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a)- 3. Suppose that there is one riskless asset and one risky asset. The return on the risky asset is specified as follows: 0% with
a)- 3. Suppose that there is one riskless asset and one risky asset. The return on the risky asset is specified as follows: 0% with probability p and 20% with probability l-p. On the other hand, the risk free rate is 5%. Assume that you are an expected utility maximizer and your utility function is (x) with a > 0. You now have an 1-2 initial wealth of Wo, and by allocating Wo between the assets, you are trying to maximize the expected utility arising from the wealth at the end of the investment, ie fraction a invested in the risky asset and fraction (1-a) invested in the riskless asset. Now answer the following questions, Set up your optimization problem b Derive the first order condition of your optimization problem Show that the demand for the risky asset a.* does not depend on W. d Show that the demand for the risky asset a* is decreasing in 2. a)- 3. Suppose that there is one riskless asset and one risky asset. The return on the risky asset is specified as follows: 0% with probability p and 20% with probability l-p. On the other hand, the risk free rate is 5%. Assume that you are an expected utility maximizer and your utility function is (x) with a > 0. You now have an 1-2 initial wealth of Wo, and by allocating Wo between the assets, you are trying to maximize the expected utility arising from the wealth at the end of the investment, ie fraction a invested in the risky asset and fraction (1-a) invested in the riskless asset. Now answer the following questions, Set up your optimization problem b Derive the first order condition of your optimization problem Show that the demand for the risky asset a.* does not depend on W. d Show that the demand for the risky asset a* is decreasing in 2
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