Please explain qu1 and the concept behind the CARA function (a) What characterizes a CARA utility function? Give an example of such a utilityfunction and show why it is displays CARA.(b) It can be shown that an investor with a CARA utility function who faces normallydistributed risk has preferences represented by:aE [u(w)] = E [w] - Var [w]2where w is wealth and a is a risk-aversion parameter. Suppose the investorsoriginal wealth is given by wo and that there is a risky asset with rate of returndistribution r~ N(µ, σ²). There is also a risk-free asset with a rate of return rf.The investor seeks to allocate x to the risky asset and wo x to the risk-free one.What is the expected wealth and its variance resulting from this allocation?(c) Find the optimal allocation x* and discuss how it depends on the model parame-ters.

The utility function measures the consumer's satisfaction as a consumption function of real goods,…

Answered: (a) What characterizes a CARA utility…

(a) What characterizes a CARA utility function? Give an example of such a utility function and show why it is displays CARA.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

Please explain qu1 and the concept behind the CARA function

(a) What characterizes a CARA utility function? Give an example of such a utility
function and show why it is displays CARA.
(b) It can be shown that an investor with a CARA utility function who faces normally
distributed risk has preferences represented by:
a
E [u(w)] = E [w] - Var [w]
2
where w is wealth and a is a risk-aversion parameter. Suppose the investors
original wealth is given by wo and that there is a risky asset with rate of return
distribution r~ N(µ, σ²). There is also a risk-free asset with a rate of return rf.
The investor seeks to allocate x to the risky asset and wo x to the risk-free one.
What is the expected wealth and its variance resulting from this allocation?
(c) Find the optimal allocation x* and discuss how it depends on the model parame-
ters.

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