Portfolio Management For Risk Return Profile of the Client

Running head: PORTFOLIO MANAGEMNT
Portfolio Management
Name of the Student:
Name of the University:
Author Note:

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Table of Contents
Introduction:...............................................................................................................................3
Discussion:.................................................................................................................................3
Defining Asset Classes:..........................................................................................................3
Selection of Companies for the Portfolio:..............................................................................4
What is benefits of Diversification?.......................................................................................5
Return, Standard Deviation and Correlation of the Stocks:...................................................6
Efficient Frontier or Investment Opportunity set:..................................................................7
Capital Allocation Line:.........................................................................................................9
Optimal Risky Portfolio and Minimum Variance Frontier:.................................................10
Comparison of Minimum Variance Portfolio and Optimal Risky Portfolio:.......................12
Conclusion:..........................................................................................................................12
References:...............................................................................................................................14

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Introduction:
A portfolio comprises of various asset classes when it is constructed depending upon
the risk return profile of the client. The asset classes can be classified as equity, bonds,
alternative investments and risk free investments. Thus an optimal portfolio for an investor is
constructed depending upon the risk return profile of the client to suffice the objectives of the
client for investment. Thus, upon deciding the asset classes the next action in the
management process involves selection of the various investments in each asset class. Thus,
the aim of this report is to elaborate on the creation of a two stock portfolio. The stocks which
are selected for the purpose of investment is United Overseas Bank and Capita-Land. The
stocks are trading at the Singaporean stock exchange and are analysed over 5 years using
monthly data (Minh and Tam 2017).
The report tends to provide the historical return which has been provided from the
stock, along with the creation of portfolio with different weights given to the stocks. The
portfolio standard deviation is also calculated in the report for the different weights given to
each of the stock. The optimal risky portfolio and the minimum variance portfolio is also
calculated and highlighted in the following report (Geller 2016).
Discussion:
Defining Asset Classes:
The investor has a number of opportunities to different in different asset classes
according to the risk and return preference of the investor. The asset classes are provided in
the following bullets,
 Equity which can be categorized as Domestic or International.

3PORTFOLIO MANAGEMNT
 Bonds can be classified as investment grade bonds or speculative bonds.
 Alternative investments can be classified as commodities, real estate, private equity,
hedge funds and venture capital.
 Risk free investments which can be taken as sovereign bonds or government
securities.
Thus each of the asset class comprise of different risk and return which is selected by
the investor as per his risk tolerance level. The equity asset class is considered the most risky
which has a low correlation with rest of the asset class. The mixture of a portfolio comprising
of all the asset class provides benefits of diversification. Thus, a risk loving investor can
invest in the equity asset class or can invest in alternative investment such as private equity or
hedge fund. A risk fearing investor can invest in a portfolio of bonds or government securities
which provide a sense of security for the investor. The rational investor would invest in a
portfolio which comprises of all the asset classes to receive the benefit of diversification from
the portfolio (Kess and Mendlowitz 2016).
Selection of Companies for the Portfolio:
The company which are selected for the portfolio are Capita-land and united overseas
bank, which are trading at the Singaporean stock exchange. The basic information for the
company which are selected are provided in the following bullets,
 Capita-Land: The Company is a largest company which is in the real estate industry.
It is listed in Singapore and has a portfolio which comprises of properties which are
located globally. The group focuses its business in Singapore and China as the
primary markets with extension of business to Malaysia and Vietnam.
 United Overseas Bank: This is financial institution which is located in Singapore and
has its operations which are spread world-wide. The Bank provides various financial

