Portfolio Management and Risk Analysis

The provided document is a solved assignment for portfolio management. It involves calculating the standard deviation of a portfolio, identifying the proportion of T-bill fund and each of the two risky funds, and determining the overall risk involved in investment. The solution utilizes optimal capital allocation (CAL) to calculate the standard deviation of the portfolio, which is found to be at 20.56%. Additionally, it determines that 11.92% of the fund is contributed by T-bill, reducing risk and allowing for high-risk investments.

Running head: INVESTMENT AND PORTFOLIO MANAGEMENT
Investment and Portfolio Management
Name of the Student:
Name of the University:
Authors Note:

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Table of Contents
PART A:.....................................................................................................................................2
1. Stating the finding on investment:.........................................................................................2
2. Stating the factors examined by Fama-French that might explain stock returns:..................2
3. Stating the measure of risk implemented by Fama-French model for the investors:.............3
4. Describing the implications of CAPM model and Fama-French model on investors:..........3
5. Providing summary of the academic paper and the reason Fama-French model was used in
the paper:....................................................................................................................................4
PART B:.....................................................................................................................................7
a) Depicting the expected return and standard deviation of the minimum-variance portfolio:. 7
b) Depicting the expected return and standard deviation of optimal risky portfolio:................9
c.i) Calculating standard derivation of the portfolio:...............................................................10
c.ii) Calculating the portion of T-bill fund and each of the two risky funds:..........................11
Reference and Bibliography:....................................................................................................12

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PART A:
1. Stating the finding on investment:
The researcher in the article mainly indicates the performance of value stock in
accordance with growth stocks. The researcher highlighted the misgivings in growth stock
and benefits provided by value stocks. In addition, the researcher pointed out the investors in
expectation of higher return from growth stock increase its value, which does not occur at
last. The researcher has conducted relevant evaluation and detect the validity of capital asset
pricing model. Moreover, the financial performance of the companies consists of growth
stock do not provide all the relevant return to the shareholder. On the other hand, the
researcher pointed out the value stock being undervalued can provide high return from
investment to the investors. The researcher also pointed out the financial performance of
value stock were more than growth stocks, as founded in US Stocks (Chandra 2017).
2. Stating the factors examined by Fama-French that might explain stock returns:
Fama-French states relevant factors for analysing the overall financial performance of
the company and detect overall growth, which could increase return from investment.
Moreover, Fama-French mainly states that two factors are needed for analysing the overall
average return of the stocks. The factors are market risk factors and value growth risk factor,
which is indicated by Fama-French that the use of both the factors could help in detecting the
actual returns from investment. The identified factors might help in detecting the actual
returns of the company, which might allow the investor to identify stock with least returns.
The value growth factors are mainly detected by differentiating between international
portfolio of high book-to-market stock and the return provided by portfolios with low book-
to-market stocks. In this context, Pagdin and Hardy (2017) mentioned that Fama-French

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models is helpful in detecting stock with the low risk, which could help in geniting high level
of return from investment.
3. Stating the measure of risk implemented by Fama-French model for the investors:
The Fama-French model mainly focuses its overall risk measure on two different
forms, which could help in detecting stocks returns and increase profits from investments.
The risk attributes are market risk factor and a value-growth risk factor, which is needed for
analysing the actual risk hindering operational capability of the company. Moreover, CAPM
model mainly focuses on one factor, which does not help in detecting the actual financial
position of the company. Furthermore, the risk implementation of Fama-French might help in
generating high level of profits. The market risk factor helps in evaluating the actual returns
from investment, which could be provided by a stock. In addition, the value-growth factor
would allow investors in detection the actual value of stock and the return it could provide
from investment (Kashyap 2016).
4. Describing the implications of CAPM model and Fama-French model on investors:
CAPM model mainly has relevant implications to the investors, which help in
detecting the risk and return from investment. In addition, the CAPM model helps in
determining the return and risk in stocks. This might help in detecting return and risk
involved in investments of the company, which might allow investors to generate high level
of returns. Raab and Stahn (2017) stated that CAPM model evaluates beta and expected
return of stocks, which is essential to create portfolio with low risk and high returns.
Moreover, the Fama-French model is used in evaluating examine multi-factor models,
which could help in detecting risk that could impact expected return of stock. In addition, the
Fama-French model evaluates two additional dimensions of risk that get rewarded nature of

