Portfolio Management : Assignment

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Portfolio Management

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Introduction
This report is aimed at performing risk and return analysis of stocks and portfolio
applying various statistical measures such as arithmetic mean, geometric mean, regression,
variance, covariance, and correlation. Arithmetic mean and geometric mean are used to compute
average returns and variance is the indicator of risk. The covariance and correlation are
considered to be effect in finding out the relationship between the returns of two stocks. This
identification of relation is necessary to formulate an optimum portfolio. In this report, three
stocks namely Google, Amazon, and Rio Tinto have been selected for analysis. Further, a
portfolio having composition of these stocks with equal weights has also been formed to analyze
the risk and return in relation to portfolio. Apart from this, this report also highlights the
significance of portfolio in terms risk diversification.
A Brief about Companies
Google (Alphabet Inc)
Alphabet Inc also popularly known as Google is a USA based company engaged in the
business of online advertising and branding. The company was founded in the year 1998 and
since then it grown manifold spreading business in every corner of world. The stock of Alphabet
Inc is listed on Nasdaq. The financial performance of the company is improving rapidly. In the
year 2017, the company reported revenues of $110,855 million and net profit of $12,662 million
(Yahoo finance, 2018).
Amazon Inc
Amazon is the world leader in online retail sales of consumer goods. The company
having its headquarters in United States operates globally in many countries. Apart from retailing
of consumer goods, the company also provides web services through one its segments namely
Amazon Web Services. The company was founded in the year 1994 and since then it has
expanded surprisingly to reach the customers in every part of the world. The stock of company is
listed on Nasdaq. In the year 2017, the company reported revenues of $177,866 million and net
profit of $3,033 million (Yahoo finance, 2018).
Rio Tinto
Rio Tinto is a giant company engaged in the business of exploration of minerals such as
iron ore, coal, gold, copper and diamond. The company was founded in way back 1873 and since
then it has operated successfully. The company has its headquarters in UK and it operates
globally in many countries. The company’s stock is listed on New York Stock Exchange in
USA. As per the financial statements of 2017, it generates revenues of $40,030 million with net
profit of $8,762 million (Yahoo finance, 2018).
Part-I (a)
Taking the price data of past 28 weeks (Excel attached), arithmetic and geometric mean
of returns have been computed. The arithmetic mean shows simple average of the returns over

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the period. The geometric mean is improved version to calculate the average of data series. Both
the arithmetic mean and geometric mean are used to assess the performance of stocks and
portfolios. Applying the arithmetic mean and geometric mean on the historical data set one can
get the basis to predict the future trend in returns on the stocks (Kevin, 2015). In the current
report, the arithmetic mean and geometric mean have been computed in relation to three selected
stocks and the market index, the results of which are presented as below:
discrete rate of return= current closing price− previous closing price
previous closing price
S&P
500 Google Amazon
Rio
Tinto
Arithmetic
mean 0.20% 0.45% 1.50% 0.81%
Geometric
mean 0.17% 0.37% 1.42% 0.73%
Part-I (b)
Further, apart from the analysis of return, the analysis of risk is of equally importance. Hence, in
order to address the risk, variance, covariance, and correlation of stocks have been computed
(Baker & English, 2011). The variance indicates the total risk of stock which comprises of
systematic as well as unsystematic risk. The covariance and correlation shows relationship
between the returns of two assets. The summary of results of data analysis of the present case is
shown below:
Variance= 1
n−1 ∑
i=1
27
(ri−r )2 , Standard deviation= √Variance
Variance 0.06% 0.17% 0.18% 0.17%
Co-variance Matrix
S&P 500 Google Amazon Rio Tinto
S&P 500 1
Google 0.0852% 1
Amazon 0.0569% 0.1093% 1
Rio
Tinto 0.0683% 0.0982% 0.0541% 1
Correlation
coefficients
S&P 500 Google Amazon Rio Tinto

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S&P 500 1.00
Google 90.1967% 1.00
Amazon 57.9792%
65.5352
% 1.00
Rio
Tinto 61.4784%
32.1401
%
32.1401
% 1.00
Part-I (c)
From the figures presented above, it could be observed that S&P 500 (market index) is
showing arithmetic mean and geometric mean of 0.20% and 0.17% respectively. This shows that
the market earns on an average a return of 0.20% over a period of week. Further, the selected
stocks are also showing positive mean values which indicate that these stocks are providing
satisfactory return to the investors. All three stocks are generating higher returns as compared to
the stock market. Among the stocks, Amazon could be observed to be generating the highest
returns. Further, observed that Google has been the lowest earner among the stock but it is
earning returns higher than the market.
A trend in the stock prices of Google over the period of past 28 weeks is shown in the
chart given below:
Figure 1: Google stock over past 6 months
[Source: https://finance.yahoo.com/quote/GOOG/ ]
It could be observed that the stock performed exceptionally well in the month of January
2018. The stock prices reached to the peak during the month of January. The company’s

