portfolio group assignment report 2015.docx
TRANSCRIPT
Portfolio Management INVE3001
Group Assignment
Name & Student ID: Gavin Ting Kok Shen / 17505521; 7E2B1428
Jason Lim Hock Lian / 16710023; 7E3A1795
Tan Chu Ying / 17417053; 7E2B1506
Tutor’s Name: Dr Md Shibley Sadique
Tutorial Date & Time: Wednesday, 6.00pm
Semester and Campus Details: Semester 1, 2015 – Miri, Sarawak.
Table of Contents1.0 Introduction..........................................................................................................2
2.0 Report: Part 1.......................................................................................................3
Question (1)............................................................................................................3
A) Calculate the discrete rate of return and continuously compounded rate of return for 27 weekly periods..................................................................3
B) Calculate Arithmetic mean return and Geometric mean return............3
Question (2)............................................................................................................4
A) Variance of return for each stock and index...........................................4
B) Standard deviation of each stock and index...........................................5
C) Covariance and Correlation Coefficients................................................5
Question (3)............................................................................................................6
Comparing results from question 1 and question 2........................................6
Considering of each stock’s performance:......................................................7
3.0 Report: Part 2.......................................................................................................8
Question 1...............................................................................................................8
A) Weekly rate of return equally weighted portfolio and the Expected Return..................................................................................................................8
B) Variance of equally weighted portfolio (Used of Matrix Algebra).........9
Question 2...............................................................................................................9
A) Compare and Examine the Portfolio return with each selected stocks and stock index...................................................................................................9
4.0 Report: Part 3.....................................................................................................11
Question 1.............................................................................................................11
A) Yield of the Treasury bill.........................................................................11
Question 2.............................................................................................................12
A) Security Characteristic Line (SCL) for each stocks and equally weighted portfolio.............................................................................................12
Question 3.............................................................................................................14
A) Total risk of each stock and the portfolio.............................................14
Question 4.............................................................................................................14
A) Comment on each stock’s and portfolio performance.........................14
B) Comment on each stock’s and portfolio risk characteristics based on both systematic and unsystematic risk..........................................................15
5.0 Report: Part 4.....................................................................................................16
Appendix...................................................................................................................20
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1.0 Introduction
In this reports, the three companies selected are companies that are listed on
New York Stock Exchange (NYSE).
First company, Johnson & Johnson which is a Health Care Industry company
operate for more than 120 years, focusing on bringing up new ideas, new products
and new service that are innovation to advance the health and happiness of people
(Johnson & Johnson 2015). Code for the company on New York Stock Exchange is
(NYSE: JNJ).
Second company, JPMorgan Chase and Co which is a company operated for
approximately 200 years, oldest financial institutions in U.S and operate in more than
60 countries around the world (JPMorgan 2015). The company is in Banking Industry
and code for the company on New York Stock Exchange is (NYSE: JPM).
Last company is The AES Corporation which is a company operated nearly 35
years, stand as a global energy industry leader and largest Independent Power
Producer (IPP) in United States (The AES Corporation - About Us 2015). The
company is in Electrical Industry and code for the company on New York Stock
Exchange is (NYSE: AES)
To measure the values of these stock, we will be taking Standard & Poor’s 500
Index to compare and evaluate. Standard & Poor’s 500 known as S&P 500 in NYSE,
a well-diversified portfolio and it is the leading indicator for overall United States stock
market (Standard & Poor's 500 Index 2015).
The historical stock price data for 3 stocks and stock market (S&P 500) index
are collected from Yahoo Finance on 28 weeks basis from 22nd September 2014 to
30th March 2015 and prices taken from every Monday of the week.
All the date, number of weeks, opening price of each week, average volume
traded and adjusted closing price of each stock and index can be seen in Appendix 1
to Appendix 4.
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2.0 Report: Part 1
Question (1)
A) Calculate the discrete rate of return and continuously compounded rate
of return for 27 weekly periods.
Discrete rate of return is measuring the rate of changes in the value of a
particular asset over a period of time (Analyst Notes 2015). As for calculation of
discrete return, we just need current stock price and previous stock price (Pareek
2011). The formula can be seen in below,
Discrete Return=(Stock PriceT−Stock PriceT−1 )
Stock PricecT−1
Continuously compounded rate of return also measuring the rate of changes in
the value of a particular asset but assuming that it is continuously compounding.
As for the calculation, we are taking stock price at time 1 divided by stock price at
time 0 (Pareek 2011). To be precise, the natural logarithm of the stock ending
price over the stock beginning price which arrive the formula as follow (Analyst
Notes 2015). The formula can be seen in below,
Continuosly Return=lnStock PriceTStock PriceT−1
The formula input in excel is using log
which derive [=LN (Stock Price T/Stock Price T-1)].
As a result, both discrete and continuously return are calculated and can be
refer to both Appendix 5 and Appendix 6.
B) Calculate Arithmetic mean return and Geometric mean return. Arithmetic mean is the measure of central tendency which known as the
average of a set of numbers or the center of a set of numerical values (Arithmetic
Mean 2015). To be precise, the use of Arithmetic mean is to look for the average
Holding Period Return (HPR) for a time series of returns where the formula can be
seen as follow,
HPR Average=∑T=1
n HPRTn
n= the number of time periods (Bodie et al. 2013). To calculate the Arithmetic
mean, we first sum up all the rate of return of each stock and index, then divided by
the total of 27 weeks as per requirement of the question. The formula input in excel is
[=AVERAGE (Sum of Discrete Return)]
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Geometric mean similar with Arithmetic mean in term of measure of central
tendency but Geometric mean calculate in a way that HPR are being compounded
over multiple periods thus the formula can be seen in below (Bodie et al. 2013),
HPR Average=¿¿
Basically adding 1 to each return and because geometric considered of
compounding therefore it need to be the power of 1 divided by number of periods
then minus 1 that previously added. In excel, it is calculated by [=SUMPRODUCT
(GEOMEAN (Discrete Return X +1))-1].
As a result, The AES Corporation has the lowest arithmetic return of
(0.2852%) and geometric return of (0.3646%). The highest average return based on
arithmetic mean is S&P 500 which is 0.2081% while it also score 0.1884% of
geometric return and it is highest among all the stocks. In between, Johnson &
Johnson has both negative arithmetic and geometric return while JPMorgan Chase
has both positive arithmetic and geometric return.
