61FIN3FMO – FINANCIAL MODELING

LAB ACTIVITIES 7 – EFFICIENT FRONTIER & PORTFOLIO

Activity 1. Calculate the envelope set for the four assets below and show that the individual assets
all lie within this envelope set.
A Four Assets Portfolio Problem
Variance-Covariance Matrix
Stock1 Stock2 Stock3 Stock4 Mean Returns
Stock1 0.10 0.01 0.03 0.05 6%
Stock2 0.01 0.30 0.06 -0.04 8%
Stock3 0.03 0.06 0.40 0.02 10%
Stock4 0.05 -0.04 0.02 0.50 15%
You should get a graph that looks something like the folowing:
Activity 2.
The table below provides the stock prices of the 14 largest companies on the Vietnamese stock
market, all of which are part of the VN30 index. Stock prices are extracted based on the first
trading day of each month over the past 5 years (from January 2020 to June 2025).
1. As an individual investor, you are interested in the following questions:
a) What are the monthly returns of each stock, their average monthly return, and the
annualized average monthly return?
b) What are the monthly variance and monthly standard deviation of each stock, as well as the
annualized standard deviation?
2. You are planning to construct your own investment portfolio using the above stocks.
Based on the information you have calculated, you have two options:
a) Choose 5 stocks that you believe offer reasonable diversification for your portfolio.
Your decision must be explained in writing — why you chose these stocks and why you assigned
those specific weights.
Your justification should include:
• Growth expectations and risks under the current global economic outlook
• Assessment of the Vietnamese economic environment
• Industry-specific context for each stock
• Your personal preferences
b) What are the variance-covariance matrix and the correlation matrix of these 5 stocks?
c) Alternatively, assign random weights and your preffered weights to these 5 stocks (use the
RANDARRAY function or equivalent to generate the weights).
3. Calculate the expected return and risk (standard deviation) of both portfolios.
Plot the envelope frontier and illustrate:
• Individual stocks
• Your assigned-weight portfolio
• The randomly-weighted portfolio
Along with their respective risks and returns.
4. Provide commentary on your investment decision.
Reflect on the rationale and effectiveness of your chosen portfolio allocation.
 ACB BID FPT HPG MBB MSN MWG SAB TCB VCB VHM VIC VNM VRE
1/2/2020 6.6 26.8 24.8 9.9 8.1 46.1 37.4 93.5 11.5 39.5 62.6 102.2 79 34.4