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financial performance in the fourth quarter of 2017 attracted the investors in January 2018 and
this caused the share price to go record high (Statt, 2018). However, the rising trend could
sustain for long and the stock started slopping downward in the immediately next month. Google
though performed well in the fourth quarter as compared to the previous quarter but it was not
better than the industry average. This caused change in the market sentiments and stock went
down.
Figure 2: Rio Tinto stock over 6 months
[Source: https://finance.yahoo.com/chart/RIO]
Rio Tinto could be observed to be growing gradually over the period of past 6 months.
The stock went high in the month of February and March because the company reported good
financial performance in the preceding quarter. Then the stock dropped down in April 2018. The
drop in stock in April could be attributed to the overall mining industry downturn due to slow
increase in demand of minerals.
The variance of S&P 500 (Market index) is 0.06% which is lower than the variance of
stocks. The variance of Google, Amazon and Rio Tinto, is 0.17%, 0.18%, and 0.17%
respectively. This shows that the risk of stocks taken individually is higher than the risk of
market.
The covariance of stocks and market and covariance among the stocks is positive. However, the
covariance values are lower than 1 which indicates that the covariance is less than perfect
positive. This indicates an opportunity to diversify and reduce the risk by forming a portfolio of
stocks (Baker & English, 2011).

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Part-II (a)
In order to form a portfolio, the investment has been made Google, Amazon, and Rio
Tinto in equal proportions. The return and variance of equally weighted portfolio has been
computed as shown below:
E ( RP )=∑
j=1
m
W j E ( Rj )
Var ( r p ) =w 12 Var ( r 1 ) +w 22 Var ( r 2 ) + w 32 Var ( r 3 ) +2 w 1 w 2Cov ( r 1 , r 2 ) + 2 w 1 w 3Cov ( r 1 , r 3 ) +2 w 2 w 3 Cov ( r 2,
Stocks
Google Amazon Rio Tinto
Weights 33.3333% 33.3333% 33.3333%
Weekly Average
Returns 0.4512% 1.5039% 0.8146%
Variance 0.1670% 0.1802% 0.1698%
Covariance 0.1093% 0.0683% 0.0982%
Portfolio return 0.9232%
Variance 0.0614%
Part-II (b)
It could be observed that the portfolio weekly return is worked out to be 0.9232% and
variance is 0.0614%.
The return of portfolio is greater than the return on market index which implies that the
portfolio is performing better than the market. Further, comparing the return of portfolio with the
stocks individually, it could be observed that the portfolio is earning higher returns than Google
(0.45%) and Rio Tinto (0.81%). However, Amazon with a return of 1.50% is outperforming the
portfolio.
The variance of portfolio is 0.0614% which is equal to the variance of S&P 500
indicating that the portfolio is not riskier than market. It has been observed that the risk is
reduced significantly by forming a portfolio. The individual variances of stocks are very high
comparing with the variance of portfolio. Thus, overall it could be inferred that the risk and
return has been optimized by forming the portfolio of stocks (Pandya, 2013).
Part-III (a)
The risk free rate of return has been computed using the 26 weeks yield on 180 days
Treasury bill. The average of weekly yield is worked out to be 1.56%. Since, it is annualized
therefore; it has been converted into weekly yield which works out to be 0.0286%. Please refer
attached excel for calculations and data.
Part-III (b)

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The summary of results of regression analysis applied on the discrete returns of stocks is
shown as below:
Security Characteristics Line
The security characteristics line is the graphical presentation of the systematic risk of a
security and the return earned on that security. The slope of security characteristics line is known
as beta and the point of interception is called alpha. Beta represents the portion of security’s
return earned driven by the market movements while the alpha is constant. Thus, in plotting the
security market, two important elements are necessary these are alpha and beta (Chance &
Brooks, 2015). The computation of these elements is shown in the table given below:
Security Characteristic Line
Google Amazon
Rio
Tinto
Y (return of stock)
0.4512
%
1.5039
% 0.8146%
X (return of s&p
500)
0.2005
%
b (beta) 1.5343 1.0244 1.0544
a (alpha) 0.0076 0.0171 0.0103
Characteristic Line of stocks
Google Y= -0.0076+1.5343*0.2005%
Amazon Y= -0.0171+1.0244*0.2005%
Rio Tinto Y= -0.0103-1.0544*0.2005%
Characteristic Line of portfolio
Y (return of
portfolio)
0.9232
%
X (return of s&p
500)
0.2005
%
b (beta) 1.19
a (alpha) 0.0116
Y= -0.0116+1.19*0.2005%

