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Intermediate Financial Theory Danthine and Donaldson Solutions to Problems CHAPTER I. 1.1. U is a utility function, i.e., U(x) > U(y) Û x ℏ y then f(U(x)) > f(U(y)) Û U(x) > U(y) Û x ℏ y 1.2. Utility function […]

CHAPTER 12. 12.1. a) Markets are complete. Find the state prices from 1q3 1.1 1 qqq 8q15q10q5 3 321 321     3/1q 02424.0q 55151.0q 3 2 1    b) The put option has a price […]

CHAPTER 13. 13.1. a.       06944.ln25.1ln5.44.1ln25.96.833.ln5.2.1ln5.96.1EU 2 b. The maximisation problem of the representative agent is   232322222121121211110232322222121121211110 232322222121 2 121211110 s.t. ))ln()ln()ln(())ln()ln(()ln(max cqcqcqcqcqceqeqeqeqeqe cccccc    (take consumption at date 0 as […]

CHAPTER 14. 14.1 a. .17 .07 .09 1.51.5 A C B i Er i b b. Using A, B ; we want BAAAP b)w1(bw0b  )1)(w1()5(.w0 AA  1w,2w;1w5. BAA  Using B, C : CCBBP bwbw0b  )5.1(w)1(w0 CB […]

CHAPTER 17. 17.1. a) These utility functions are well known. Agent 1 is risk-neutral, agent 2 is risk-averse. b) A PO allocation is one such that agent 2 gets smooth consumption. c) Given that agent 2 is risk-averse, he buys […]

CHAPTER 18. 18.1. The maximization problem for the speculator’s is:     fppcEUmax f* f Let us rewrite the program in the spirit of Chapter IV:       fppcUEfW f*  . The FOC […]

CHAPTER 3. 3.1. Mathematical interpretation: We can use Jensen’s inequality, which states that if f(.) is concave, then       XEfXfE  Economic interpretation: Under uncertainty, the important quantities are risk aversion coefficients, which depend on […]

CHAPTER 4. 4.1 Risk Aversion: (Answers to a), b), c), and d) are given together here) 0 Y 2 Y R 2R Y 2 R 0 Y 2 )Y(‘‘U 0 Y 1 )Y(‘U Y 1 )Y(U )1( 2 A R […]

CHAPTER 5. 5.1. For full investment in the risky asset the first order condition has to satisfy the following:       0rr ~ r ~ 1Y‘UE f0  ~ Now expanding    r 1Y‘U […]

CHAPTER 6. 6.1 Let 1  = 2  = 3  =  be the total risk common to every asset. For an equally weighted portfolio: P 22 i 3 1i 2 i 2 P;) 9 1 (3w  […]

CHAPTER 8. 8.1 A high  does not say anything about the level of diversification. The  speaks about the co-variations between the returns on an asset or a portfolio and the returns on the market 8.2 The CML describes […]

CHAPTER 9. 9.1. a) Given preferences and endowments, it is clear that the allocation {(4, 2, 2) ,(4, 2, 2)} is PO and feasible. In general, there is an infinity of PO allocations. b) Yes, but only if one of […]

CHAPTER 10. 10.1 a) The CCAPM is an intertemporal model whereas the CAPM is a one-period model. The b) The key contribution of the CCAPM resides in that the portfolio problem is indeed inherently intertemporal. The link with the real […]

CHAPTER 11. 11.1. a)   7424.0q 8224.0q 91.0q r1 1 q 3 2 1 i i i      b) The matrix is the same at each date. The n-period A-D matrix is then   […]