Overall, we can see that S&P 500 and JPMorgan Chase perform better than
Johnson & Johnson and AES Corporation based on both Arithmetic and Geometric
return. In addition, all the arithmetic mean is greater than geometric mean, the
complete table for the calculation can be refer to Appendix 7.
Question (2)
A) Variance of return for each stock and index
Variance is used to measure the volatility which also known as measuring the risk
or uncertainty that investor might receive when purchasing a stock, the largest the
value of variance indicate that value are more far than mean thus higher the risk
(Variance 2015).
In Excel, variance formula is simply [=VAR.S (All Discrete Return)] thus arrive the
value of variance 0.0461% for Johnson & Johnson, 0.1006% for JPMorgan, 0.1666%
for The AES Corporation and 0.0410% for S&P 500. Overall, S&P 500 has the lower
risk or uncertainty compared with the three selected stocks then follow by Johnson &
Johnson, JPMorgan and The AES Corporation.
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B) Standard deviation of each stock and index
Standard deviation also the measurement of dispersion of a set of numbers from
its mean, it simply just square root the answer of variance which is the formula as
below, Standard Deviationσ=√Variance
In Excel, standard deviation are just calculated as [=STDEV.S (28 weeks Discrete
Return)] thus arrive the value of standard deviation 2.0246% for S&P500, 2.1477%
for Johnson & Johnson, 3.1723% for JPMorgan and 4.0816% for AES. Since
standard deviation also the measurement of risk, the lower the value the better it is.
Both variance and standard deviation table for each stock and index are able to
seen in Appendix 7 as well.
C) Covariance and Correlation Coefficients.
Covariance and correlation coefficients are both measure how two variables are
related. Covariance usually measure whether the two variable are positively related,
negatively related or unrelated (Covariance 2015). For example, if stocks were to say
positively related, then the two assets are tend to move together. Covariance is not
standardized therefore the value can be in a huge range and thus difficult to
determine how strong the relationship between the selected variables (Covariance &
Correlation 2015). Covariance formula shown as follow (Bodie et al. 2013),
COV (X ,Y )=∑i=1
n
¿¿¿
In Excel, by inputting the formula of [=COVAR (Two Discrete Return on Array 1
and Array 2)], we arrive the covariance of different pair of stocks as well as
covariance of each stock and index and this can be seen in Appendix 8.
As mentioned, correlation coefficients also measure how two variables are related
but it is a more standardized therefore it able to determine whether the relationship
are strong or weak (Covariance & Correlation 2015). The number for correlation
coefficient ranges from -1 to +1 which is from weakest to strongest. Correlation
formula shown as follow (Bodie et al. 2013),
r(X ,Y )=COV (x , y )
Sx S y
In Excel, by inputting the formula of [=CORREL (Discrete Return of A, Discrete
Return of B)], we arrive the correlation coefficients of different pair of stocks as well
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as correlation coefficients of each stock and index and this can be seen in Appendix
8. Further discussion of correlation coefficient will continue in next part.
Question (3)
Comparing results from question 1 and question 2.
In Appendix 9 & 10, different Figures showing different stock weekly discrete
return comparing with weekly discrete return of S&P 500. Among all, the most stable
stock is Johnson & Johnson because the movement of stock in 27 weeks are less
volatility thus it moves almost as close as S&P 500. This also can be prove from the
calculation of correlation coefficients indicate that JNJ has a 0.7779 with S&P 500
which shows both are strong positively related.
From Figure 1.2 in Appendix 9, it shows that JPMorgan movement is more
volatile but in general, the stock is still moving along together with market indicated
from their 0.7858 strong positive correlation coefficient value with S&P500.
In the case of AES Corporation, the stock has a week positive correlation
coefficient value of 0.4647 thus it shows that the stock doesn’t move along with S&P
500 from Figure 1.3 in Appendix 10. Instead, it is more volatile than both JNJ and
JPMorgan as well as market index.
Although different stock has different correlation coefficient value compare
with S&P 500, but most noticeable in Appendix 10 Figure 1.4, is that all the stocks
has a same dropping point at week 11th which fall around the week in between
December 1st to December 7th 2014
One of the reason behind this was that during last quarter of 2014, it was
announced by Organization of Petroleum Exporting Countries (OPEX) that oil
production will be decrease thus hitting the world economy, energy stocks especially
as well as several currencies (Carlson 2014).
Another issue raised was that not only the decrease of oil production affected
the market, but also dispute of ISIS, slowing down economy in China and noticeable
disease “Ebola” causes different industry performance thus bringing down the world
economy performance (Gibson 2014).
Considering of each stock’s performance:
Johnson & Johnson
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Based on Appendix 7, JNJ has a negative value of (0.1251%) average return
throughout the selected financing period. One of the major factor is that JNJ stock
price was affected after the announced of 2014 earnings was lower from what
analysts estimated, the stock’s price thus declined in approximately of 1% (Cortez
2014). JNJ announced that that will reconstruct their capital and save about %1billion
in the next few years by reinforce their finance and human resources department
(Cortez 2014).
JPMorgan Co.
The company shows a positive arithmetic mean return of 0.1215% and even
The Street Quant rated JPMorgan as a stock to buy (Fukushima 2014). The
Company was generally moves from underperform to outperform the market along
the selected financing period (Fukushima 2014).
JPMorgan are well managed in term of their expenses and investment for
such, the company announced that they will cutting down approximately 6% of
branches because most of their customers has moved to online transaction
(Fukushima 2015). In addition, it was also strongly supported by the company’s good
standing EPS growth, ROE, and high gross profit margin (Fukushima 2015).
The AES Corp.
AES Corporation hits the highest negative return of (0.2852) throughout the
selected financing period. One of the factor was that the drop in crude oil, hitting most
of the energy sector as well as S&P 500 energy shares (Shell 2015). Despite the
whole economy’s factor, the company itself wasn’t doing that good during last
financial year. The company was rated by The Street Quant as a stock that should
not be bought at the moment which falls at the grade of C+ stock (The AES
Corporation Business Summary 2015). The company was encounter with the issue of
high debt and low performance of the stock itself although the company has a good
records in EPS growth (The AES Corporation Business Summary 2015).
