Question

1. Suppose you are able to borrow or lend limitless amounts of at a certain rate of interest. Illustrate and explain the implications for the efficient frontier, and also for portfolio selection decisions where investors have the same information but differing degrees of risk aversion. No calculations are necessary in this section.   

2. Suppose the rate of interest on borrowing is higher than the rate of interest at which you can lend. Illustrate and explain the implications for the efficient frontier, and also for portfolio selection decisions where investors have the same information but differing degrees of risk aversion. No calculations are necessary in this section.

3. With reference to your research

(i)         Suggest one additional way in which your frontiers could be made more efficient.                                                  

(ii) Identify one key limitation of your analysis.     

Answer 1

1. The efficient frontier is the set of optimal portfolios, expected to return high for a given level of risk. that means with different levels of risk we are going to get different rates of return.  Portfolios that lie below the efficient frontier are sub-optimal because they do not provide enough return for the level of risk. here the question has given the freedom on the amount of borrowing and lending at a given rate of interest. so this information is symmetric to all the borrowers or lenders. this is known as a modern theory of Portfolio.  Profits can be maximized by selecting an efficient portfolio that is also an optimal portfolio.   portfolios can consist of any number of assets with differing proportions of each asset, there is a wide range of risk-return ratios. If we plot all the sets of risk-return possibilities on the graph then it will give the investment opportunity set. the X-axis is portfolio risk and Y-axis is expected portfolio return. combining all efficient set it will give us efficient frontier. The efficient frontier can be combined with an investor's utility function to find the investor's optimal portfolio, the portfolio with the greatest return for the risk that the investor is willing to accept. In figure 1 the investor want to be on the efficient frontier line to get the best for their risk-taking attitude.

2. When the rate of borrowing is more than the rate of interest for lending then the borrower wnt to be nearer to the minimum variance portfolio point. However, there are many possible portfolios on many risk-indifference curves that do not yield the highest return for a given risk. All of these portfolios lie below the efficient frontier. The optimal portfolio is a portfolio on the efficient frontier that would yield the best combination of return and risk for a given investor, which would give that investor the most satisfaction. The high rate of borrowing shows a high level of risk, so there is an expectation from the borrower side to get high returns as the borrowing person ready to pay a high. the risk-averse investor is always trying to be on the efficient frontier with the optimal use of his investment with an optimal tolerance level of risk. the lending rate is low as the risk related to the lending investor is comparatively low or neutral so chances of risk are low and it is nearer to minimum variance portfolio.

3.i) A frontier can be efficient when it is tangent to the capital market line. this tangent point will be the best point for a frontier to invest.

ii) here the most important limitation is the perfect information. the other limitation is the availability of options with the investors is limited so his choice is also limited with less information.