City University of Hong Kong
EF3320 Security Analysis and Portfolio Management
Semester A 2023/2024
Session: C02
Group: 25
Group Project
Student Name Student ID
Chan Kit Ngai 57848833
Ding Man 57856046
Ni Zhu Xu 57855850
SUN Yi Tian 57856095
Wang Yu Yan 56809385
Dear City College Supervisor:
In response to your request, our team has written this report to answer all of your
questions about the Endowment Fund's investment portfolio arrangement. We hope that this
portfolio will assist you in completing your investment policy decisions for City College. (All
the data we used are converted to annual data)
Part 1. Analysis of the current portfolios with five risky assets
A). The performance of current City College portfolios and benchmark (Q1)
The following table shows the performance of current City College Portfolios and other two
benchmark portfolios from 2004 to 2020, Value-weighted market portfolio (VWRETD) and
Real Estate investment (REITs).
Performance statistics
City College
Portfolio
VBMFX REITs
E(r) 8.5942% 10.2294% 10.3932%
S.D. 10.8315% 15.0624% 14.3661%
Sharpe 0.6817 0.5985 0.6389
Table 1-1 Performance statistics table
From the above table, the expected return of City College’s current portfolio is 8.5942%,
which is much lower than those of VBMFX and REITs, 10.2294% and 10.3932%,
respectively. However, the current portfolio of City College has the lowest standard deviation
compared to VBMFX and REITs, which suggests the lowest risk among these portfolios.
Furthermore, the Sharpe ratio of the City College portfolio is obviously higher than two of
the benchmarks, with 0.6817.
To conclude, the performance of the current City College portfolio was better than 2
benchmarks from 2004 to 2020.
B). Portfolio Efficient Frontier (Q2)
Assuming the target return ranges from 1% to 20%, we use the solver module in Excel to find
the points on the portfolio efficient frontier of five risky assets, which contains the allocation
weights as well as the corresponding standard deviation when setting the different targeting
returns. According to the Portfolio Frontier diagram, the red point is the minimum variance
portfolio.
Figure 2-1 Portfolio Frontier
C). Current portfolio Efficient Frontier (Q3)
The current City College portfolio is not efficient. According to the above portfolio frontier
diagram, the current portfolio point lies inside the efficient frontier graph, and it is not the
yellow optimal portfolio point, which has the same expected return as the current portfolio
(8.59%) with a lower standard deviation (7.89%).
SMLSTK MEDSTK LRGSTK VBMTX REITs
Current
Portfolio 0.10 0.15 0.30 0.35 0.1
Efficient
Portfolio -0.8703 1.2081 0.1436 0.5847 -0.0661
Table 3-1 Investment Proportions of both Current and Efficient Portfolios
Part 2. Analysis of the Current Portfolio with five risky assets and
Risk-Free asset (T-bill)
A). Optimal risky portfolio weights allocation (Q4)
The optimal risky portfolio point is the tangent point of the capital allocation line (CAL) and
portfolio frontier graph, which occupies the highest Sharpe ratio.
Figure 4-1 Tangency point for optimal risky portfolio
We use the Excel Solver to find the highest Sharp ratio point which is the optimal risky
portfolio. The weight of each risky asset can be negative and over 1 due to allowance for
short sales of risky assets and borrowing the risk-free asset.
SMLSTK MEDSTK LRGSTK VBMFX REIT Total
Weight -0.1114 0.2194 0.0959 0.8772 -0.0810 1.000
Table 4-1 Required weight for constructing optimal portfolio
Expected return of Tangency portfolio 0.0522
Standard deviation of Tangency portfolio 0.0388
Table 4-2 Expected return and standard deviation of the tangency portfolio
B). Efficient portfolio with the same expected return as the Current Portfolio with
Risk-free Asset investment. (Q5)
In this part, we are concerned with buying risk-free asset investments with the existing 5
risky assets in the current portfolio. It is required that the expected return is equal to the
existing portfolio return round (8.59%). According to the formula, (E(rc) = E(rp) * w1 + rf *
w2), we can get the equation, 8.59% = 5.22% * w + 1.21% * (1-w). So, the weight for the
tangency portfolio is 184.04% and the weight for the risk-free asset investment is –84.04%.
SMLSTK MEDSTK LRGSTK VBMFX REITs T-bills
Weight -0.2051 0.4037 0.1765 1.6143 -0.1490 -0.8404
Table 5-1 Weight for the efficient portfolio with Risk-free assets investment
Expected return of the efficient portfolio 8.59%
Standard deviation of the efficient portfolio 6.22%
Table 5-2 Expected return and standard deviation of the efficient portfolio including Risk-free asset investment
C). Efficient complete portfolio of “Floor” expected return rate (Q6)
By the requirement of the City College, the expected return rate cannot be below 0.8% per
month, so the minimum expected return rate is 9.6% annually. According to the formula,
(E(rc) = E(rp) * w1 + rf * w2), we can get the equation, 9.6% = 5.22% * w + 1.21% * (1-w).
So, the weight for the tangency portfolio is 209.23% and the weight for the risk-free asset
investment is –109.23%.