Optimum stock
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From our report analysis so far, the best performance will still be S&P 500 with
the highest average return of 0.2081% and lowest risk of 2.0246%.
If analysis were based on each single stock, then it will first be JPMorgan with
the average return of 0.1215% but moderate risk of 3.1723 then followed by JNJ with
the average return of (-0.1251%) but lower risk of 2.1477.
While for AES, it might not be suitable to hold or buy at the moment, as stock
are characterise with low risk low return, high risk high return (Sullivan 2012) . The
AES stock feature a highest risk of 4.0816, but the return is on a highest negative
value of (0.2852) compare to the other selected stocks therefore rational investor
might not go for this stock despite whether the investor is risk lover or adverse.
The result of risk and return of 3 selected stocks as well as S&P 500 can be
seen in Appendix 11.
3.0 Report: Part 2Question 1
A) Weekly rate of return equally weighted portfolio and the Expected Return.
The weight for a complete of portfolio must always be equal to 1 or in other words,
sum of the proportion weight of all stocks in a portfolio must always be 100%
(Working with Portfolio Constraints 2015). Since in this report only selected 3 stocks,
then the weight of each stock is 0.3333 because value of 1 divided by 3 stocks which
mean equally weighted.
The weekly rate of return of equally weighted portfolio are calculated by using the
formula input to excel [= (0.3333*(Week 1 stock A Discrete Return) + (0.3333*(Week
1 Stock B Discrete Return) + (0.3333*Week 1 Stock C Discrete Return) thus the
complete weekly return are able to be seen in Appendix 12.
To calculate the expected return for the equally distributed portfolio, we used the
formula as follow (Bodie et al. 2013),
E (Rp )=(Weight A×ReturnA )+(WeightB×ReturnB )+(WeightC×ReturnC )
Where the (Weight A, B, C) is 0.3333, Return (A) is average return of JNJ, Return (B) is
average return of JPMorgan and Return (C) is average return of AES thus arrive the
expected return of -0.0962%. This can be refer to Appendix 13.
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B) Variance of equally weighted portfolio (Used of Matrix Algebra).
To calculate the variance of 3 stocks portfolio are using a different formula than
calculating for single assets. In order to calculate the variance for the portfolio, we
first need to get the weights of each assets and correlations between pairs of assets
only then able to use the covariance matrix formula as follow (Programming in R:
Modelling Investment Portfolios with Matrix Algebra 2015),
σ 2p=(W AW BW C )( σ A2 σ AB σ AC
σ AB σ B2 σBC
σ AC σ BC σc2 )(W A
WB
W C)
Thus arrive the portfolio variance value of 0.0064%. After getting the value
variance 0.0646%, square root it and we are able calculate portfolio standard
deviation by using the formula below (Bodie et al. 2013),
σ (r p )=√Variance
And we arrive the portfolio standard deviation value of 2.5430%. In addition, full
calculation for both variance and standard deviation are showed in Appendix 14.
Question 2
A) Compare and Examine the Portfolio return with each selected stocks and
stock index.
Table 1
StockExpected Return
VarianceStandard Deviation
JNJ -13% 0.04% 2.14%
JPMorgan 12% 0.10% 3.17%
AES -29% 0.16% 4.08%
S&P 500 21% 0.04% 2.02%
Equally Distributed
Portfolio-9.62% 0.06% 2.54%
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Talks about return.
Comparison of each stock and Equally Distributed Portfolio return and
corresponding variances.
From the table 1 above, we can clearly see that S&P 500 score a highest
return of 21% while AES score the highest loss of 29% during the financial period.
JPMorgan rank at the 2nd with the high return of 12% follow by “Equally distributed
Portfolio” rank at 3rd with a negative return of (9.62) then follow by JNJ and AES.
The negative return of the equally distributed portfolio might cause from the
high loss encounter by AES and JNJ with only one assets (JPMorgan) has positive
return. In addition, comparing with big index like S&P 500 might still not enough
because S&P 500 consists of 500 well-diversified assets.
Well-diversified occur when portfolio consists of different assets such as stock,
bond are most importantly they must not perfect positively related (Bodie et al. 2013).
From the correlation coefficient table in Appendix 8, there are no pairs of asset that
are perfect correlated therefore by adding more negative correlated assets might able
to overcome the issue like currently encounter by Equally Distributed Portfolio which
are when two stocks are down, one are only able to help minimize losses.
In term of the risk of “Equally distributed assets”, it is better holding single
assets such as AES. As mentioned, as long as portfolio increase the amount assets
that are not perfect correlated then it will able to lower down the risk because portfolio
is diversifying the risks.
Based on the 3rd column of the table 1, AES has the highest risk of 4.08, then
JPMorgan with the risk of 3.17%, JNJ with 2.14% and followed by S&P 500 with the
lower risk of 1.99%.
Although the “Equally Distributed Portfolio” has a negative return, but the risk
that investor might face is only 2.54% which is way better than holding single assets
such as AES Corp with the high risk of 4.08%. From the table 1, although JNJ has a
lower risk compare with “Equally Distributed Portfolio” but the return of stock fall
deeper than the “Equally Distributed Portfolio”.
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Table 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
-10.0000%
-5.0000%
0.0000%
5.0000%
10.0000%
Equally Distributed Portfolio
Equally Distributed Portfolio
WeeksWe
kk
ly D
isc
rete
Re
turn
In addition, from the table 2, we can see that the portfolio performance doesn’t
seems to be volatile because the stock’s movement doesn’t move up and down in a
huge range based on the discrete rate of return in Appendix 12.
Overall, holding a portfolio with different correlated assets is better than
holding a single assets because it able investor to reduce the risk that may
encountered with.
4.0 Report: Part 3 Question 1
A) Yield of the Treasury bill. In this report, the yield of the Treasury bill are taken from the federal reverse of
United States (Selected Interest Rates - Historical Data 2015). The period are slightly
different than our selected stocks period as the weekly time given by federal reverse
is on every Friday while our stock is on Monday. The date taken are from 26 th of
September 2014 to 27th of March 2015 while our selected stocks date taken from 22nd
September 2014 to 30th of March 2015. Full details of the weekly rate are able to be
seen in Appendix 15.