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returns. The second implications are that value stock have higher returns than growth stock in
the market all around the world. Moreover, the earnings-to-price, cash flow-to price and
dividend-to-price is evaluated for detecting the actual financial capability of the stock to
generate high returns.
5. Providing summary of the academic paper and the reason Fama-French model was
used in the paper:
The overall academic paper “The Five-Factor Fama-French Model: International
Evidence” writer by Nusret Cakici, states the impact of Fama-French Model in detecting
returns of the stock (Cakici 2015). In addition, the financial market of 23 countries are mainly
evaluated to determine financial performance of the organisation. Moreover, the researcher in
academic paper has effectively depicted the overall use of five-factor model, which could
help in detecting the financial performance of the organisation. Furthermore, the data used
from 23 stock market is evaluated based on Fama-French Model for determining the impact
of extra two factors, whether they add explanatory power or a much weaker in Japan and
Asian portfolios. The research paper mainly evaluates the gross profitability and investment
factors include in Five-Factor Fama-French Model and whether its calculation could help in
understanding the return form investment.
The discussion section of the academic paper in panel A that mainly indicates the
intercepts from the Fama-French three-factor regressions for the 25 size-book-to-market
portfolios. In addition, the panel B section provides intercepts from the Fama-French five-
factor regressions, and their t-statistics. Both the analysis part might help in detecting the
financial viability of Fama-French three-factor and Fama-French five-factor. The regression
analysis mainly helps in detecting that lower number of significant alphas, which could help
in detecting performance of the model. The results of the regression analysis mainly help in

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understanding the significance of alphas for the 5-factor model and 3-factor model. This
relatively helps in identifying the financial performance of the company. However, the
academic paper indicates that 5-factor model does not provide adequate measure or better
description of average returns than three-factor model for the portfolios. This relatively
indicates that the three-factor model is sufficient for the analysis of the return provide by the
portfolios (Cakici 2015).
However, from the evaluation it could be detected that five-factor model is considered
doubtful for major of the countries such as Japan and Asia-Pacific. However, the academic
paper also states that three-factor model is much better option for the investors, as it applies
to all the territories of the world and allows investor to detect actual return that will be
provide from investment (Cakici 2015). Moreover, the objective of academic paper is to
detect the impact of gross profitability and investment, as a relevant factor of five-factor
Fame-French model. In addition, the researcher indicates that the new factors do not have any
explanatory power for the stocks listed in Japan and Asia Pacific. The academic paper sheds
light on the five-factor Fame-French model and how it could not provide all the relevant help
to the investor in different reigns of the world.
The researcher focuses on the results obtained from the academic paper, which states
that five-factor Fame-French model perform much better in regional condition in comparison
with the global condition. Furthermore, the academic paper’s outcome indicates that markets
all around the world are not fully integrated, which relatively reduces the impact of five-
factor Fame-French model on different markets all around the world. However, from the
evaluation it could be detected that the five-factor Fame-French model has fairly performed
in US market. The calculation of SMB, HML, RMW, and CMA is conducted in the research
report, which might help in depicting the overall significance of five-factor Fame-French

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model. The researcher has used T-test, correlation, and other statistical tools for deriving the
relationship between the calculation of different five-factor of Fame-French model.
The result section of the academic paper mainly indicates the correlation between
Global, North America and Europe, which helps in deriving the efficiency and attractiveness
of five-factor Fame-French model in identifying the stock with high value. However, the
result also indicates that correlation between Japan and Asia Pacific are relatively different in
comparison with Global, North America and Europe markets. This relatively indicates the
vulnerability of five-factor Fame-French model in identifying the stock with high value,
which could be used by investors.
Moreover, the academic paper sheds light on the fact that five-factor Fame-French
model is not always the best possible options for evaluation. This derivation is concluded by
evaluating the 25 size-book-to-market portfolios, the 25 size-GP portfolios, and the 25 size-
Investment portfolios, where their applicability is in doubt for other regions of the world. The
researcher indicates that the five-factor Fame-French model is not a viable approach for other
countries or regions of the world, as it would not provide the accurate data for the evaluation.
The result also evaluates the impact of RMW, CMA and HML, which could help investors in
their decision-making process. Moreover, from the valuation it could be detected that RMW
and CMA has smaller magnitude than HML, which might not help in detecting the actual
return capability of the stock.
The results of the research also evaluate the Asset pricing test, which relatively
suggest that Five Factor Model is not an adequate model for investor. According to the Asset
pricing test, GP portfolios, size investment portfolios and size-book-to-market portfolios has
not performed adequately and indicates that they cannot function in other regions of the
world. However, from the valuation it is also indicated that asset pricing test suggest that

