(a) What characterizes a CARA utility function? Give an example of such a utility function and...

 

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(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: 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(, 2). 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. (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: 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(, 2). 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.