Treasure security basically backed by United States Treasury where it is
important indicator for the economy such as inflation rates movement. Treasury
securities has many category such as 91 days, 182 days, one year, two years and
even up to ten years. Since those securities are backed by U.S treasury, it consider
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as risk-free assets but of course, the longer the time, the riskier it is because things
can be offbeat in the long run (Treasury Bills 2015).
Back to the treasury bills we extracted, it is basically a short-term debt at a
discount which mean discount from the face value (91 Day T Bill Treasury Rate
2015). In our report, the average discount rate is 8.1071% based on the calculation
from Appendix 16.
Since yield that are reported is in 6 months figured, we don’t need to divide it
by 52 weeks but 26 weeks thus those rate will be the proxy of our risk-free rate.
Question 2
A) Security Characteristic Line (SCL) for each stocks and equally weighted portfolio. Security Characteristic Line known as the Security Market Line (SML) is a line
formed by regression analysis based on the result of excess return over the risk-free
rate on the market (Characteristic Line 2015). To calculate the excess return, we take
each stock discrete return minus the risk-free rate according to the same week. As a
result, the full table of the excess return for Johnson & Johnson, JPMorgan Chase,
The AES Corp as well as the Equally Weighted Portfolio can be seen in Appendix 16
& 17. After the complete calculation, then regression analysis are able to be formed.
Security Characteristic Line are to indicate a stock’s abnormal return which is
known as the (Alpha) where the line intercept with vertical line and indicate the
different between systematic (not diversifiable) risk and unsystematic risk
(diversifiable) risk where it can be tell from the slope of the line (Harvey 2015). The
formula to find out regression is,
SecurityCharacteristic Line :
(Ri )=α i+ βi (RM )+e i
While in Excel, we simply use the Data Analysis, X variable for S&P 500 and Y variable for each stock. The result can be seen in Appendix 18, 19 and 20.
Beta is the sensitivity of share’s return to the market return. Market beta is
always equal 1 therefore when a stock’s beta higher than 1 that means the stock is
more aggressive than market while a stock’s beta lower than 1 that means the stock
is more defensive or less volatile (Bodie et al. 2013).
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Based on the calculation of beta using the excel function of [=Slope (Excess Return of stocks, Excess Return of Market), the result is
Stock Beta (Slope)Johnson & Johnson 0.823532702JPMorgan 1.232700842AES Corp 0.919200835Equally Weighted Portfolio 0.991712486
Which can see that JPMorgan is more volatile while Johnson & Johnson and AES Corp is more defensive.
While using the regression method, it shows a slightly different value of beta which are
Stock Beta (Regression)Johnson & Johnson 0.8165JPMorgan 1.2425AES Corp 0.9240Equally Weighted Portfolio 0.9942
Which still can see that JPMorgan is more volatile than the market while Johnson & Johnson and AES Corp is more defensive.
Alpha is representing the stock’s abnormal return (Bodie et al. 2013). When conducting the regression analysis in excel, the value of Alpha is automatically calculated. The Alpha of each stock are
Stock AlphaJohnson & Johnson -0.0032JPMorgan -0.0010AES Corp -0.0053Equally Weighted Portfolio -0.0032
From the result, it clearly shows that all the stocks has negative alpha return
which mean underperformed of its benchmark.
Although slope function and regression function calculated slightly different
beta, but when equation of regression of equation formed, it calculated the same
result as slope function in Excel. From the regression graph, we can see that
Johnson & Johnson dots are moving upwards and it stick closely to the regression
line, JPMorgan and Equally Weighted Portfolio dots are moving upwards as well but
dots are not close to regression line as Johnson and Johnson does. AES Crop
regression graph, dots are disperse and all over the place.
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A complete of summary output as well as the regression graph are able to be
seen in Appendix 18 for Johnson & Johnson, Appendix 19 for JPMorgan and
Appendix 20 for The AES Corp.
Question 3
A) Total risk of each stock and the portfolio.A total risk is a risk that are include both systematic and unsystematic risk.
Systematic risk is the risk that non-diversifiable risk because it affecting the whole
economy as well as the market such as natural disasters or events that cannot the
avoided (Bodie et al. 2013). On the other hand, unsystematic risk is diversifiable
because it only comes from internal issue such as a firm management department
therefore by upgrading or improving that department might reduce the unsystematic
risk (Bodie et al. 2013).
Total risk is calculated based on the formula as below,
σ i2=β i2σm2+σ ¿
Where β i2σm2 is the systematic risk and σ ¿ as the unsystematic risk.
Johnson and Johnson has proportion systematic risk of 0.602653546 and
proportion unsystematic risk of 0.397346454, JPMorgan has proportion systematic
risk of 0.000061891 and proportion unsystematic risk of 0.999938109, AES Corp has
proportion systematic risk of 0.207889944 and proportion unsystematic risk last but
not least Equally Weighted Portfolio has proportion systematic risk of 0.623390182
and proportion unsystematic risk of 0.376609818. Among all the stocks, JPMorgan
has the lowest non-diversifiable risk but also scoring a high diversifiable risk. As a
result, based on the calculation in Appendix 22, JPMorgan might need to improve
internal management to overcome high diversifiable risk issue.
Question 4
A) Comment on each stock’s and portfolio performance.
Overall from the research, we can see that a well-diversified portfolio like S&P
500 can have a stable mean return even there are some economic issue during the
period of last quarter of 2014. In general, all the stock are still considerable because
based on the beta of JNJ 0.8235, JPMorgan 0.0123, AES Corp 0.9192 and Equally
Weighted Portfolio 0.9917, all are less volatility than the market.
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Among the three selected stocks and Equally Weighted Portfolio, none of them
has positive abnormal return but small relatively negative alpha for each of the stocks
thus it means that their share price is overvalued and underperformed against its
benchmark, causing low rate of return for its level of risk.
Based on Appendix 19, JPMorgan Chase & Co's shows sensitive to the market
due to its high beta of 1.2425 compare to Johnson & Johnson beta value of 0.8235,
AES beta value of 0.9192 Corporation and Equally Weighted Portfolio beta value of
0.9917. Among all, Johnson & Johnson has lowest beta of 0.8165 although earlier on
calculation it has negative return which indicate that the stock’s volatility is lesser
than the market. However, JP Morgan Chase & Co's shows lowest alpha of -0.0010
that gives least abnormal return.
