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1 ECMT2130 - 2021 semester 1 mid-semester exam 2 solutions

Author: Geoﬀ Shuetrim

1. (0 points) Portfolio optimisation data

Andrew is able to invest in 4 risky assets. Using a sample of data he has estimated the average simple monthly rates of return and the variances/covariances of those simple monthly rates of return for the various risky assets.

His estimates are contained in columns A to N of this Excel spreadsheet (supplied separately), along with the correlation matrix implied by the variance and covariance estimates. He has also included CAPM Beta estimates for each of the assets.

Use the information in the spreadsheet to answer the following related questions in your exam. Use the spreadsheet to perform the necessary calculations. Document the calculations clearly in the spread- sheet by placing informative labels next to cells that contain important formulae to ensure that your calculations are easy to review.

Upload your ﬁnal Excel spreadsheet, with all of the original data, and your calculations for related exam questions, as part of your response to the following question. The spreadsheet formulae and solver conﬁguration will be reviewed as part of assessing your marks for the parts of question 2 involving optimisation calculations.

Solution:

Question 1 just supplies data for question 2.

2. (15 points) Andrew’s portfolio optimisation analysis Answer this question using the data from question 1.

If you use the Microsoft Excel solver for parts A and C (and you should), then add a worksheet to the Spreadsheet and set up the solver twice, once in each of two worksheets, so that markers can see the way that you have set up the solver for both parts of this question. You will need to create your own new column of weights in the new worksheet when you set up the solver to answer part C.

(a) (5 points) As a percentage, what is the standard deviation of the return on a fully invested portfolio of risky assets that minimises risk while achieving an expected simple monthly rate of return of 2.5% (0.025)? A fully invested portfolio involves all wealth being invested.

(b) (5 points) As a percentage, what is the standard deviation of the return on a zero investment portfolio of risky assets that minimises risk while achieving an expected simple monthly rate of return of 2.5% (0.025)? A zero investment portfolio involves no net wealth being invested.

(c) (1 point) Explain the diﬀerence between the standard deviation of the return on the optimal port- folio for part A and the standard deviation of the return on the optimal portfolio for part B.

(d) (2 points) Is the optimal portfolio in part A on the eﬃcient frontier? Explain your answer. (e) (2 points) Is the optimal portfolio in part B on the eﬃcient frontier? Explain your answer.

Solution:

(a) (5 points) The standard deviation of the return on a fully invested portfolio of risky assets that minimises risk while achieving an expected simple monthly rate of return of 2.5% is 9.6%? See the Excel solution for details of the problem and solver conﬁguration.

(b) (5 points) The standard deviation of the return on a zero investment portfolio of risky assets that minimises risk while achieving an expected simple monthly rate of return of 2.5% is 11.3%? See the Excel solution for details of the problem and solver conﬁguration.

(c) (1 point) To achieve the high expected returns, the optimal portfolios in A and B both short asset 3 to take a big position in asset 4. The standard deviation of the return on the optimal portfolio for part A is lower than the standard deviation of the return on the optimal portfolio for part B because, for portfolio B to achieve the same expected return as portfolio A, it has to use additional leverage, making the positions in the two highest-return and highest standard deviation assets more extreme. This is because, without investing any funds, all expected returns on the portfolio need to be achieved through expected return diﬀerentials across assets.