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Thus, the beta of Google, Amazon, and Rio Tinto has been found to be 1.53, 1.02, and
1.05 times respectively. Beta shows the relative volatility of the stocks to the market as a whole
(Chance & Brooks, 2015).
The graphical representation of security characteristics line showing the prediction of Y
is as below:
It could be observed that the characteristics line of Google predicting Y is quite volatile
which shows that the volatility of the stock relative to the market is high. High volatility of the
stock relative to the market means high beta.
The characteristics line of Amazon is less volatile as compared to Google which shows
that Amazon has lower beta than Google. The Beta of Google is 1.54 times as against the beta of
1.02 times of Amazon.

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The characteristics line of Rio Tinto is similar to that of Amazon. This implies that the
volatility level of returns of Amazon and Rio Tinto is similar. The beta values of Amazon and
Rio Tinto are also similar.
Further, Jensen’s Alpha has also been computed to assess the performance of stocks and
portfolio. The Jensen’s alpha is computed by deducting the risk free rate of return from the
CAPM return of the stock and dividing the resultant figure by standard deviation. The summary
of results of which are shown below:
Jensen's Alpha
CAPM-RF
Google
Amazo
n
Rio
Tinto
Portfoli
o
CAMP
0.2926
%
0.2047
%
0.2099
% 0.2336%
RF (risk free
rate)
0.0282
%
0.0282
%
0.0282
% 0.0282%
Jensen's Alpha
0.2644
%
0.1765
%
0.1817
% 0.2055%
Part-II (c)
Apart from the above, the analysis of risk has been done in more detail by segregating the
total risk into systematic and unsystematic components (Kevin, 2015). The summary of results
has been shown as under:
Total risk, systematic and unsystematic risk
Google Amazon Rio Tinto Portfolio
Total risk (weekly) 0.17% 0.18% 0.17% 0.06%
Total risk
(annualized) 9.43% 10.21% 9.59% 3.16%
Systematic risk 235.41% 104.94% 111.18% 142.17%

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(beta)^2
Unsystematic risk
-
225.98% -94.73% -101.59%
-
139.00%
Part-III (d)
The beta shows systematic risk of stocks (Kevin, 2015). It could be observed that beta of
Google (1.53) is higher than the beta values of other two stocks namely Amazon (1.02) and Rio
Tinto (1.05). This analysis shows that Google is riskier than other two stocks.
The bifurcation of total risk into systematic and unsystematic shows that the unsystematic
risk is negligible. The entire risk of stocks and portfolio is absorbed by the systematic risk factor
only. Thus, the unsystematic risk (company specific risk) is not a material concern for the
investors.
Further, Jensen’s alpha has been observed to be 0.2644%, 0.1765%, and 0.1817% in case
of Google, Amazon, and Rio Tinto. This shows that stock of Google better performer comparing
to other two stocks. Further, the Jensen’s alpha of portfolio has been found to be 0.2055% which
indicates that the portfolio is performing even better than the individual stocks (Kevin, 2015).
Part-IV
The analysis of risk and return of a stock is critical for the investor to decide whether to
invest in that stock or not (Kevin, 2015). For this purpose, an analysis of risk and return through
various statistical measures such as arithmetic mean, geometric mean, variance, covariance, and
correlation has been done. The analysis of return using the historical data gives a solid basis to
predict the future trend in the stock’s performance. Therefore, the analysis in relation to the
return of stocks and portfolios is of great value to an investor. Further, the statistical measures
applied to assess the risk also provide a great help to the investor to make a choice for
investment.
In order to form a portfolio, it is of paramount importance to know the relationship
between the returns of stocks. The portfolio comprising stocks with less perfect positive
correlation would result in risk diversification. Therefore, it is important to analyze the
relationships between the returns of two stocks to optimize the return and risk through formation
of portfolio. Apart from this, an analysis of total risk segregating it into systematic and
unsystematic has been done in this report which is also important for an investor. The investor
should know the degree of risk caused by the systematic and unsystematic risk factors. This
knowledge would be helpful in designing in a perfect portfolio with optimum risk and return.
Thus, the analysis done in relation to the risk and return in this report is highly useful for
the investors. However, this analysis is subject to certain limitations. For instance, future aspect
of the performance of stocks is ignored in this analysis as it confines to historical data only.
Further, this analysis is purely based on the data and figures and it ignores the other factors such
as reputation of company in market. Moreover, this analysis also does not provide insight into
the financial performance of the company as it confines only to the analysis of stock prices.

