,     under the CAPM,

A – Rf = σA(2) zA + ρAB σA σB zB ,

where zi = wi ( m – Rf ) / σm(2) , i = A, B; Rf is the return on the riskless asset, σm is the standard deviation of the market portfolio, {σA σB } are, respectively, the standard  deviations of stocks A and B, and ρAB is the correlation coefficient between stocks A and B. [10 marks]

3. Suppose that a risk averse investor with wealth w can invest an amount λ in a   risky asset that gives a random rate of return r. Show that, if absolute risk          aversion is decreasing, then the investor optimally holds more of the risky asset as they get richer. [15 marks]

SECTION B

Answer ONE question from this section

4. What is meant by the disposition effect? Critically discuss the possible explanations of this effect.

5. Explain what is meant by the equity premium puzzle. What are the possible explanations of this puzzle, and how well does each such explanation fit the empirical evidence?