3. (a) What characterizes a CARA utility function? Give an example of such a utility function. (b) It can be shown that an investor with a CARA utility function who faces normally distributed risk has preferences represented by: E lu(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 w and that there is a risky asset with rate of return distribution r ~ N(p, o'). There is also a risk-free asset with a rate of return r. The investor seeks to allocate r to the risky asset and w - x to the risk free one. What is the expected wealth and its variance resulting from this allocation? (c) Find the optimal allocation r* and discuss how it depends on the model parame- ters