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Therefore, in order to get insight of the financial performance, ratio analysis or trend
analysis of financial performance over the period of past few years is desirable. Further, an
analysis industry in relation to future performance could also be conducted to get overview of the
industry wide growth or downturn.

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References
Baker, K.H. & English, P. 2011. Capital Budgeting Valuation: Financial Analysis for Today's
Investment Projects. John Wiley & Sons.
Chance, D.M. & Brooks, R. 2015. Introduction to Derivatives and Risk Management. Cengage
Learning.
Kevin, S. 2015. Security Analysis And Portfolio Management. PHI Learning Pvt. Ltd.
Pandya, F.H. 2013. Security Analysis and Portfolio Management. Jaico Publishing House.
Statt, N. 2018. Alphabet profit miss sends stock down, but Google ad and cloud sales remain
strong. Accessed May 14, 2018 https://www.theverge.com/2018/2/1/16961214/alphabet-
google-q4-2017-earnings-report-announcement-youtube
Yahoo finance. 2018. Alphabet Inc: Financial. Accessed May 14, 2018
https://finance.yahoo.com/quote/GOOG/financials?p=GOOG
Yahoo finance. 2018. Amazon Inc: Financial. Accessed May 14, 2018
https://finance.yahoo.com/quote/AMZN/profile?p=AMZN
Yahoo finance. 2018. Rio Tinto Plc: Financials. Accessed May 14, 2018
https://finance.yahoo.com/quote/RIO/financials?p=RIO

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Appendix-1
Company: Google
SUMMARY
OUTPUT
Regression Statistics
Multiple R
0.9019
67
R Square
0.8135
44
Adjusted R
Square
0.8057
75
Standard
Error
0.0180
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Observation
s 26
ANOVA
df SS MS F
Significa
nce F
Regression 1 0.033969
0.033
969
104.7
167 3.13E-10
Residual 24 0.007785
0.000
324
Total 25 0.041755
Coeffici
ents
Standard
Error t Stat
P-
value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept
-
0.5328
9 0.150279
-
3.545
98
0.001
644 -0.84305
-
0.2227
3
-
0.84305 -0.22273
X Variable
1
1.5343
22 0.149937
10.23
312
3.13E
-10 1.224867
1.8437
76
1.22486
7
1.84377
6
Company: Amazon

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SUMMARY OUTPUT
Regression Statistics
Multiple R
0.5797
92
R Square
0.3361
59
Adjusted R
Square
0.3084
99
Standard
Error
0.0352
99
Observation
s 26
ANOVA
df SS MS F
Significa
nce F
Regression 1 0.015143
0.015
143
12.15
325
0.00190
7
Residual 24 0.029904
0.001
246
Total 25 0.045047
Coeffici
ents
Standard
Error t Stat
P-
value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept
-
0.0114
4 0.294525
-
0.038
83
0.969
347 -0.61931
0.5964
33
-
0.61931
0.59643
3
X Variable 1
1.0244
21 0.293855
3.486
151
0.001
907
0.41793
5
1.6309
07
0.41793
5
1.63090
7
Company: Rio Tinto
SUMMARY
OUTPUT
Regression Statistics
Multiple R
0.6147
84
R Square
0.3779
59

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Adjusted R
Square
0.3520
41
Standard
Error
0.0331
68
Observation
s 26
ANOVA
df SS MS F
Significa
nce F
Regression 1 0.016043
0.016
043
14.58
269 0.000832
Residual 24 0.026403
0.001
1
Total 25 0.042446
Coeffici
ents
Standard
Error t Stat
P-
value
Lower
95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept
-
0.0483
8 0.276747
-
0.174
83
0.862
677 -0.61956
0.5227
94
-
0.61956
0.52279
4
X Variable
1
1.0544
17 0.276117
3.818
729
0.000
832 0.484539
1.6242
94
0.48453
9
1.62429
4