Final exam for Asset Pricing 2020 Insper PDF

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The final exam for PhD level Asset pricing ...

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Final Exam

April 17, 2020 Asset Pricing, PhD Business Economics, 2020

Instructions: You should upload your exam at the Blackboard at the end. If you have difficulties with the Blackboard, send your exam by email to [email protected]. Maximum time: 4 hours, including time for uploading your answer sheet. 1. (2.5 pts) True or False? Discuss your answer . (a) (0.5 pt) In a equilibirum for a complete market economy with agents whose preferences are represented by time-separable expected utility with the same time-discount preference parameter, perfect risksharing (perfectly correlated marginal utilities) will be obtained, even if agents have different beliefs. (b) (0.5 pt) An asset pricing model for an arbitrage-free economy is a specification for the SDF. So, any asset pricing model can be expressed as linear factor model with a single factor, that is the conditional expectation of the excess return for any asset can be written as: Et [Rit+1 − Rf,t+1 ] = βif t λf t where βif t is the conditional covariance between the return i and the single factor f , and λf t is the factor risk premium. (c) (0.5 pt) The existence of assets with high Sharpe ratios implies necessarily a very volatile SDF. (d) (0.5 pt) Entropy bounds for the SDF extend Hansen-Jaganathan volatility bounds for the SDF when the SDF is lognormal. (e) (0.25 pt) If returns are not predictable then markets are efficient. (f) (0.25 pt) If returns are predictable then markets are not efficient. 2. (2.5 pts) Assume joint lognormality of asset returns and the SDF: 1

(a) (0.5 pt) Derive the Hansen-Jaganathan bound for the conditional volatility of the log SDF, σ mt. (b) (1.0 pt) Derive a mean standard deviation frontier for adjusted con2 ditional expected log returns (Et ri,t+1 + σ it/2) as a function of the conditional standard deviation of log returns, σ it, for an economy where asset prices are determined by a SDF Mt+1 (log SDF mt+1 ). What is the Sharpe ratio for the tangency portfolio? (c) (1.0 pt) Suppose a Consumption CAPM model where the representa1−γ P∞ ∗ C t+j . Suppose tive investor has utility given by Ut = Et j=0 e−r j 1−γ also that the log consumption growth is normal with mean µc and variance σc2. Draw the frontier of item b for this case. What is the Sharpe ratio for the tangency portfolio? How does it depend on risk aversion and volatility of consumption growth? 3. (2.0 pts) Campbell-Shiller approximations: (a) (1.0 pt) Let rw,t+1 be the log of return on a wealth portfolio which yields the consumption flow Ct as its dividend. Show that: rw,t+1 ≈ κ0 + κ1 zt+1 − zt + ∆ct+1    Ct+1 Pt where zt ≡ log C = log and ∆c t+1 Ct t 

(b) (0.5 pt) Show that zt ≈

∞ ∞ X X κ0 κ1j ∆ct+1+j − Et κ1j rw,t+1+j + Et 1 − κ1 j=0 j=0

(c) (0.5 pt) Interpret the equation in item b). Is it valid under irrational expectations? What kind of rationality is necessary for it to be valid? 4. (3.0 pts) Essay question. The three puzzles: equity premium, riskfree rate and volatility of equity returns (a) (1.0 pt) Describe the three puzzles. More specifically, what are the difficulties for the ability of standard consumption-based CAPM with power utility to fit the three moments: mean equity premium, mean riskfree rate and standard deviaton of equity returns? (b) (0.75 pt) How does the long-risk model of Bansal and Yaron (2004) solve the puzzles? What are the mechanisms? (c) (0.75 pt) How does the Campbell-Cochrane habit formation model solve the puzzles? What are the mechanisms? (d) (0.5 pt) Compare the two approaches: what are the advantages and drawbacks of each one?

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