1. In a world where security prices are jointly normally distributed, rational investors who are risk averse will choose an optimal portfolio from those along an efficient frontier. In other words, given a choice of two portfolios with the same level of expected return, they will choose the portfolio with the lowest standard deviation  a. In the absence of a risk free-security, explain the relationship between an investor's level of risk aversion and the optimal portfolio they would choose on the efficient frontier given classic Modern Portfolio Theory (MPT). (4 marks)  b. In the presence of a risk free-security, explain the relationship between an investor's level of risk aversion and the optimal portfolio they would choose on the efficient frontier given classic MPT. (4 marks)  c. In the absence of a risk free-security, explain how an investor's choice of an optimal portfolio might differ from that in Question 1.a, given "Goals based" behaviour similar to that described by Das et al(2018). (4 marks)

a. In the absence of a risk-free security, the relationship between an investor's level of risk aversion and the optimal portfolio they would choose on the efficient frontier, according to classic Modern Portfolio Theory (MPT), is inversely proportional. This means that the more risk averse an investor is, the less risk they are willing to take on, and therefore, they would choose a portfolio on the efficient frontier that has a lower standard deviation (i.e., lower risk). Conversely, an investor with a lower level of risk aversion is willing to take on more risk for the potential of higher returns, and would therefore choose a portfolio on the efficient frontier with a higher standard deviation.

b. In the presence of a risk-free security, the relationship between an investor's level of risk aversion and the optimal portfolio they would choose on the efficient frontier changes. According to classic MPT, an investor can now form a combination of the risk-free asset and a portfolio on the efficient frontier, creating a capital market line (CML). The investor's level of risk aversion will determine where on the CML they will choose to invest. More risk averse investors will choose to invest more in the risk-free asset and less in the risky portfolio, while less risk averse investors will invest more in the risky portfolio and less in the risk-free asset.

c. In the absence of a risk-free security, an investor's choice of an optimal portfolio might differ from that in Question 1.a, given "Goals based" behaviour similar to that described by Das et al(2018). This is because goals-based investing focuses on achieving specific financial goals rather than maximizing returns for a given level of risk. Therefore, an investor's choice of portfolio would be influenced more by their individual goals and less by their level of risk aversion. For example, an investor with a goal to save for a down payment on a house in five years might choose a portfolio with lower risk and lower expected return, even if they are not particularly risk averse, because they cannot afford to lose their investment.