Based on standard deviation value in Appendix 7, AES Corp is more risky
compare to other stocks as it reaches highest standard deviation of 4.0816% while
JPMorgan ranked at 2nd position with the and 99.99% of unsystematic risk is showed
at JP Morgan Chase & Co. Therefore, JP Morgan Chase & Co has highest
unsystematic risk among stocks and portfolio.
B) Comment on each stock’s and portfolio risk characteristics based on
both systematic and unsystematic risk.
Based on Appendix 22, holding a portfolio is better than holding single based
on the higher value of unsystematic risk. Unsystematic risk as discuss earlier on
are the risk that came from company or internal sources which mean the risk are
able to be reduce which generally decrease the total portfolio risk. In addition,
high unsystematic risk often result the company stock in risk and might affect the
reputation in general.
Appendix 22 indicate that equally weighted portfolio has alpha of -0.0032 thus
showing that portfolio is overpriced. However, standard deviation of portfolio is
2.54% which is the third highest among three stocks and market index. Such
occasion signify that risk of portfolio will not be lowered down by diversified of its
stock. Reason being that the correlation coefficient among three stocks does not
show negative sign. This further clarify that when one share price decrease, the
other two share price will fall as well. In addition, equally weighted portfolio shows
lowest percentage of unsystematic risk of 37.66%.
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As a result, we can see that investing in portfolio, risk can be diversified and
reduce loss on riskier stock when particular stock can turn out to be bad
investment such as AES’s stock. However, it is not an efficient and effective way
for all of the portfolio. An efficient portfolio can signify higher return for the given
level of risk or less risk for a given return. Furthermore, it does show method on
lessen risk through diversification. Reason is due to the behaviour and
preferences of investor as risk seeker is willing to put their money on stock that is
at high risk.
5.0 Report: Part 4In this report, regression analysis shows the relationship between returns of
each stock and equally weighted portfolio to market index. It helps the investors to
anticipate future expected return and decide on investment decision as it helps
providing quantitative support and shows a line of best fit for data point (Bodie et al.
2013).
However, there is downfall for regression analysis this is because market
index may vary over time due to changes of economy, market changes or currency
exchange crisis. Furthermore, extracting data of 28 weeks can be regard as short
time, indicating failure to build stable reasonable relationship. To further elaborate,
regression analysis can be unusable in the financial world as it failed to produce
statistically effective judgement regards to company's value but it can only be apply
to theory base for understanding purpose.
Portfolio analysis can access the performance of each stock in regards to risk
and return. Portfolio analysis represent underperforming or excess risky stock and
helps to assist investor to set aside investment in order to meet their financial
objectives (Ehow 2014). Furthermore, investors can make decision in allocating
investment as they are able to select the risk and return of each stock. However,
portfolio analysis provide downfall as well. For instance, analysing stock that is from
historical closing price is not efficient way as past performance cannot be assure for
future accurate outcome.
The further analyses are focusing at fundamental analysis. Fundamental
analysis contain the sheer determination of company's stock price from its earnings
and dividend, future interest rate and risk assessment. To further elaborate, financial
analyst is trying to learn of future performance of a company by looking into
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economic ways such as company’s position in the industry, assessment of the
company management and overall forecast of the industry. As fundamental analysis
is difficult to analyse and is not available to the public, investor has the privilege to
purchase it from investment firm at a certain price. This can grant them access to buy
low price of shares of a company and can make higher return.
Page 19 of 49
ReferencesAnalyst Notes 2015. "CFA Exam: Study Notes, Practice Questions and Mock
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Page 22 of 49
AppendixAppendix 1
Johnson & Johnson (JNJ) Historical Price on every MondayDate Open Average Volume Adjusted Close
