GMU logo

Plan for Unit 3, Efficient Frontier
Complete Part Three of class project

You will estimate the efficient frontier of risky assets. You will learn Markowitz optimization using the excel solver.

Combining all risky assets (ETF). Efficient frontier of risky (only) assets.

Assume no short selling or using leverage is allowed. (What does this mean?)
  1. Compute the correlation matrix of the nine industry sector ETFs. What is the meaning of the correlations? Which industries do you expect to be most correlated? Why? Least correlated? Why? Now examine the correlations matrix. What does it show? What is the correlation on average? Which industries are most correlated? Which industries are least correlated?(40min)
  2. Compute the covariance matrix of the returns. What does the main diagonal represent? What do the off-diagonal elements represent? How would you describe the intuition behind these measures?(40min)
  3. Compute the expected return and standard deviation of a an equally weighted portfolio of the nine industries. Compare its return and standard deviation with the return and standard deviation of each of the nine industries. What can you tell about the effect of diversification?(30min)
  4. Perform efficient portfolio optimization using ten points on the efficient frontier (ten efficient portfolios). The first point should be the minimum variance portfolio. There will be no short positions. What is the highest return portfolio that you can achieve under this condition? What is its standard deviation? Determine eight equally spaced targets for returns (or standard deviations) between the minimum variance portfolio and the 'rightmost' portfolio on the frontier. Perform the efficient optimization.(60min)
  5. Plot the efficient frontier. For illustration, construct an equally weighted portfolio of the nine ETFs. Is it on the efficient frontier? Is the DIA ETF on the efficient frontier? Note: these results are in-sample; they compare expected returns and risk based on the same sample with which we did the optimization. Out-of-sample results will compare future returns and risk given the optimization based on the current sample. (60min)
  6. Individually, find (numerically) the optimal portfolio for you (the investor, i.e. the one that gives you the maximum utility). In other words, given your risk aversion, which of the portfolios on the ten frontier provides the best risk-return trade-off for you? (60min)
  7. What is your utility at this optimal risky portfolio? What are the allocations in the asset classes in this portfolio? (20min)
  8. On the graph of all risky efficient portfolios, plot your indifference curve which goes across your optimal risky portfolio. (40min)

Adding the risk-free asset to the set of risky portfolios. Overall optimal portfolio.

  1. Plot the new efficient frontier with the risk-free rate on it. Start a new graph, with all risky portfolios on it. (40min)
  2. What are the weights of the asset classes (industry ETFs) in the optimal risky portfolio? (30min)
  3. What is the return and standard deviation of the optimal Risky portfolio? (30min)
  4. What is the allocation in the risky asset in your (the investor's) overall optimal portfolio?(30min)
  5. What is your utility when you invest in the overall optimal portfolio? (20min)
  6. Put together the following summary, based on all the calculations you've done so far: Compare the utility that you had when you invested in(30min):

    1. Just one ETF.
    2. Just one ETF combined with the risk-free asset.
    3. A portfolio of all ETFs.
    4. A portfolio of all ETFs and the risk-free asset.