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regional factors always perform better in comparison to the Global factors. this indicates that
the use of Five Factor Fama French model could eventually allow investing to support their
investing me within the regional limits. This would eventually help in improving the return
generation capacity of the investors. The researcher also portrays that the use of Fama French
model could allow investors to support the investing needs nationally, while the problems
might rise during the international investment schemes. Lastly, the academic paper possess
doubt on the applicability of Five Factor Model in performing adequately all around the
world. The research also states that viability of the model falls when investing in the markets
of Japan and Asia Pacific. This relatively limits the capability of Five Factor Model in
supporting investors during their investment schemes.
PART B:
a) Depicting the expected return and standard deviation of the minimum-variance
portfolio:
Particulars Expected return Standard
Deviation
Variance
Stock Fund
(S)
15% 32% 10.24%
Bond Fund
(B)
9% 23% 5.29%
Correlation 0.15
Covariance 1.10%
Covariance matrix Stock Fund Bond Fund (B)

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(S)
Stock Fund (S) 5.29% 1.10%
Bond Fund (B) 1.10% 10.24%
Minimum variance
portfolio
Value
Wmin(S) 1 – 68.58%
Wmin(S) 31.42%
Wmin(B) (10.24% - 1.10%) / ((10.24% + 5.29% - (2 * 1.10%)))
Wmin(B) 68.58%
Mean (31.42% * 15%) + (68.58% * 9%)
Mean 10.89%
Standard deviation SQRT(((31.42%^2) * 15%) + ((68.58%^2) * 9%) + (2 * 31.42% *
68.58% * 1.10%))
Standard deviation 19.94%
Stock Fund
(S)
Bond Fund
(B)
Expected return Standard deviation Sharpe ratio
0.00% 100.00% 9.000% 23.000% 15.2174%
10.00% 90.00% 9.600% 21.415% 19.1455%
20.00% 80.00% 10.200% 20.368% 23.0756%
30.00% 70.00% 10.800% 19.943% 26.5752%
31.42% 68.58% 10.885% 19.937% 27.0121%
40.00% 60.00% 11.400% 20.181% 29.2354%

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50.00% 50.00% 12.000% 21.058% 30.8668%
60.00% 40.00% 12.600% 22.500% 31.5549%
64.66% 35.34% 12.880% 23.338% 31.6209%
70.00% 30.00% 13.200% 24.408% 31.5474%
80.00% 20.00% 13.800% 26.680% 31.1089%
90.00% 10.00% 14.400% 29.234% 30.4444%
100.00% 0.00% 15.000% 32.000% 29.6875%
10.000% 15.000% 20.000% 25.000% 30.000% 35.000%
8.000%
9.000%
10.000%
11.000%
12.000%
13.000%
14.000%
15.000%
16.000%
Minimum variance
portfolio; 10.885%
Efficient Frontier of the Portfolio
b) Depicting the expected return and standard deviation of optimal risky portfolio:
Optimal risky portfolio Value
Stock -Risk free rate 9.500%
Bond -Risk free rate 3.500%
W(S) ((9.5% * 5.29%) - (3.5% * 1.10%)) / ((9.5% * 5.29%) +
(3.5% * 10.24%) - ((9.5% + 3.5%) * 1.10%))
W(S) 64.66%

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W(B) 1- 64.66%
W(B) 35.34%
Mean (64.66% * 15%) + (35.34% * 9%)
Mean 12.88%
Standard deviation SQRT(((64.66%^2) * 15%) + ((35.34%^2) * 9%) + (2 *
64.66% * 35.34% * 1.10%))
Standard deviation 23.34%
10.000% 15.000% 20.000% 25.000% 30.000% 35.000%
8.000%
9.000%
10.000%
11.000%
12.000%
13.000%
14.000%
15.000%
16.000%
Optimal risky
portfolio; 12.880%
Efficient Frontier of the Portfolio
c.i) Calculating standard derivation of the portfolio:
Particulars Value
Return 12.00%
ERc 31.62%
Rf 5.50%
Standard deviation of the
portfolio
(12% - 5.5%) / 31.62%

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Standard deviation of the
portfolio
20.56%
From the above table, standard deviation of the portfolio is calculated, which is at the
levels of 20.56%. The standard deviation is detected by detecting the overall reward to
variability ratio for identifying the actual risk involved in investment. Moreover, the use of
optimal CAL has helped in identifying the overall standard deviation of the portfolio. Stettina
and Horz (2015) stated that the detection of risk is essential to understand the risk to reward
ratio provided from investment.
c.ii) Calculating the portion of T-bill fund and each of the two risky funds:
Particulars Value
Rf 5.50%
Mean 12.88%
Return 12.00%
Proportion without T-bill fund (12% - 5.5%) / (12.88%-5.5%)
Proportion without T-bill fund 88.08%
Proportion with T-bill fund 1- 88.08%
Proportion with T-bill fund 11.92%
The calculation of T-bill portion in the portfolio is detected by using the means of any
portfolio along with optimal CAL. This has helped in detecting the actual funds of the
portfolio, which consist of T=bill fund. The 11.92% of the fund is contributed by T-bill,
which could help in reducing risk from investment. Aouni, Colapinto and La (2014)