SMLSTK MEDSTK LRGSTK VBMFX REITs T-bills
Weight -0.2331 0.4590 0.2006 1.8353 -0.1694 -1.0923
Table 6-1 weight for the efficient portfolio of “Floor” rate
Expected Return of the Efficient Portfolio 9.60%
Standard deviation of the efficient portfolio 7.07%
Table 6-2 The Floor Expected return and standard deviation of the efficient portfolio
Part 3. Analysis of the new portfolio with seven Risky Assets
A). New portfolio frontier (Q7)
Figure 7-1 Comparison portfolio frontier with seven and five different risky assets
According to the above figure, we can observe that the new portfolio with seven risky assets
has a lower standard deviation than the portfolio consisting of five risky assets for the same
expected return point. As a result, investing in the two more risky assets is also a beneficial
choice for City College.
B). New efficient portfolio of “Floor” expected return rate
Based on the previous calculation, the City College’s required “Floor” rate is 9.6% annually.
To achieve the “Floor” rate of return, the following table shows the detailed allocation for the
weighted of seven risky assets.
SMLSTK MEDSTK LRGSTK VBMFX REITs EEM USERX
Weight -1.0006 1.3924 0.3280 0.5003 -0.0324 -0.2419 0.0541
Table 7-1 weight for the new efficient portfolio of the “Floor” rate
Expected Return of the Efficient Portfolio 9.60%
Standard deviation of the efficient portfolio 8.93%
Table 7-2 The Floor expected return and standard deviation of the new portfolio
C). New efficient portfolio of “Floor” expected return rate with constraints (Q8)
The following table demonstrates the new detailed proportion of the seven risky assets in the
portfolio to achieve the “Floor” rate (9.6%). However, it set two restrictions which are each
weight of risky asset less than 40% and short sales are no longer allowed.
SMLSTK MEDSTK LRGSTK VBMFX REITs EEM USERX
Weight 0 0.2685 0.4 0.2531 0 0 0.07845
Table 8-1 weight for the new efficient portfolio of the ‘Floor” rate with constraints
Expected return of the efficient portfolio 9.60%
Standard deviation of the efficient portfolio 11.86%
Table 8-2 The Floor expected return and standard deviation of the new portfolio with constraints
In conclusion, compared with B) and C) in part 2, the standard deviation of the efficient
portfolio obviously increases when we set two restrictions for investment with the same
expected return.
D). The portfolio of several risky assets is better than individual stock (Q9)
Asset allocation methods are to hold diverse assets in a portfolio and aim for the best
trade-off between return and risk under a specific level of risk aversion, based on previous
data and scientific mathematical models. Meanwhile, individual stock selection is totally
based on analyzing their historical data and forecasting their possible trends somehow
subjectively. Therefore, we will argue that asset allocation is more beneficial than individual
stock selection considering City College’s investment expectations and risk aversion, in terms
of diversifying risks, optimizing returns, and maintaining discipline and stability.
Firstly, asset allocation can not only attain the optimal return but also differentiate the risks.
Asset allocation can attain the highest Sharpe ratio and optimized return under a certain level
of aversion. Nevertheless, many individuals invest in an ad hoc manner, resulting in either too
aggressive or conservative investments. Thus, the return is not adequate and stable.
Comparatively, in a portfolio, an investment is divided into diverse classes, and a mix of each
asset can help balance the school’s returns. Furthermore, portfolio risk is spread across asset
classes and is protected from the negative impacts of a dip in any individual asset, though
multi-factors and deviations related to an individual stock are hard to foresee.
Moreover, asset allocation can maintain a more stable return and lower the possible stress
regarding investment safety than the individual stock selection. A portfolio contains many
assets allowing City College to be diversified so that firm-specific uncertainty can be
eliminated by diversification in a portfolio, lowering the influence of idiosyncratic risk on the
gross return. Unlike relying on an individual stock, asset allocation can hedge the price
volatility caused by some unanticipated event, increase the stability of return, and further
reduce board members’ stress regarding investment safety. In return, board member’s
confidence helps to invest in regular intervals. These methods also have advantages in
maintaining discipline, avoiding over-invest and under-invest in a particular sector, compared
with individual ones.
Finally, our calculation results have indicated the advantage of asset allocation compared
with the current investment motion of picking a few individual stocks. Our service of asset
allocation not only provides an optimized investment portfolio, which can give higher returns
with lower risks but also offers a scientific capital allocation option. That is where our service
has advantages over the motion of picking several individual stocks.
Reference
Yahoo! (2023, December 3). Ishares MSCI emerging markets ETF (EEM) stock price,
news, quote & history. Yahoo! Finance.
https://finance.yahoo.com/quote/EEM?p=EEM&.tsrc=fin-srch
Yahoo! (2023b, December 3). U.S. Global Investors Funds Gold and Precious Metals Fund
(USERX) stock price, news, Quote & History. Yahoo! Finance.
https://finance.yahoo.com/quote/USERX?p=USERX&.tsrc=fin-srch
Appendix
Annualized Return and Standard Deviation
Correlation Matrix
Covariance Matrix
Bordered-Covariance Matrix
Efficient Portfolios Plotting Efficient Frontier
Data for the Points Used to Graph the CAL Line
Covariance Matrix of 7 Risky Assets
Efficient Portfolios Plotting Efficient Frontier