Mar 30, 2015 101.24 6,061,200 101.55Mar 23, 2015 102.47 8,334,100 100.34Mar 16, 2015 99.74 8,459,400 102.4Mar 9, 2015 100.2 7,942,900 99.21Mar 2, 2015 102.51 7,938,500 100.11Feb 23, 2015 100.74 8,617,400 102.51Feb 17, 2015 99.39 9,154,800 100.26Feb 9, 2015 101.06 13,458,600 98.93Feb 2, 2015 100.49 8,854,100 100.4Jan 26, 2015 101.8 9,284,400 99.44Jan 20, 2015 101.55 12,831,300 101.49Jan 12, 2015 105.17 10,160,900 103.32Jan 5, 2015 104.48 8,143,000 104.21Dec 29, 2014 104.64 5,150,200 103.79Dec 22, 2014 105.69 6,164,700 104.33Dec 15, 2014 104.77 12,687,700 104.82Dec 8, 2014 108.42 7,714,000 103.7Dec 1, 2014 107.89 6,784,900 107.76Nov 24, 2014 107.92 6,961,200 107.5Nov 17, 2014 108 6,472,100 107.11Nov 10, 2014 108.07 5,838,800 106.71Nov 3, 2014 107.83 7,250,200 106.75Oct 27, 2014 103.07 9,064,400 106.34Oct 20, 2014 98.83 7,635,900 101.75Oct 13, 2014 101.46 15,979,200 97.38Oct 6, 2014 105.68 8,483,900 99.88Sep 29, 2014 106.38 8,018,000 103.72Sep 22, 2014 108 5,988,600 105.67
Page 23 of 49
Appendix 2
JPMorgan Chase & Co. (JPM) Historical Price on every MondayDate Open Average Volume Adjusted Close
Mar 30, 2015 60.88 20,656,500 60.56Mar 23, 2015 61.75 13,597,500 59.16Mar 16, 2015 61.5 14,498,200 61.34Mar 9, 2015 60.84 15,408,100 60.6Mar 2, 2015 61.28 15,406,000 60.49Feb 23, 2015 59.5 17,746,000 60.88Feb 17, 2015 59.36 14,055,600 59.41Feb 9, 2015 57.42 16,698,400 59.28Feb 2, 2015 54.53 18,071,700 57.51Jan 26, 2015 56.41 19,897,900 54.02Jan 20, 2015 56.04 23,050,400 56.31Jan 12, 2015 59.28 31,705,800 55.56Jan 5, 2015 62.06 21,077,000 58.95Dec 29, 2014 62.42 12,312,100 62.08Dec 22, 2014 62.16 11,031,200 61.74Dec 15, 2014 60.74 19,741,100 61.13Dec 8, 2014 62.6 19,823,300 59.26Dec 1, 2014 59.98 13,795,400 61.89Nov 24, 2014 60.7 9,380,900 59.38Nov 17, 2014 60 10,076,000 59.67Nov 10, 2014 61.25 11,920,500 59.5Nov 3, 2014 60.79 12,801,400 60.67Oct 27, 2014 58.45 14,890,500 59.7Oct 20, 2014 56.1 12,995,700 57.98Oct 13, 2014 58.5 27,256,300 55.47Oct 6, 2014 60.78 15,566,600 57.76Sep 29, 2014 60.03 17,389,400 59.52Sep 22, 2014 60.94 13,914,200 59.38
Page 24 of 49
Appendix 3
The AES Corporation (AES) Historical Price on every Monday
Date Open Average Volume Adjusted Close
Mar 30, 2015 12.52 3,694,100 12.64Mar 23, 2015 12.83 4,224,000 12.39Mar 16, 2015 12 6,028,900 12.74Mar 9, 2015 12.26 7,885,800 11.83Mar 2, 2015 12.91 7,904,100 12.14Feb 23, 2015 11.9 8,956,000 12.87Feb 17, 2015 11.85 5,398,900 11.8Feb 9, 2015 12.05 7,543,100 11.77Feb 2, 2015 12.24 5,960,200 11.98Jan 26, 2015 12.67 5,139,400 12.13Jan 20, 2015 13.44 6,127,200 12.48Jan 12, 2015 12.87 6,804,900 13.16Jan 5, 2015 13.67 5,898,200 12.7Dec 29, 2014 14.22 4,188,200 13.49Dec 22, 2014 13.5 4,248,600 14Dec 15, 2014 13.7 8,699,600 13.29Dec 8, 2014 13.65 5,949,200 13.08Dec 1, 2014 13.8 6,121,800 13.47Nov 24, 2014 14.14 4,285,500 13.65Nov 17, 2014 13.43 5,303,400 13.88Nov 10, 2014 13.42 7,273,600 13.26Nov 3, 2014 14.15 8,614,300 13.25Oct 27, 2014 13.71 4,546,200 13.85Oct 20, 2014 13.3 4,670,700 13.47Oct 13, 2014 13.21 7,719,700 13.03Oct 6, 2014 14.21 5,671,700 13Sep 29, 2014 14.15 3,802,300 13.87Sep 22, 2014 14.65 2,926,900 13.95
Page 25 of 49
Appendix 4
Standard & Poors 500 Historical Price on every MondayDate Open Average Volume Adjusted Close
Mar 30, 2015 2,064.11 2,917,690,000 2,086.24Mar 23, 2015 2,107.99 3,299,628,000 2,061.02Mar 16, 2015 2,055.35 3,900,998,000 2,108.10Mar 9, 2015 2,072.25 3,465,796,000 2,053.40Mar 2, 2015 2,105.23 3,409,900,000 2,071.26Feb 23, 2015 2,109.83 3,312,386,000 2,104.50Feb 17, 2015 2,096.47 3,315,117,500 2,110.30Feb 9, 2015 2,053.47 3,626,410,000 2,096.99Feb 2, 2015 1,996.67 4,164,222,000 2,055.47Jan 26, 2015 2,050.42 3,905,778,000 1,994.99Jan 20, 2015 2,020.76 3,856,005,000 2,051.82Jan 12, 2015 2,046.13 4,055,114,000 2,019.42Jan 5, 2015 2,054.44 3,872,572,000 2,044.81Dec 29, 2014 2,087.63 2,551,852,500 2,058.20Dec 22, 2014 2,069.28 2,391,420,000 2,088.77Dec 15, 2014 2,005.03 5,086,390,000 2,070.65Dec 8, 2014 2,074.84 3,992,236,000 2,002.33Dec 1, 2014 2,065.78 3,657,260,000 2,075.37Nov 24, 2014 2,065.07 2,942,725,000 2,067.56Nov 17, 2014 2,038.29 3,400,928,000 2,063.50Nov 10, 2014 2,032.01 3,234,462,000 2,039.82Nov 3, 2014 2,018.21 3,730,468,000 2,031.92Oct 27, 2014 1,962.97 3,762,182,000 2,018.05Oct 20, 2014 1,885.62 3,589,572,000 1,964.58Oct 13, 2014 1,905.65 4,962,132,000 1,886.76Oct 6, 2014 1,970.01 4,072,602,000 1,906.13Sep 29, 2014 1,978.96 3,761,592,000 1,967.90Sep 22, 2014 2,009.08 3,229,072,000 1,982.85
Page 26 of 49
Appendix 5
Page 27 of 49
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Joh
nso
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Jo
hn
son
(JN
J)JP
Mo
rgan
Ch
ase
& C
o.
(JP
M)
Appendix 6
Page 28 of 49
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2,10
4.50
-0.2
748%
-0.2
752%
24M
ar 2
, 201
512
.14
-5.6
721%
-5.8
393%
24M
ar 2
, 201
52,
071.
26-1
.579
5%-1
.592
1%25
Mar
9, 2
015
11.8
3-2
.553
5%-2
.586
7%25
Mar
9, 2
015
2,05
3.40
-0.8
623%
-0.8
660%
26M
ar 1
6, 2
015
12.7
47.
6923
%7.
4108
%26
Mar
16,
201
52,
108.
102.
6639
%2.
6290
%27
Mar
23,
201
512
.39
-2.7
473%
-2.7
857%
27M
ar 2
3, 2
015
2,06
1.02
-2.2
333%
-2.2
586%
28M
ar 3
0, 2
015
12.6
42.
0178
%1.
9977
%28
Mar
30,
201
52,
086.
241.
2237
%1.
