3. The returns in an economy are given by rj = 0; + Bjf+aj for j= 1,...,J. In addition, there is a risk free security. The random variables (1,...ai) are i.i.d normal random variables with zero mean and standard deviation, o. The random variable f is a standard normal random variable, and is independent of the e's. Derive the amount invested in a typical security j by an investor with constant absolute risk aversion preferences (risk aversion p) and wealth was a function of the a's, B's, o, w, p and the risk free rate. a. Show that the proportion (of wealth invested in risky securities) invested in each security is independent of p. b. Show that a greater than the risk free rate is neither necessary nor sufficient for the optimal amount invested in the jth security to be positive (for example, consider two risky securities). 3. The returns in an economy are given by rj = 0; + Bjf+aj for j= 1,...,J. In addition, there is a risk free security. The random variables (1,...ai) are i.i.d normal random variables with zero mean and standard deviation, o. The random variable f is a standard normal random variable, and is independent of the e's. Derive the amount invested in a typical security j by an investor with constant absolute risk aversion preferences (risk aversion p) and wealth was a function of the a's, B's, o, w, p and the risk free rate. a. Show that the proportion (of wealth invested in risky securities) invested in each security is independent of p. b. Show that a greater than the risk free rate is neither necessary nor sufficient for the optimal amount invested in the jth security to be positive (for example, consider two risky securities)