Microsoft Word - Project 2.docx
QNT2020 Project 2
Asset Allocation Problem
Due: 05/14/2023 11:59PM
Investment advisory firms offer investment advice and provide their clients with the best
mix of financial assets to invest in with different risk tolerance levels. Assume that you work for
XYZ investment advisory firm that uses an asset allocation model to recommend the portion of
each client’s portfolio to be invested in three funds, Alpha, Bravo, and Charlie. Table 1 shows
XYZ’s general guidelines of the minimum and maximum percentage of the total portfolio value
invested in these three funds. For example, if a client has $100,000 to invest, the amount of
Alpha fund in the portfolio will be between $20,000 to $40,000 ($100,000*20% to
$100,000*40%.) In addition, XYZ attempts to assess the risk tolerance of each client and adjust
the portfolio to meet the needs of the individual investor.
Table 1. Min/Max percentage of the total portfolio
Fund Minimum Percentage Invested Maximum Percentage Invested
Alpha 20% 45%
Bravo 15% 50%
Charlie 30%
Now you have a new client Mr. Smith who has $800,000 to invest. Based on an evaluation
of Mr. Smith’s risk tolerance, you assign a maximum risk index of 0.05 for him. Table 2 shows
the individual risk rating of the funds based on XYZ’s risk indicators. An overall portfolio risk
index is computed as a weighted average of the risk rating for the three funds, where the
weights are the fraction of the client’s portfolio invested in each of the funds. Additionally,
annual yields forecasted by XYZ are also shown in Table 2. Based on the information provided,
how should Mr. Smith be advised to allocate the $800,000 among Alpha, Bravo, and Charlie
funds? What is the annual yield you anticipate for the investment recommendation?
Table 2. Risk ratings and yields of the funds
Fund Risk Rating Annual Yields
Alpha 0.1 18%
Bravo XXXXXXXXXX%
Charlie XXXXXXXXXX%
You are asked to develop a linear programming model that will provide the maximum yield
for the portfolio. Create a spreadsheet model to develop an optimal feasible solution of the
investment portfolio to present to Mr. Smith. Write up a report to recommend how much of
the $800,000 should be invested in each of the three funds and what the annual yield is.
Additionally, use the model to do some analysis and answer the following questions:
1. Assume that Mr. Smith’s risk index could be increased to 0.06. How much would the
yield increase, and how would the investment recommendation change?
2. Refer again to the original situation, in which Mr. Smith’s risk index was assessed to be
0.05. How would your investment recommendation change if the annual yield for the
Alpha were revised downward to 17.5% or even to 16%?
3. Assume that the client expressed some concern about having too much money in the
Alpha. How would the original recommendation change if the amount invested Alpha is
not allowed to exceed the amount invested in Bravo?
Report Format
1. Please submit your project report in pdf format. Also submit your worksheets.
2. You can use the following outline for your project report:
a. Introduction: introduce the problem, provide some background
. Problem Statement: describe the problem you are proposing to solve,
c. State the assumptions (if any)
d. Data Description: list the sources of data you expect to extract data for
developing the analysis. Provide any references you used. Describe the data
(explain any terms that are specific to your dataset)
e. Methods: discuss your modelling approach and identify the decision variables.
What is the objective function? What is the nature of the objective function
(linear, non-linear, etc.)? What are your constraints? What is the nature of your
constraints (linear, integer, binary)? What are your decision variables? What
solver method did you adopt to develop the portfolio investment
ecommendation?
f. Results: discuss the outcome of your analysis.
g. Additional Results: answer above additional analysis questions.
h. Conclusion: Do you have a recommendation?
3. Include tables and visuals to support your analysis (if any).
4. Your project report should be 5-7 pages.