Identify the global minimum variance portfolio

Assignment Help Portfolio Management

Reference no: EM131473622

Assignemnt: Portfolio Optimization

I. You will find an Excel workbook called AssignmentData.xlsx which is needed to complete this assignment. It contains weekly index data for five asset classes and one in-dividual asset (Gold).

Due to the reputation of "Education Institution of America" for producing work-ready graduates, you are head-hunted by a small asset management company to work part- time as a portfolio manager whilst you complete your degree.

It is your first day on the job and your boss is keen to see how much you really know. She provides you with a list of five asset classes and tasks you and your team to investigate the e?cient asset allocation between these asset classes. Moreover, you are asked to satisfy a 17% expected return target on the portfolio you construct. To get started you decide to collect historical performance data for the last five years in order to estimate the expected return and variance-covariance structure of the asset classes (the data in the Excel file).

To perform the asset allocation you decide to construct a minimum variance portfolio. You recall the 17% expected return target imposed by your boss and note that there was no mention of short-selling constraints. In order to construct this portfolio you should copy the assignment data into an Excel workbook and perform the following tasks/answer the following questions:

1. (a) Transform the index values into simple weekly returns (you do not need to report these in your submission).

(b) Using the returns data, estimate (and report) the vector of expected returns for the five asset classes, as well as the variance-covariance matrix of these returns. These expected returns etc. should be annualized (i.e., in annual units).

(c) Report which of the asset classes are e?cient and which are ine?cient. For each of the ine?cient asset classes, find another asset class that dominates it.

(d) Compute and report the parameters A, B, C and .

(e) Construct and plot the MVS (with short sales allowed) for expected (annual) returns ranging between -10% and 35%. Your figure should also indicate the positions of the five asset classes.

(f) Identify the global minimum variance portfolio (MVP), i.e. report the portfolio weights (in the five asset classes), expected return, and variance of the MVP.

(g) Determine and report the portfolio weights for the e?cient portfolio with 17% expected return.

II. You are eager to impress so you send the results to your new boss just before you leave for your lunch break. Upon your return, the boss has looked at your report and notes that the risk of the portfolio is a little higher than she expected and wondered if adding an additional asset would help reduce the risk. Knowing all about diversification, you suggest that maybe adding an asset that has a low correlation with the existing five asset classes might help. "Gold!", your boss exclaims. You have heard many stories about gold being a great diversifier and so you offer to do the analysis again with the additional asset (gold) included in the portfolio. Using the additional gold index data in the Excel spreadsheet, perform the following tasks:

2. (a) Using the same methodology as in Question 1 (simple returns etc.), reconstruct the vector of (annual) expected returns and the variance- covariance matrix for the five asset classes plus gold (i.e., six assets in total).

(b) Compute and report the new A, B, C and parameters.

(c) Construct and plot the new MVS (with short sales allowed) for expected (annual) returns ranging between -10% and 35%. You should also plot the MVS from 1.(e) for comparison and indicate the positions of the five asset classes and gold.

(d) Identify the new global minimum variance portfolio (MVP), i.e. report the port- folio weights (in the six assets), expected return, and variance of the MVP.

(e) Determine and report the new portfolio weights for the e?cient portfolio with 17% expected return.

(f) Calculate and report the reduction in risk of the 17% returning e?cient portfolio that can be achieved by adding gold to the portfolio.

III. You inform your boss of these findings and she is happy with the addition of gold to the portfolio and the reduction in risk. However, she informs you that the 15% returning portfolio you have constructed is not as ‘e?cient' as it might be as you have forgotten all about the risk-free asset... oops! You quickly do some research and determine that the appropriate risk-free rate to use is 1% per annum. Perform the following tasks to adjust your portfolio weights:

3. (a) Construct and plot the MVS (with short sales allowed) for the five asset classes and gold plus the risk-free asset paying 1%.

(b) Identify the tangency portfolio, i.e. report its portfolio weights, expected return, and variance of returns. Furthermore, illustrate its tangency property graphically by plotting the MVS from 2.(c) on the same set of axes.

(d) Calculate and report the reduction in risk of the 17% returning e?cient portfolio that can be achieved by adding the risk-free asset bond to the portfolio of six risky assets.

IV. A little embarrassed from your mistake of not including the risk-free asset, you send the new updated results to your boss at 4:50pm. She is impressed with your e?ciency as well as the e?ciency of the portfolio. However, she hasn't quite finished with you just yet! She is worried about the need to short sell certain asset classes in the currently proposed portfolios. Many of the firm's clients do not like, and some do not allow, short selling in their portfolios. Therefore, your boss wants you to investigate the effect a no short sales constraint will have on the MVS without a risk-free asset and any subsequent investment decisions. To do this you are asked to perform the following tasks:

4. (a) Construct and plot the risky asset only MVS with no short sales allowed for the five asset classes plus gold. (Recall you will need Solver to do this.)

(b) Plot the MVS for the unconstrained problem-found in 2.(c)-on the same set of axes. Also, indicate the positions of the five asset classes plus gold.

(d) Identify and report the range of expected returns for which the short sales con-straint is not binding.

(e) Discuss the compositions of the portfolios at the end-points of the MVS with no short sales.

Attachment:- Assignment_Data.rar

Reference no: EM131473622

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