4PORTFOLIO MANAGEMNT
services across the globe with the core business in Asia-Pacific, Western Europe and
North America.
Thus the companies which are selected one is related to the real estate industry while
the other company which is selected is from the financial services sector. The selection of the
companies from different industries is to provide a benefit of diversification to the portfolio
which would reduce the unsystematic risk from the portfolio (Horstmeyer 2019).
What is benefits of Diversification?
The benefits of diversification is the crux of the modern portfolio theory which
highlights the inclusion of different asset classes and diversified securities to reduce the
unsystematic risk from the portfolio. The unsystematic risk which is the risk pertaining to the
specific company due to particular situation or circumstances, can be reduced by investing in
different securities in the portfolio. Thus the investor is awarded a return which is specific to
the systematic risk which the investor has taken in the portfolio. Thus, diversification rewards
the consumers for the systematic risk while the unsystematic risk is removed from the
portfolio (Rutterford 2016).
Thus, for an instance two securities say A and B have variance of 10% and 15%. The
portfolio is equally weighted and the correlation of the stock A and B is 0.265. Thus, the risk
of the portfolio or the standard deviation of the portfolio is provided from the following
formula (Way, Lafond, Lillo, Panchenko and Farmer 2019).
Portfolio Risk= √ ( ( variance of Stock A∗Weight Of stock A ) + ( variance of Stock B∗Weight Of stock B ) + 2∗Stan
Thus the portfolio risk or the standard deviation of the portfolio is highlighted in the
following bullets,
 Variance of A 10% while Variance of B 15%.

5PORTFOLIO MANAGEMNT
 Weight of the portfolio 50% each.
 Correlation of the portfolio 0.265.
 Thus the standard deviation from the portfolio is
SQRT((10%*0.5^2)+(15%*0.5^2)+(2*10%*15%*0.5*0.5*0.265)) = 6.45%
Thus the portfolio has reduced the standard deviation or the risk which the investor
would had taken if had invested in either of the stock (Heinze 2018).
Return, Standard Deviation and Correlation of the Stocks:
The historical return of the stock is calculated on a monthly basis, for a period of 5
years. This is converted into annual return by multiplying by 12 for each of the two stocks.
The standard deviation of the stocks is also calculated on a monthly basis which is then
calculated on an annual basis by multiplying with the square root of 12, for each of the two
stocks. The correlation is calculated by using the historical returns from the two stocks
(Pedersen, Fitzgibbons and Pomorski 2019). Thus the calculation which has been done has
been provided in the figure below,
Figure 1: Stock Return and Risk
Source: By the Author
The average monthly return from the stock of United Overseas Bank is 0.3%, while
the Stock of CapitaLand had a monthly return of 0.13%. The average standard deviation on a
monthly basis for the stock of United Overseas Bank is 5%, while CapitaLand had an average

6PORTFOLIO MANAGEMNT
standard deviation of 6%. Thus the risk from the stock of CapitaLand is 6% which is greater
than the stock of 5% while the return is lower for the stock of CapitaLand (Simaan, Simaan
and Tang 2018).
This highlights that the stock of CapitaLand is more risky than the stock of United
Overseas Bank which is also highlighted from the annual returns of the stock being at 2% and
4% respectively. However, the risk of the two stocks is almost similar around 19% - 20%, but
the return is lower for CapitaLand. The correlation between the two stocks is 0.63912, which
highlights a strong positive correlation between the stocks. This means when the stock of
United Overseas Bank increases by 1%, the stock of CapitaLand moves in the same direction
by 0.63912%. The stock moves in the same direction, but with a strength of 0.63912 which
highlights a positive correlation among the stocks (Calvo, Ivorra and Liern 2016).
If the correlation between the stocks would had been lower the benefits of
diversification between the stocks would had been higher and the risk of the portfolio would
be reduced. Thus, this means the higher the correlation between the two stocks the lesser the
benefits of diversification from the portfolio, while the lower the correlation between the two
stocks the higher the benefits of diversification between the stocks (Ferreira 2017).
The company CapitaLand is a real estate company which provides a portfolio of
properties and the company United Overseas Bank is a banking company and the correlation
among the two stocks is strongly positive. Thus, investing in the portfolio containing these
two stocks is not recommended, since if the economy would had been booming then the
return from the portfolio would had been positive comprising these two stocks. However, as
per the current conditions which is prevailing in the market due to the corona virus outbreak
economic slowdown or more precisely recession has been taken place in the economy. Thus

