Learning Outcomes. After watching this video, you will be able to understand the difference between the mean-variance frontier and the efficient frontier. Define the minimum variance portfolio, that is, MVP. Diversification and efficient frontier. In the last video, we saw what happens when we combined two risky assets into a portfolio. We saw specifically that for some combination of X and Y, the standard deviation of the portfolio is lower than the individual standard deviations of X and Y. This is the idea of diversification. In this video, we will discuss the idea of diversification in a little more detail and introduce the concept of efficient frontier. Let's revisit the picture from last class. Look at the black line when the correlation is plus 1. In this case, the standard deviations of all combinations of X and Y are always greater than that of asset X. This shows that diversification is not possible when the assets' returns are perfectly positively correlated. Diversification is possible only when asset returns are less than perfectly positively correlated, that is, rho is less than plus 1. Next, look at the pink curl when the correlation between asset returns is a negative 1. There is one point where the curve touches the vertical axis. At this point, the risk is zero. This says when there is perfect negative correlation between two assets returns, one particular combination of two risky assets is riskless. In other words, this combination completely diversifies away all risk. Let's extend the 2 risky asset case to 3 risky assets by adding under the risky asset Z. The expected return standard deviation for X are still 10% and 7% respectively. The numbers for Y are at 20% and 10% respectively, and those for Z are now 15% and 12% respectively. We're also given that the correlation between X and Y's returns is 0.1, that between X and Z is zero, and that between Y and Z is 0.9. First, let's plot the investment opportunity set for each pair of investments. The blue curve is for X and Y, the green curve is for Y and Z, and the pink one is for X and Z. With each pair of risky assets, the investment opportunity set is just a curve or a line. What if we look at investing in all three assets at the same time? Then the investment opportunity set is a whole area. In the picture, this is the entire area within the black curve. Each point within this are represents a possible combination of X, Y, and Z. The black curve is called the mean variance frontier and plots the optimal combinations of X, Y and Z. What does optimal combination of X, Y, and Z mean? The mean variance frontier joins portfolios of X, Y, and Z that yield the least risk at each level of expected return. Another way of looking at optimal combinations is what is the maximum expected return at each level of risk. Looking at the optimal combinations this way at each level of risk, the expected return on the top part of the mean variance frontier is always greater than the expected return on the bottom part of the mean variance frontier. In other words, the top part always dominates the bottom part. If we exclude the bottom part of the mean variance frontier, the top part is called the Efficient Frontier. It maximizes the expect return at each level of risk and minimizes risk at each level of expected return. In terms of risk return combinations, no risk return combination to the left of or above the efficient frontier is feasible. An important point to note the portfolio called MVP. It stands for the Global Minimum Variance Portfolio. Using X, Y and Z, this is the one portfolio that has the least variance or risk across all port folios in the investment opportunity set. Given risky asset, X,Y and Z, no combination of this assets will help us achieve a lower risk. In our example of 3 risky assets, how do we determine the efficient frontier? We will talk about two-fund separation and how it may be used to draw the efficient frontier next time.
