You will estimate the efficient frontier of risky assets.
You will learn Markowitz optimization using the excel solver.
Plan for Unit 3, Efficient Frontier
Complete Part Three of class project
Combining all risky assets (ETF). Efficient frontier of risky
Assume no short selling or using leverage is allowed. (What does this
- 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
- 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)
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)
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)
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)
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)
What is your utility at this optimal risky portfolio? What are the
allocations in the asset classes in this portfolio? (20min)
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
Plot the new efficient frontier with the risk-free rate on it. Start
a new graph, with all risky portfolios on it. (40min)
What are the weights of the asset classes (industry ETFs) in the
optimal risky portfolio? (30min)
What is the return and standard deviation of the optimal Risky
What is the allocation in the risky asset in your (the investor's)
overall optimal portfolio?(30min)
What is your utility when you invest in the overall optimal
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):
- Just one ETF.
- Just one ETF combined with the risk-free asset.
- A portfolio of all ETFs.
- A portfolio of all ETFs and the risk-free asset.