2162
%
Th
e A
ES
Co
rpo
rati
on
(A
ES
)S
tan
dar
d &
Po
ors
500
Appendix 7
Average mean return
JNJ: [=AVERAGE ('Appendix 5 & 6'! D4:D30)]
JPMorgan: [=AVERAGE ('Appendix 5 & 6'! J4:J30)]
The AES Corp.: [=AVERAGE ('Appendix 5 & 6'! D35:D61)]
S&P500: [=AVERAGE ('Appendix 5 & 6'! J35:J61)]
Geometric mean return
JNJ: [=SUMPRODUCT (GEOMEAN ('Appendix 5 & 6'! D4:D30+1))-1]
JPMorgan: [=SUMPRODUCT (GEOMEAN ('Appendix 5 & 6'! J4:J30+1))-1]
The AES Crop. [=SUMPRODUCT (GEOMEAN ('Appendix 5 & 6'! D35:D61+1))-1]
S&P 500: [=SUMPRODUCT (GEOMEAN ('Appendix 5 & 6'! D35:D61+1))-1]
Variance JNJ Standard Deviation JNJ
=VAR.S ('Appendix 5 & 6'! D4:D30) =STDEV.S ('Appendix 5 & 6'! D4:D30)
Variance JPMorgan Standard Deviation JPMorgan
=VAR.S ('Appendix 5 & 6'! J4:J30) =STDEV.S ('Appendix 5 & 6'! J4:J30)
Variance AES Corp. Standard Deviation AES Corp.
=VAR.S ('Appendix 5 & 6'! D35:D61) =STDEV.S ('Appendix 5 & 6'! D35:D61)
Variance S&P 500 Standard Deviation S&P 500
=VAR.S ('Appendix 5 & 6'! J35:J61) =STDEV.S ('Appendix 5 & 6'! J35:J61)
Page 29 of 49
Appendix 8
Page 30 of 49
The
AES
Corp
orat
ion
0.00
0544
215
0.00
0390
371
0.00
1665
919
0.00
0384
043
Stan
dard
& P
oors
500
0.00
0338
270
0.00
0504
729
0.00
0384
043
0.00
0409
889
John
son
& Jo
hnso
n0.
0004
6127
60.
0004
0920
10.
0005
4421
50.
0003
3827
0JP
Mor
gan
Chas
e &
Co.
0.00
0409
201
0.00
1006
356
0.00
0390
371
0.00
0504
729
Cova
rianc
eJo
hnso
n &
John
son
JPM
orga
n Ch
ase
& Co
. Th
e AE
S Co
rpor
atio
n St
anda
rd &
Poo
rs 5
00
The
AES
Corp
orat
ion
0.62
0816
212
0.30
1491
349
10.
4647
5063
6St
anda
rd &
Poo
rs 5
000.
7779
4612
10.
7858
6768
10.
4647
5063
61
John
son
& Jo
hnso
n 1
0.60
0592
976
0.62
0816
212
0.77
7946
121
JPM
orga
n Ch
ase
& Co
. 0.
6005
9297
61
0.30
1491
349
0.77
7946
121
Corr
elat
ion
coef
ficie
nts
John
son
& Jo
hnso
nJP
Mor
gan
Chas
e &
Co.
The
AES
Corp
orat
ion
Stan
dard
& P
oors
500
Appendix 9
Figure 1.1
Johnson & Johnson V Standard and Poor’s 500
Figure 1.2
JPMorgan Chase & Co. V Standard and Poor’s 500
Page 31 of 49
Appendix 10
Figure 1.3
The AES Corporation V Standard and Poor’s 500
Figure 1.4
Three selected stock and S&P 500
Page 32 of 49
Appendix 11
Page 33 of 49
Ari
thm
eti
c M
ean
Sta
nd
ard
De
via
tio
n-0
.125
12.
1477
%0.
1215
3.17
23%
-0.2
852
4.08
16%
0.20
812.
0246
%
Appendix 12
Page 34 of 49
Jo
hn
so
n &
Jo
hn
so
n (
JN
J)
JP
Mo
rga
n C
ha
se
& C
o.(
JP
M)
Th
e A
ES
Co
rpo
rati
on
(A
ES
)E
qu
all
y W
eig
hte
d P
ort
foli
o
We
ek
Da
te
Ad
jus
ted
c
los
ing
p
ric
eD
isc
rete
ra
te o
f re
turn
Ad
jus
ted
c
los
ing
p
ric
eD
isc
rete
ra
te o
f re
turn
Ad
jus
ted
c
los
ing
p
ric
eD
isc
rete
ra
te o
f re
turn
Ba
se
d o
n D
isc
rete
Re
turn
1S
ep
22
, 2
01
41
05
.67
59
.38
13
.95
2S
ep
29
, 2
01
41
03
.72
-1.8
454%
59
.52
0.23
58%
13
.87
-0.5
735%
-0.7
27
6%
3O
ct 6
, 2
01
49
9.8
8-3
.702
3%5
7.7
6-2
.957
0%1
3-6
.272
5%-4
.31
02
%4
Oct
13
, 2
01
49
7.3
8-2
.503
0%5
5.4
7-3
.964
7%1
3.0
30.
2308
%-2
.07
88
%5
Oct
20
, 2
01
41
01
.75
4.48
76%
57
.98
4.52
50%
13
.47
3.37
68%
4.1
29
4%
6O
ct 2
7,
20
14
10
6.3
44.
5111
%5
9.7
2.96
65%
13
.85
2.82
11%
3.4
32
6%
7N
ov
3,
20
14
10
6.7
50.
3856
%6
0.6
71.
6248
%1
3.2
5-4
.332
1%-0
.77
39
%8
No
v 1
0,
20
14
10
6.7
1-0
.037
5%5
9.5
-1.9
285%
13
.26
0.07
55%
-0.6
30
1%
9N
ov
17
, 2
01
41
07
.11
0.37
48%
59
.67
0.28
57%
13
.88
4.67
57%
1.7
78
6%
10
No
v 2
4,
20
14
10
7.5
0.36
41%
59
.38
-0.4
860%
13
.65
-1.6
571%
-0.5
92
9%
11
De
c 1
, 2
01
41
07
.76
0.24
19%
61
.89
4.22
70%
13
.47
-1.3
187%
1.0
50
0%
12
De
c 8
, 2
01
41
03
.7-3
.767
6%5
9.2
6-4
.249
5%1
3.0
8-2
.895
3%-3
.63
71
%1
3D
ec
15
, 2
01
41
04
.82
1.08
00%
61
.13
3.15
56%
13
.29
1.60
55%
1.9
46
8%
14
De
c 2
2,
20
14
10
4.3
3-0
.467
5%6
1.7
40.
9979
%1
45.
