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If the two states were of equal probability agent 1 would have a bit less need to smooth, and thus intrmediate demand would be relatively smaller.

To show this note that the expected return on the portfolio is constant independently of the chosen allocation. The CCAPM makes a full investors homegeneity assumption but does not require specific utility functions.

EconPapers: Intermediate Financial Theory

Both models lead to a linear relationship explaining expected returns on individual assets and portfolios. Massachusetts Institute of Technology. The answer to a indicates we should care since complete markets are required to guarantee that a Pareto optimal allocation is reached. This example has these features.

The implied allocations are thus: Both models would be compatible if the market portfolio were simply another way to synthesize the several factors identified by the APT: However, the outcome is very different: So we have to compute these data from the sample statistics that we are given.

Agent 2, however, will receive lower prices — either way — for the securities he issues. Also, logarithmic utility function is DARA. Since there are 2 units invested in total, 2x is invested in technology 1.

Solutions to Exercises

At that price, check that the demand for asset Q by agent 1 is zero: Graphically this corresponds to the fact that in Fig 3. The return on the market portfolio could be one of them, however.


The premium is slightly bigger in scenario B, while it is a lot higher in C. So the answer are: We need to find the proportions of A and C that give the same b as asset B. Note that this reasoning is generic as long as the futures price is below the cost of production. In more general contexts, these payments may have distortionary effects. Solving the program for agent 1 gives the following FOC: A-D security from calls: These issues are at the heart of many political discussions in a world where redistribution across agents is not costless.

A-D pricing focuses on the concept of states of nature and the pricing of future payoffs conditional on the occurrence of specific future states. The valuation of the endowment stream is price space 2.

MRS is constant when the utility function is linear additive that is, the indifference curve is also linear: While in the former the key information is the price of one unit of consumption good in a specific future date-state, in the latter the key ingredient extracted from observed prices is the expected excess return obtained for bearing one unit of a specified risk factor.

Under uncertainty, the important quantities are risk aversion coefficients, which depend on the first and second order derivatives. Business Finance Solutions to Exercises advertisement. The allocation is Pareto optimal, as expected from the fact that markets are now complete. Given the value of the optimal z, the FOC wrt y can be written as: 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.


If these redistributive payments and taxes are lump-sum transfers, they will not affect the decisions of individuals, nor the pricing of the security.

As a consequence, the increase in price may well lead to a fully rational increase in demand. The APT opens up the possibility that more than one factor are priced in the market financiaal are thus necessary to explain returns. For example, the allocations below are both Pareto optimal: Now only 1,0 is traded.

He thus chooses to diversify. 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. The figure shows excess demand for good 2 and excess supply for good 1, a situation which requires p2 to increase and p1 to decrease to restore market clearing.

Of course, the riskneutral probabilities are the same as in b.

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From the viewpoint of social welfare there seems to be no argument not to search for the realization of a Pareto Optimum. Moreover if the investor cares only about the first two moments he will invest equal amounts in the assets to minimize variance.

In that sense the law of demand does not apply in such a context.