Investors Decision For Future Investment

pages Pages: 4word Words: 890

Question :


  1. On worksheet Ex 2 construct an efficient multi asset portfolio of risky assets using the selected mutual funds in Exhibit 1 p.6 of the case. 
  2. Analyse the effect of adding a risk-free asset to a portfolio containing risky assets. Assume the risk-free rate is 8%. 
  3. Recommend an optimal portfolio that provides the highest return for the specified risk level with the constraint that: 
    1. The sum of the portfolio weights should equal 100%. 
    2. The weight of any risky asset in the portfolio should not exceed 18% to ensure that the portfolio is diversified. 
    3. No short selling or borrowing. 
  4. Answer the quiz taking the required figures from your spreadsheet. 
  5. Write a report to the investor (assume this is the ‘Uncle’ as described in the case): 

Discuss investor risk preferences and the implied risk profile of the uncle; 

Explain the fundamental concepts behind the optimal portfolio of risky assets; 

Explain how the addition of a risk-free asset in a portfolio was useful for generating a higher risk adjusted return; 

and finally make your recommendation. 

Report Length 

The maximum length of your report is two pages – can be less. A third page, the appendix, can contain only figures and tables that can be referenced in the body of your report (i.e., pages 1 and 2) simply by Fig.1 or Table.1. A fourth page can only be used for references. 

The report is to be A4 1.15-spaced, size 11 points, font Times New Roman. Use margins of at least 2.54 cm (1 inch). 

The marker may choose to ignore any content of the report that is non-conforming. Space constraints may mean that not all topics can be fully covered in your response and you may need to prioritise your findings. 

Excel Spreadsheet 

Use the excel spreadsheet provided. 

Your spreadsheet should be shown with formula i.e. do not hard code values prior to submitting (e.g., leave figures as formula as appropriate). Your assignment will score zero if the spreadsheet does not provide the supporting information used in the Report and/or the quiz responses. 

6. Originality 

All work must contain original work or if other information sources are used in the preparation of the report these must be acknowledged appropriately. The University defines plagiarism in its rules: "Plagiarism involves using the work of another person and presenting it as one's own." Plagiarism is a serious breach of the University's rules and carries significant penalties. You must read the University’s practices and procedures on plagiarism. 

The policies and procedures explain what plagiarism is, how to avoid it, the procedures that will be taken in cases of suspected plagiarism, and the penalties if you are found guilty. Penalties may include a deduction of marks, failure in the unit, and/or referral to the University Discipline Committee. 

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Answer :

  1. The worksheet provides summary of risk and return for selected 10 funds. Average return per quarter has been calculated using ‘Average’ formula on 20 quarter returns provided in Exhibit A of worksheet. This has been used as the basis to calculate annualized return, annual variance and standard deviation. 

Further, the weights assigned in Exhibit D of the worksheet have been used to calculate portfolio return, risk and standard deviation as well as Sharpe Ratio.

Then, the ‘Data solver’ has been used to calculate maximum portfolio return in cell R28 subject to constraints of weights being not more than 18% and total being 100% and portfolio variance not to exceed 10%. This results in maximum return of 25% with risk being 10%. 

Another sheet ‘Ex 2 (without 18% constraint)’ has been added that calculates maximum return without the constraint of weights not being more than 18%. This results in maximum return of 28.35% with risk being 10%. 

The results of this sheet have been used to populate ‘Ex 1’ as it has a two asset portfolio model.

  1. In ‘Ex 2’, after considering 8% risk free asset, the Sharpe Ratio is 0.94. Without considering the risk free asset, the Sharpe Ratio increases to 1.38, leading to change in market portfolio.


The following pages in the report discuss the investor situation and how he wants to make decisions regarding future investment. The report will also provide recommendation on the basis of investor’s risk appetite, return requirement and preferences regarding investment instruments.

Investor Situation

The investor is retired and has limited appetite for risk of investments and wants maximum possible returns with the preferred constraints. Further, the investor made some investments in one balanced fund that continues to give negative returns despite a shooting stock market index.

Hence, now the investor wants to invest in a portfolio of good performing mutual funds and diversify across funds rather than one single mutual fund.

Further, the constraints provided include no investment in individual stocks due to high risk and preference is for mutual funds only. Additionally, the investor wants to invest across funds and create a portfolio of multiple funds in order to diversify risk. The investor prefers long term returns and does not want to be involved in short selling of securities. The investor needs maximum possible return with the portfolio risk of not more than 10 per cent.

Fund Selection

Basis comprehensive mutual fund information available on, quarterly return data (previous twenty quarters) for ten mutual funds has been selected (available in Exhibit 1). Basis the quarterly return available; annualized return, standard deviation and risk variance for various funds has been calculated. A variance-covariance matrix has also been created.

Portfolio Creation

Basis above, a portfolio of the ten funds has been created by assigning weights the sum of which equal to 100%. Portfolio return and risk (variance and standard deviation) and Sharpe ratio has been calculated.

Scenario 1:

Using ‘Data Solver’ tool in MS-Excel, the portfolio return has been maximized using constraints that include:

  1. Portfolio risk limited to 10%
  2. Weightage for each fund limited to 18%

This resulted in 25.00% expected return with a risk of 3.27% and includes following investments:

Investment with Portfolio risk limited to 10%Scenario 2:

Another scenario has been generated where the weightage constraint of 18% has been removed. This resulted in 28.25% expected return with a risk of 10% and includes following investments:

Investment 18% removed weightage constraint


Given that the investor wants to diversify as far as possible and also wants to minimize risk, it is recommended that the investor considers Scenario 1 that has investments across more number of funds and has much lower risk variance of 3.27%. Although Scenario 2 generates marginally higher return of 28.35%, the risk variance is high at 10% and also, the investments are across only two mutual funds.

It must be noted that all calculations have been performed on the basis of historical performance of these funds and is subject to market risk.

 scenario for Uncle and how he wants 

is report provides recommendation to the investor as per the risk and return preferences requested. 

Discuss investor risk preferences and the implied risk profile of the uncle; Explain the fundamental concepts behind the optimal portfolio of risky assets; Explain how the addition of a risk-free asset in a portfolio was useful for generating a higher risk adjusted return; and finally make your recommendation.