2/3/2020 6.5 30.5 21.8 10.2 7.8 40.5 34.8 87.2 10.4 38.6 62.8 102 72.6 30.2
3/2/2020 7.3 25.8 23.6 9.2 7.9 39.7 34.1 72.3 10.9 35.6 59.3 93.7 70 28.6
4/1/2020 5.4 18.3 17.9 7.1 5.5 39.8 19.6 52.3 7.5 28.3 40.4 76.4 63 19.3
5/4/2020 5.9 20.1 21.4 8.7 6.1 46.4 25.4 65.9 8.4 29.3 47.8 81.6 65.4 23.5
6/1/2020 7.2 23.7 24 11.4 6.9 51.1 27.5 75.6 10.3 37.6 58.3 86.4 77.8 27.8
7/1/2020 6.7 22.4 22.9 11.3 6.5 44.9 26.2 69.3 9.6 36 56.7 80.9 77.8 26.5
8/3/2020 6.7 21.2 22.8 11.6 6.2 42.6 24.3 71.9 9 34.3 57.8 77.9 74.1 25.7
9/1/2020 7.9 23.6 25.3 12.5 6.9 44.2 30 80.8 10.5 36.1 58 82.4 83.6 27.3
10/1/2020 8.4 23.4 25.7 13.7 7.6 44.4 33.6 78.5 11.1 36.9 56.8 82.2 90.4 27.7
11/2/2020 9.2 22.2 26.2 15.5 7.9 68.4 34.5 78.9 10.4 37.3 55.9 94.7 89 25.5
12/1/2020 10.2 23.8 28 18 9.2 67.2 37.6 83.1 11.9 40 61.4 93.3 90.8 28.3
1/4/2021 10.7 28 30.5 21.4 10.6 72.8 39.1 85.7 16 43.4 67.8 96 90.4 31.7
2/1/2021 10 22.7 32.2 19.4 9.8 67.1 40.1 74.3 15.6 39.9 65.1 88 85.8 30
3/1/2021 12.5 25.6 39.5 23.4 12.6 74.8 43.7 80.7 19.5 43.5 75.9 96.4 88.2 34.3
4/1/2021 12.7 25.5 40.4 24.5 13 75.6 43.6 77.5 19.9 42.5 73 109.3 84.3 33.9
5/4/2021 12.9 24 42 30.2 13.9 78.5 45.2 69.8 21 43.5 73.1 118.8 76.5 31.3
6/1/2021 15.8 27.9 51.3 38.2 17 87.6 44.3 66.7 25.7 45.5 76.6 106.7 75.1 30.7
7/1/2021 16.9 27.5 52.3 36.3 19.4 93.7 49 72.6 25.8 51 86.4 105.4 76.8 31.8
8/2/2021 16.7 24.7 56.3 32.5 17.3 112.5 55.1 67.2 24.6 42.5 79.7 95.6 73.1 27.5
9/1/2021 15 22.6 55 33.9 16.8 110.1 53.8 64.4 23.4 43.6 78.9 94.1 74.5 27.9
10/1/2021 14.8 22.5 55.3 36.7 16.5 115.6 61.6 66.8 23.8 42.1 74.8 87.7 77.2 28.2
11/1/2021 15.3 24.3 57 38.3 17.1 120.2 63.5 70.2 25 42.5 81.9 95.8 77.4 31.2
12/1/2021 15.7 25.7 58.4 33.7 17.7 123.8 67.8 67.8 25.4 43.4 80.5 106 75.2 29.7
1/4/2022 16.1 27.4 55.6 32.2 17.5 140.6 67.3 68 24.7 44.7 82.7 101 74.6 31.2
2/7/2022 16.3 34.8 53.2 29.6 20.3 122.3 65.4 66.7 25.6 52.3 79.9 91.2 73 35.5
3/1/2022 15.9 32.3 55.6 32.3 20.4 129.5 66.4 73.7 24.4 48.1 75.8 79.2 69.2 33.5
4/1/2022 15.7 32.5 66 31.4 20 121.2 76.2 73.2 24.4 46.9 74 82.1 71.4 34.1
5/4/2022 14.9 27.3 62.2 28.9 17.4 112.3 73 72.4 20.4 45.3 62.7 79.7 63.4 30
6/1/2022 14.6 25.8 66.5 23.6 16.6 114.2 71 67.8 17.9 45.6 70.3 79.3 62.9 30.1
7/1/2022 14.1 25.7 63.4 20.4 14.6 108.7 69.1 68.1 17.5 41.9 61.4 72.6 64.4 28.7
8/1/2022 14.7 28.6 60.5 20.7 15.9 109.4 60.2 81 18.7 43.6 60 64.7 65.6 29
9/5/2022 14.4 29 62.8 21.7 17 115.5 71.2 83.2 18.7 46.8 61 64 69.2 27.6
