QUESTION 1

The following data is provided: Monthly returns which include those for three assets classes for the six-year period to the end of December 2013.

Date SA Equity SA Bond SA Cash 31-Jan-08 -5.6% -0.5% 1.0% 29-Feb-08 12.5% -0.8% 0.8% 31-Mar-08 -3.0% -0.5% 0.9% 30-Apr-08 4.2% -0.7% 0.9% 31-May-08 3.7% -2.5% 0.9% 30-Jun-08 -4.4% -1.7% 0.9% 31-Jul-08 -8.7% 8.5% 1.1% 31-Aug-08 0.3% 1.3% 0.9% 30-Sep-08 -13.2% 2.4% 1.0% 31-Oct-08 -11.6% -0.5% 1.0% 30-Nov-08 1.3% 4.6% 0.9% 31-Dec-08 1.5% 6.9% 1.0% 31-Jan-09 -4.2% -2.4% 0.9% 28-Feb-09 -9.9% -2.9% 0.8% 31-Mar-09 11.0% 0.0% 0.9% 30-Apr-09 1.6% 1.0% 0.8% 31-May-09 10.3% -0.4% 0.7% 30-Jun-09 -3.1% -0.2% 0.7% 31-Jul-09 10.1% 1.3% 0.7% 31-Aug-09 3.2% 1.6% 0.7% 30-Sep-09 0.2% 0.1% 0.6% 31-Oct-09 6.0% -0.2% 0.6% 30-Nov-09 2.1% 0.1% 0.6% 31-Dec-09 2.9% 1.2% 0.6% 31-Jan-10 -3.5% 0.3% 0.6% 28-Feb-10 0.4% 2.0% 0.6% 31-Mar-10 7.9% 2.1% 0.6% 30-Apr-10 -0.1% 1.3% 0.6% 31-May-10 -5.1% -0.4% 0.6% 30-Jun-10 -3.2% 0.3% 0.6% 31-Jul-10 8.0% 4.1% 0.6% 31-Aug-10 -3.6% 3.0% 0.6% 30-Sep-10 8.7% 0.8% 0.5% 31-Oct-10 3.6% 1.0% 0.5% 30-Nov-10 -0.5% -2.0% 0.5% 31-Dec-10 6.2% 1.7% 0.5% 31-Jan-11 -2.2% -2.1% 0.5% 28-Feb-11 2.8% 0.1% 0.4% 31-Mar-11 0.5% 0.5% 0.5% 30-Apr-11 2.2% 2.3% 0.4% 31-May-11 -0.8% 1.4% 0.5% 30-Jun-11 -2.0% 0.2% 0.5% 31-Jul-11 -2.0% 1.5% 0.4% 31-Aug-11 -0.3% 3.5% 0.5% 30-Sep-11 -3.6% -2.1% 0.5% 31-Oct-11 9.3% 2.8% 0.5% 30-Nov-11 1.6% 0.0% 0.5% 31-Dec-11 -2.4% 0.7% 0.5% 31-Jan-12 5.7% 2.1% 0.5% 29-Feb-12 1.7% 0.2% 0.4% 31-Mar-12 -1.4% 0.1% 0.5% 30-Apr-12 2.8% 1.8% 0.5% 31-May-12 -3.6% 0.0% 0.5% 30-Jun-12 1.9% 3.3% 0.4% 31-Jul-12 2.7% 4.0% 0.5% 31-Aug-12 2.7% 0.1% 0.5% 30-Sep-12 1.6% 0.9% 0.4% 31-Oct-12 4.2% -0.6% 0.5% 30-Nov-12 2.6% 0.9% 0.4% 31-Dec-12 3.2% 2.3% 0.4% 31-Jan-13 3.2% 0.1% 0.4% 28-Feb-13 -1.9% 0.7% 0.4% 31-Mar-13 1.2% 0.2% 0.4% 30-Apr-13 -2.5% 4.1% 0.5% 31-May-13 8.5% -4.6% 0.4% 30-Jun-13 -5.7% -1.5% 0.4% 31-Jul-13 4.4% -0.7% 0.5% 31-Aug-13 2.6% -1.3% 0.4% 30-Sep-13 5.1% 3.9% 0.4% 31-Oct-13 3.6% 0.4% 0.4% 30-Nov-13 -1.1% -1.4% 0.4% 31-Dec-13 3.0% 1.1% 0.5% 

The Cape Retirement Fund may only invest in the asset classes for which returns have been provided. The Investment Consultants and Trustees of the Fund have indicated that the risk and return requirements of the Fund indicate that exposures (weights) to the asset classes must, at all times, be constrained as follows:

 Equities (ALSI) Bonds (ALBI) Cash (STEFI) Minimum 30% 5% 5% Maximum 75% 40% 20% 

Also, a composite benchmark, against which the fund will be measured, will be constructed according to the following weights to the asset classes:

 Equities(ALSI) Bonds (ALBI) Cash (STEFI) Total exposure 60% 30% 10% 100% 

Youu (and yourr team) have been appointed as the portfolio manager for the fund and must present yourr proposal as to how youu will construct the investment to ensure an optimal portfolio. The portfolio construction will be based on an asset allocation "mix" that will apply to the whole period (i.e. one optimal asset allocation must be determined for the 6-year period).

Since youu are aware of the several weaknesses in optimisation models, particularly the potential error maximising, youu have decided to generate/simulate at least one thousand different possible allocations to the asset classes (ensuring that the constraints are adhered to) to examine the possible return and risk profiles of the different asset class allocations. The Trustees have insisted that youu use Beta (as per the CAPM model) and standard deviation as yourr risk measures relative to the benchmark portfolio. In addition, they insist that the portfolio Beta (relative to the benchmark portfolio) may not vary by more than 0.30 above or below the Beta of the benchmark portfolio.

QUESTIONS

A) Yourr presentation must show yourr graph (based on yourr results using the data provided) in which youu clearly indicate the minimum variance portfolio and the optimal portfolio - clearly indicate the Capital Market Line. Use standard deviation and beta as yourr risk statistics ensuring that each are presented in separate graphs.

B) Show your recommended optimal portfolio based on the use of the Beta constraints indicated by the Trustees.

C) Motivate yourr final proposed optimal portfolio that youu believe will best meet the needs of the Fund.

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Use Excel to get quick results and this is what i tried to solve: