H Consider an individual facing the prospect of having high income, yí > 0, with probability and low income, yɩ, with probability 1 — T, YH > YL. Prior to learning whether realized income is high or low, the individual is able to go into the market and purchase (or sell) two types of assets. Let the Asset 1 have a return structure such that it pays R₁, units of goods if y = yн and pays R₁,1 units of goods if y = yL. Similarly, let Asset 2 have a return structure such that it pays R₂,è units of goods if y = yí and pays R₂,L units of goods if y = y₁. The individual is endowed with w units of wealth to spend in the asset market but this wealth is not storable and hence cannot be save to purchase consumption goods. Denote by a₁ the amount of Asset 1 purchased by the individual and a2 the amount of Asset 2 purchased by the individual. The individual's problem is to maximize the expected utility from consumption sub- ject to the constraints that consumption must be financed out of income and the realized return from the asset portfolio as well as a constraint that spending on the asset portfolio must be financed out of the non-storable endowment wealth w. Consumption and portfolio spending satisfies the following constraints, Yн + R₁,Hª₁ + R₂,Hª2 YL + R₁,Lª₁ + R₂, La2 a₁ + a₂. Note that a₁ and a2 can be positive (purchase) or negative (sell). CH = CL = W = (1) (3)
H Consider an individual facing the prospect of having high income, yí > 0, with probability and low income, yɩ, with probability 1 — T, YH > YL. Prior to learning whether realized income is high or low, the individual is able to go into the market and purchase (or sell) two types of assets. Let the Asset 1 have a return structure such that it pays R₁, units of goods if y = yн and pays R₁,1 units of goods if y = yL. Similarly, let Asset 2 have a return structure such that it pays R₂,è units of goods if y = yí and pays R₂,L units of goods if y = y₁. The individual is endowed with w units of wealth to spend in the asset market but this wealth is not storable and hence cannot be save to purchase consumption goods. Denote by a₁ the amount of Asset 1 purchased by the individual and a2 the amount of Asset 2 purchased by the individual. The individual's problem is to maximize the expected utility from consumption sub- ject to the constraints that consumption must be financed out of income and the realized return from the asset portfolio as well as a constraint that spending on the asset portfolio must be financed out of the non-storable endowment wealth w. Consumption and portfolio spending satisfies the following constraints, Yн + R₁,Hª₁ + R₂,Hª2 YL + R₁,Lª₁ + R₂, La2 a₁ + a₂. Note that a₁ and a2 can be positive (purchase) or negative (sell). CH = CL = W = (1) (3)
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
Transcribed Image Text:Consider an individual facing the prospect of having high income, YH > 0, with
probability 7 and low income, YL, with probability 1 – T, YH > YL. Prior to learning
whether realized income is high or low, the individual is able to go into the market and
purchase (or sell) two types of assets. Let the Asset 1 have a return structure such that
it pays R1.H units of goods if y = YH and pays R1,L units of goods if y = YL. Similarly,
let Asset 2 have a return structure such that it pays R2.H units of goods if y = YH and
pays R2,L units of goods if y
to spend in the asset market but this wealth is not storable and hence cannot be save
to purchase consumption goods. Denote by a1 the amount of Asset 1 purchased by the
individual and az the amount of Asset 2 purchased by the individual.
The individual's problem is to maximize the expected utility from consumption sub-
ject to the constraints that consumption must be financed out of income and the realized
return from the asset portfolio as well as a constraint that spending on the asset portfolio
= YL. The individual is endowed with w units of wealth
must be financed out of the non-storable endowment wealth w.
Consumption and portfolio spending satisfies the following constraints,
Ун + Ri,нај + Rz, H@2
YL + R1,La1 + R2,La2
(1)
(2)
(3)
CH
CL
ai + a2.
Note that aj and az can be positive (purchase) or negative (sell).
Transcribed Image Text:Given these three cases, which case is the asset return structure incomplete and
with of these three cases are examples of complete asset return structures?
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