10/3/2022 12.7 23.1 56.1 18 13.5 94 58.6 80.7 14.7 40 50.4 55.5 63.4 26.1
11/1/2022 13.2 25 55 13.6 13 86.5 49.2 81.3 12.4 42.5 45 55.4 71.6 26.3
12/1/2022 13.2 28.6 54.4 16.5 12.8 99 43.3 77.6 13.3 45.3 53.5 66 73.6 30
1/3/2023 13.3 30.2 58.3 17.5 13 96 43.2 75.9 13.3 46.8 49.4 56.8 71.3 28.1
2/1/2023 14.8 31.4 59.7 19.2 13.6 95.2 46.3 84 13.7 50.5 48 55.2 70.1 28
3/1/2023 14.7 33.5 58.7 19 12.7 80.5 40.1 86.5 13.2 52.7 41.2 52.7 69.9 26.8
4/3/2023 14.8 33.7 58.9 19.1 13.5 76.8 38.3 81.7 14.2 52.6 52.6 58 67.6 29.6
 5/4/2023 14.4 31.8 57.1 19.4 13.1 71 37.3 75.2 14.1 50.4 48.8 51.4 62.6 27.4
6/1/2023 15 32.2 60.8 19.5 13.6 71.8 38.6 71.4 14.7 53.2 53 52 60.1 26.9
7/3/2023 15.5 32.6 63 23.8 14.9 75.4 42.3 70 15.5 56.6 55.9 51.1 64.2 27
8/1/2023 16 35.3 71.6 25 16 86.7 51.3 72.2 16.5 61 62.8 58.9 69.1 29.1
9/5/2023 16 34.8 83 25.3 16.3 81.5 53.9 72.4 17 60.3 55.3 62.3 74.2 30.2
10/2/2023 15.4 32.2 79.9 23.8 15.8 77.4 51.5 66.5 16.1 57.9 45.8 46.9 70.1 26.9
11/1/2023 15.2 29.3 73.2 21.8 14.6 59.5 34.8 52.3 13.7 58.7 38.5 40.4 65.3 22.7
12/1/2023 15.4 32.6 79.2 24.5 15.1 61.5 38.4 59.2 14.4 56.9 40.9 42.1 63.4 22.8
1/2/2024 17.2 35.5 82.2 25 16 68.4 42.1 57.9 15.6 55.9 43 44 63.8 23.1
2/1/2024 18.2 39 85.7 25.3 18.6 65.1 45.8 53.7 16.6 60.1 41.2 42.4 63 22.7
3/1/2024 19.5 44.2 95 28 20.4 70.5 46.2 54.7 20.3 65.1 44 45.3 66.8 26.7
4/1/2024 20 43.1 100.2 27.4 21.2 73.4 51 53 23 63.7 42.9 47.9 63.4 25.7
5/2/2024 18.9 40.7 109.2 25.8 19.1 68 55.2 52.8 22.7 61.5 41.2 44.4 61.9 22.8
6/3/2024 20.7 39.1 117.4 29 19.7 77.7 63.5 55.5 23.6 59 39.3 44 62.5 22.3
7/1/2024 19.9 36.3 127.7 28.4 19.5 76 65.8 56.9 22.7 57.6 37.7 41.4 62.4 21.9
8/1/2024 20 38.7 123.9 26.7 20.3 71.8 62.1 53.1 23 60.7 36.5 42.1 66.5 18.2
9/4/2024 20.6 40.5 132.1 25.3 21.2 75.3 69.1 55.2 23 60.9 42.5 44 70.3 19.7
10/1/2024 21.5 41.1 135 26.8 22.3 76.6 67.8 55.8 24.7 61.5 43.5 42.3 67.2 19.4
11/1/2024 20.8 39.5 133.7 26.6 21.4 74.5 66 53.4 23.7 62.5 41.5 41.2 63.1 17.8
12/2/2024 21 38.4 142.2 26.9 21 72.6 60.4 54.2 23.7 63 40.8 40.4 61.8 17.9
1/2/2025 21.4 38.2 152 27 21.9 70.8 60.6 55.6 24.4 61.5 40 40.6 60.9 17.3
2/3/2025 20.9 39.3 146 26.4 22.1 67.9 59.1 52.7 24.4 61.3 39 40 58.5 16.3
3/3/2025 21.7 41 140.5 28.1 23.1 68 58.8 51.7 26.1 62.4 42.6 42.1 61 17.7
4/1/2025 21.8 39 120.5 27 24.6 66.2 58.6 49.4 28 64.5 53 59.7 58.7 20
5/5/2025 20.1 34.9 108.6 25.7 23.6 62.5 61 47.9 26.5 57.1 60.9 70 55 24.9
6/2/2025 21.1 35.7 116.1 25.6 24.6 62.1 61 49.2 30.9 56.2 77 98 54.6 26.7