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stocks with lower correlation would had been more favourable in these conditions as the fall
in the portfolio would be less due to lower correlation (Zhang, Liu and Zhao 2018).
This highlights that the portfolio which is being constructed for an investor should
consider investments which have lower correlation to incorporate higher benefits of
diversification (Sturm 2019).
Efficient Frontier or Investment Opportunity set:
As per the modern portfolio management theory, the efficient frontier represents a set
of portfolio which provide different risk and return from the investments. It represents the
maximum return which can be generated from the portfolio for a defined level of risk. Thus
the return which is calculated and the risk which it creates in the portfolio, is due to different
combination at which the investments are incorporated in the portfolio. This means the
investments are given different weights in the portfolio which provides different level of risk
and return from the portfolio (Zakamulin 2016).
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
0%
20%
40%
60%
80%
100%
120%
Portfolio Weights
United Overseas Bank CapitaLand
Figure 2: Portfolio Weights
Source: By the Author

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Thus the weights of the portfolio is calculated with a range of 5% among the stocks,
with the total weight of the portfolio to be 100%. Thus the 1st portfolio has weight of 0% for
the United Overseas Bank while CapitaLand has a weight of 100%. The weight of the stock
United Overseas Bank is increasing by 5%, while the weight of the CapitaLand stock
decreases by 5%. The 21st Portfolio provides 100% weight to United Overseas Bank, while
CapitaLand has a weight of 0%. Thus the risk return characteristics of the different portfolio
are highlighted in the next graph which is the Efficient Frontier or the Investment
Opportunity set of the portfolio of stocks (Soni 2017).
17.000% 17.500% 18.000% 18.500% 19.000% 19.500% 20.000%
0.000%
0.500%
1.000%
1.500%
2.000%
2.500%
3.000%
3.500%
4.000%
Efficient Frontier
Risk
Return
Figure 3: Efficient Frontier of the Portfolio
Source: By the Author
The efficient frontier of the portfolio has been first provided by Harry Markowitz, and
is also referred to as Markowitz Frontier which has been an important part of the Modern
Portfolio Theory. Thus, this frontier seeks to maximize the return for a specific level of risk
so as to reward the investors for the risk which is undertaken by them. Thus, the different

9PORTFOLIO MANAGEMNT
level of weights of the stock in the portfolio provides different level of risk and return
(Bodnar and Zabolotskyy 2017).
Capital Allocation Line:
The capital allocation line is set of different combination of return from risk free
assets and risky assets. Thus this line highlights the return which is achieved by the investor
from the portfolio according to the level of risk. Thus, the following graph highlights the
capital allocation line of the portfolio which the investor can achieve by investing in such a
portfolio (Bodnar, Mazur and Okhrin 2017).
0% 5% 10% 15% 20% 25%
0.0000%
0.5000%
1.0000%
1.5000%
2.0000%
2.5000%
3.0000%
3.5000%
4.0000%
Capital Allocation Line
Risk
CAL Return
Figure 4: Capital Allocation Line
Source: By the Author
Thus, when the risk of the portfolio is at 0%, the return which has been generated
from the portfolio is the risk free rate of return which is 1.4250%. As the level of risk
increases the return from the portfolio also increases. The right hand corner of the portfolio
highlights the investment in the risky assets where the risk is around 20% and the return from
the portfolio is around 4%. Thus, this line highlights the level of return which should be
considered by the investor at each specific level of risk. This also highlights the portfolio

10PORTFOLIO MANAGEMNT
which is suitable for the investor which is presented as optimal risky portfolio and is
highlighted ahead in the report (Reh, Krüger and Liesenfeld 2019).
Optimal Risky Portfolio and Minimum Variance Frontier:
The optimal risky portfolio is the portfolio which provides the maximized return at a
specific level of risk from the portfolio. This return is measured as Sharpe Ratio or risk to
reward ratio and the portfolio which is the most feasible for an investor is which maximizes
the Sharpe Ratio. The investor is rewarded the highest for each unit of risk which is
undertaken by the investor in this portfolio (Bednarek and Patel 2018).
Figure 5: Portfolio Weights
Source: By the Author
The optimal risky portfolio is the portfolio on the efficient frontier which is a tangent
to the capital allocation line. The portfolio which leads to the creation of a tangent leads to
the creation of the optimal risky portfolio. The capital allocation line which provides the
return – risk combination between the risk free and risky assets. Thus the optimal portfolio is
the portfolio which provides a tangent with the capital allocation line (Chiou and
Pukthuanthong 2019).

