Intermediate Financial Theory. Book • 3rd Edition • Authors: Jean-Pierre Danthine and John B Donaldson. Browse book content. About the book. Search in. By Jean-Pierre Danthine and John B. Donaldson; Abstract: Targeting readers with backgrounds in economics, Intermediate Financial Theory, Third Edition. Buy Intermediate Financial Theory (Academic Press Advanced Finance) on by Jean-Pierre Danthine (Author), John B. Donaldson (Author).
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Documents Flashcards Grammar checker. Business Finance Solutions to Exercises advertisement. U is a utility function, i. Utility function U c 1c 2: Apply the chain rule for derivatives: When an agent has very little of one given good, he is willing to give up a big quantity of another good to obtain a bit more of the first.
MRS is constant when the utility function is linear additive that is, the indifference curve is also linear: Convex preferences can exhibit indifference curves with flat spots, strictly convex preferences cannot.
The utility function is not strictly quasi-concave here. Pareto set is the lower side and the right side of the box, or the upper side and the left side, depending on which MRS is higher. The problem of the agents is MaxU j s. Now we insert this ratio into the budget constraints of agent 2. This expression can be interpreted as p1 a demand function.
The remaining demand functions can be obtained using the same steps.
The after-trade MRS and utility levels are: This is not a surprise gheory the new utility function is a monotone transformation logarithm of the utility function used originally. The agents will make the same maximizing choice with both utility functions, and the utility level has no real meaning, beyond the statement that for a given individual a higher untermediate level is better. Since the maximizing conditions are the same as those obtained in a -c and the budget constraints are not altered, we know that xanthine equilibrium allocations will be the same too so is the price ratio.
Recall that in equilibrium there should not be excess demand or excess supply for any good in the economy. If there is, then prices change accordingly to restore the equilibrium. The figure shows excess demand for good 2 dohaldson excess supply for good 1, a situation which requires p2 to increase and p1 to decrease to restore market clearing. We can use Jensen’s inequality, which states that if f. Under uncertainty, the important quantities are risk aversion coefficients, which depend on the first and second order derivatives.
If we apply a non-linear transformation, these quantities are altered.
Indeed, R A f U. Lottery L is preferred to donadson ”sure lottery” P. Again, L is preferred to P under transformation f. P is preferred to L under transformation g.
Yes, in a non-expected utility world where there is a preferences for gambling. Yes, also, in a world where non-rational agents might be confused by the different contexts in which they are requested to make choices.
Intermediate Financial Theory
By definition, for a concave function f. We check it with the derivative of RA and RR w. The problem to be solved is: However, the outcome is very different: The premium is slightly bigger in scenario B, while it is a lot higher in C. This could have been expected because the logarithmic utility function is very curved at low values, theoty flattens out rapidly, i.
Also, logarithmic utility function is DARA. All individuals with increasing utility functions prefer A to B. Of course, any risk averse agent would prefer x A. Only two moments of a distribution are relevant for comparison: Agents like the former and dislike the latter.
Thus, given two distributions with the same mean, the one with the higher variance is less desirable; similarly, given two distributions with the same variance, the one with the greater mean return is preferred.
Thus, mean-variance dominance does not imply FSD. The certainty equivalent is defined by the equation: The insurance policy guarantees the expected payoff: The most the agent would be willing to pay is 1. As a result, the premium, as measured in probability terms, is less. Reworking the data of Table 3.
EconPapers: Intermediate Financial Theory
Graphically this corresponds to the fact that in Fig 3. State by state dominance: For full investment in the risky asset the first order condition has to satisfy the following: Take the total differential of the F. We will divide the set of risky realizations into two sets: Now we will use these observations.
This result means that the investor is going to invest in both securities — it is never optimal in this situation to invest only in one of the two assets. He thus chooses to diversify. Moreover if the investor cares only about the first two moments he will invest equal amounts in the assets to minimize variance. To show this note that the expected return on the portfolio is constant independently of the chosen allocation.
A mean-variance investor will thus choose a to minimize the variance of 16 the portfolio. We would expect s. But it does not say anything about the degree of diversification of a portfolio.
Solutions to Exercises
For an equally weighted portfolio: Without loss of generality consider asset 1. For arbitrary assets that have the same statistical characteristics as M i. The CAPM tells you to equate the expected return on the loan equal to rf. Since there is some probability of default, you must set the rate higher than rf in order to insure an expected return equal to rf.
There are two ways to solve it. The basis for answering this question is the following: Under what circumstances will the risk go down? So we have to compute these data from the sample statistics that we are given.
So the answer are: These are, in fact, two ways of asking the same questions. How could it be? This is true in particular because one would expect the risk free rate to be lower, as the demand for the risk free asset should be higher, and the return on the optimal risky portfolio to be higher, as the more risk averse investors require a higher compensation for the risk they bear. Note, however, that the Markovitz model is not framed to answer such a question explicitly.
If we imagine, as in this question, a change in the primitives of the economy, we have to turn to our intuition to guess how these given returns would differ in the alternative set of circumstances.
The model does not help us with this reasoning. For such fundamental questions, a general equilibrium setting will prove superior. If the risk free rate was constant, this would guarantee that the slope of the CML would be lower in the economy, and the reward for risk taking lower as well. This appears counter-intuitive — with less diversification opportunities those who take risks should get a higher reward —, an observation which suggests that the risk free rate should be lower in the higher correlation economy.
Solutions to Exercises
Refer to our remarks in the solution to 6. If investors hold homogeneous expectations concerning asset returns, mean returns on risky assets -per dollar invested- will be the same. Otherwise they would face different efficient frontiers and most likely would invest different proportions in risky assets. Moreover, the marginal rate of substitution between risk and return would depend on the level of wealth.
Apply this result to the R. We can intdrmediate equation 3 as: Let w j be the proportion of economy hteory wealth invested in asset j.
The matrix is the same at each date. It is determined by three considerations: We determine a term structure for each initial state.
In general, there is an infinity of PO allocations. In general one security is not sufficient to complete the markets when there are two future states. Agents will be happy to store the commodity for two reasons: For these two reasons, storing will enable them to increase their utility level. Remember aggregate uncertainty means that the total quantity available at date 2 is not the same for all the states.
If one agent is risk-neutral, he will however be willing to bear all the risks. Provided enough trading instruments exist, the consumption of the risk-averse agent can thus be completely smoothed out and this constitutes a Pareto Optimum.
Because of the variance term diminishing utility, consumption should be equated across states for each agent. There are many Pareto optima.