1. The goal of this exercise is to understand the role of correlation in the risk-return tradeoff.
Assume there are two risky securities with the following characteristics. E(r1) = 20%, σ1 = 25%, E(r2) = 6%, and σ2 = 10%. Compute the risk and return for portfolios in the investment opportunity set assuming the correlation coefficient between the returns of these securities is: (a) -1 (b) -0.5 (c) 0 (d) 0.5 (e) 1. Start with -50% in security 1 and go up to 150% in security 1 in increments of 5%. Draw the following 3 graphs and please make sure that the axes are marked clearly and all the lines are marked clearly in the graphs.
a) Expected return of the overall portfolio as a function of the weight in the riskier security. Please show the results for all 5 values of correlation in a single graph. If all the 5 lines are the same, then explain why this is so. If all the 5 lines are different, then also explain why this is so.
b) Standard deviation of the overall portfolio as a function of the weight in the riskier security. Please show the results for all 5 values of correlation in a single graph. What should be the correlation if the line is to be straight? Intuitively explain why this is so. Is it possible to reduce portfolio risk to zero? If so, what should be the correlation? What return do you think that this portfolio with standard deviation of zero will earn?
c) Expected return of the overall portfolio as a function of standard deviation of the overall portfolio. Please show the results for all 5 values of correlation in a single graph.
2. The goal of this exercise is to construct the optimal risky portfolio for a passive investor with no stock-picking skills.
There are many securities traded in the market place. To form the investment opportunity set, we have to consider all possible portfolios: all 1-asset portfolios, all 2-asset portfolios, 3-asset portfolios, 4-asset portfolios….I have given various 3-asset portfolios, where the three assets are different for each portfolio. The means (in % per year), standard deviations (in % per year), and correlation coefficients between asset returns are also given. Please download this data from BB-Vista.
Do the following:
a) Compute the mean and standard deviation for all the portfolios.
b) Draw a scatter plot of all the portfolios (investment opportunity set) on a mean-standard deviation graph
c) Highlight the minimum variance frontier based on these results. In Excel, you can use the following tool: Insert àShape à Scribble to draw the minimum variance frontier in free form.
d) Highlight the efficient frontier based on these results. Use the tol described above to highlight the efficient frontier.
e) Which portfolio has the minimum variance?
f) Which portfolio has the highest expected return?
g) Are the minimum variance and highest expected return portfolios identified in the above two steps part of the efficient frontier? Explain the result intuitively.
h) If the current risk free rate = 2% per year, which of the risky portfolios is optimal? Draw the capital allocation line. Circle the optimal risky portfolio in the graph clearly.
|Due By (Pacific Time)
||10/11/2015 12:00 am