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0% 5% 10% 15% 20% 25%
0.000%
0.500%
1.000%
1.500%
2.000%
2.500%
3.000%
3.500%
4.000% Efficient Frontier
Risk
Return
Figure 6: Optimal Risky Portfolio and Minimum Variance Portfolio
Source: By the Author
Thus the optimal risky portfolio is highlighted by a red dot in the graph which is at the
point of tangency between the Capital Allocation Line and the efficient Frontier. The
portfolio which are lower than the capital allocation line are sub optimal portfolio as they
provide a lower return for a higher level of risk. The points which is above the capital
allocation line are over optimized portfolio which provide higher return at a certain level of
risk. Thus the optimal portfolio is the portfolio which should be considered by an investor
who is risk averse to derive the maximized return over a specified level of risk (McDowell
2017).
The minimum variance portfolio seeks to provide the lowest level of risk for a given
level of expected return. This portfolio tends to highlight the minimum risk which can be

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generated from the portfolio for a specific return. This is highlighted by the black dot in the
above graph which highlights the lower level of risk with a lower level of return. This
portfolio would had generated a higher return for a lower risk if the correlation between the
two stocks would had been lower. Thus since the correlation among the stocks is strongly
positive the benefits of diversification is not high from the portfolio (Pittman, Singh and
Srinivasan 2019).
Comparison of Minimum Variance Portfolio and Optimal Risky Portfolio:
The minimum variance portfolio seeks to minimize the risk for a given level of
expected return. If the correlation among the stocks would had been lower, the minimum
variance portfolio would had provided a lower risk with a higher level of return. On the other
hand optimal risky portfolio tends to maximize return for a given level of risk, it provides a
combination of assets to benefit the investor with the highest risk to reward ratio (Sissy
Amidu and Abor 2017).
Conclusion:
The investment management process is a skill which requires selection of the stocks
as per their risk and return requirements. The two stock portfolio highlighted the benefits of
diversification which increases when the correlation among the stocks is lower. The investor
is then rewarded for the systematic risk which they have undertaken during the construction
of the portfolio. The capital allocation line is a combination of returns which can be derived
from different combination of assets in the portfolio. The capital allocation line provides the
risk free return when the risk tolerance level is 0% and keeps on increasing the return with an
increase in the risk tolerance level of the investor. This property highlights the direct
relationship between the risk tolerance level and return which is achieved from the portfolio.

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The optimal risky portfolio is the portfolio which is the point of tangency with the
capital allocation line. This portfolio seeks to maximize the risk reward ratio which is
achieved by the investor. The portfolio is the most optimum for the client and seeks to benefit
the client the most as per his risk tolerance level. The minimum variance portfolio is the
portfolio which seeks to minimize the risk with a combination of the assets in the portfolio.
The benefits of diversification has been observed by the shape of the efficient frontier
and different levels of the optimal risky portfolio and the minimum variance portfolio.

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variance portfolio. Finance Research Letters, 24, pp.175-178.
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the Sharpe ratio?. AStA Advances in Statistical Analysis, 101(1), pp.1-28.
Bodnar, T., Mazur, S. and Okhrin, Y., 2017. Bayesian estimation of the global minimum
variance portfolio. European Journal of Operational Research, 256(1), pp.292-307.
Calvo, C., Ivorra, C. and Liern, V., 2016. Fuzzy portfolio selection with non-financial goals:
exploring the efficient frontier. Annals of Operations Research, 245(1-2), pp.31-46.
Chiou, W.J.P. and Pukthuanthong, K., 2019. What Drives Variation in the International
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2019).
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Journal of Investing, 28(5), pp.38-53.

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