3424
%1
.95
74
%1
5D
ec
29
, 2
01
41
03
.79
-0.5
176%
62
.08
0.55
07%
13
.49
-3.6
429%
-1.2
03
1%
16
Jan
5,
20
15
10
4.2
10.
4047
%5
8.9
5-5
.041
9%1
2.7
-5.8
562%
-3.4
97
5%
17
Jan
12
, 2
01
51
03
.32
-0.8
540%
55
.56
-5.7
506%
13
.16
3.62
20%
-0.9
94
1%
18
Jan
20
, 2
01
51
01
.49
-1.7
712%
56
.31
1.34
99%
12
.48
-5.1
672%
-1.8
62
6%
19
Jan
26
, 2
01
59
9.4
4-2
.019
9%5
4.0
2-4
.066
8%1
2.1
3-2
.804
5%-2
.96
34
%2
0F
eb
2,
20
15
10
0.4
0.96
54%
57
.51
6.46
06%
11
.98
-1.2
366%
2.0
62
9%
21
Fe
b 9
, 2
01
59
8.9
3-1
.464
1%5
9.2
83.
0777
%1
1.7
7-1
.752
9%-0
.04
64
%2
2F
eb
17
, 2
01
51
00
.26
1.34
44%
59
.41
0.21
93%
11
.80.
2549
%0
.60
61
%2
3F
eb
23
, 2
01
51
02
.51
2.24
42%
60
.88
2.47
43%
12
.87
9.06
78%
4.5
95
0%
24
Ma
r 2
, 2
01
51
00
.11
-2.3
412%
60
.49
-0.6
406%
12
.14
-5.6
721%
-2.8
84
4%
25
Ma
r 9
, 2
01
59
9.2
1-0
.899
0%6
0.6
0.18
18%
11
.83
-2.5
535%
-1.0
90
1%
26
Ma
r 1
6,
20
15
10
2.4
3.21
54%
61
.34
1.22
11%
12
.74
7.69
23%
4.0
42
5%
27
Ma
r 2
3,
20
15
10
0.3
4-2
.011
7%5
9.1
6-3
.554
0%1
2.3
9-2
.747
3%-2
.77
07
%2
8M
ar
30
, 2
01
51
01
.55
1.20
59%
60
.56
2.36
65%
12
.64
2.01
78%
1.8
63
2%
Appendix 13
Page 35 of 49
Appendix 14
Calculation will based on formula in Report: Part 2, Question 1(B)
*Note*A = Johnson & JohnsonB = JPMorgan Chase & Co.C = The AES Corporation
Weight of Each stock Variance/Covariance MatrixJohnson & Johnson JPMorgan Chase & Co. The AES Corporation
0.3333 0.3333 0.3333
Variance/Covariance MatrixJohnson & Johnson JPMorgan Chase & Co. The AES Corporation
Johnson & Johnson 0.000461276 0.000409201 0.000544215JPMorgan Chase & Co. 0.000409201 0.001006356 0.000390371
The AES Corporation 0.000544215 0.000390371 0.001665919
Weight of Each stockJohnson & Johnson 0.3333
JPMorgan Chase & Co. 0.3333The AES Corporation 0.3333
Variance = 0.000646662
Standard Deviation = 2.5430%0.025429550
Page 36 of 49
Appendix 15
Page 37 of 49
Appendix 16
Page 38 of 49
Tre
asu
ry B
illJo
hn
son
& J
oh
nso
n
JPM
org
an C
has
e &
Co
.
Wee
kD
ate
Ris
k-F
ree
Rat
eW
ee
kD
ate
Dis
cre
te R
etu
rnE
xce
ss
Re
turn
sD
isc
rete
Re
turn
Ex
ces
s R
etu
rns
Wee
k 1
26/9
/201
40.
1154
%1
Sep
22
, 201
4
Wee
k 2
3/10
/201
40.
1538
%2
Sep
29
, 201
4-1
.845
4%-1
.999
2%0.
2358
%0.
0819
%
Wee
k 3
10/1
0/20
140.
1923
%3
Oct
6, 2
014
-3.7
023%
-3.8
946%
-2.9
570%
-3.1
493%
Wee
k 4
17/1
0/20
140.
1923
%4
Oct
13,
20
14-2
.503
0%-2
.695
3%-3
.964
7%-4
.157
0%
Wee
k 5
24/1
0/20
140.
2308
%5
Oct
20,
20
144.
4876
%4.
2568
%4.
5250
%4.
2942
%
Wee
k 6
31/1
0/20
140.
2308
%6
Oct
27,
20
144.
5111
%4.
2803
%2.
9665
%2.
7358
%
Wee
k 7
7/11
/201
40.
2308
%7
No
v 3,
20
140.
3856
%0.
1548
%1.
6248
%1.
3940
%
Wee
k 8
14/1
1/20
140.
2692
%8
No
v 10
, 201
4-0
.037
5%-0
.306
7%-1
.928
5%-2
.197
7%
Wee
k 9
21/1
1/20
140.
2692
%9
No
v 17
, 201
40.
3748
%0.
1056
%0.
2857
%0.
0165
%
Wee
k 10
28/1
1/20
140.
2692
%10
No
v 24
, 201
40.
3641
%0.
0949
%-0
.486
0%-0
.755
2%
Wee
k 11
5/12
/201
40.
3077
%11
De
c 1,
20
140.
2419
%-0
.065
8%4.
2270
%3.
9193
%
Wee
k 12
12/1
2/20
140.
3846
%12
De
c 8,
20
14-3
.767
6%-4
.152
2%-4
.249
5%-4
.634
1%
Wee
k 13
19/1
2/20
140.
4231
%13
De
c 15
, 201
41.
0800
%0.
6570
%3.
1556
%2.
7325
%
Wee
k 14
26/1
2/20
140.
5385
%14
De
c 22
, 201
4-0
.467
5%-1
.005
9%0.
9979
%0.
4594
%
Wee
k 15
2/1/
2015
0.46
15%
15D
ec
29, 2
014
-0.5
176%
-0.9
791%
0.55
07%
0.08
92%
Wee
k 16
9/1/
2015
0.34
62%
16Ja
n 5
, 20
150.
4047
%0.
0585
%-5
.041
9%-5
.388
0%
Wee
k 17
16/1
/201
50.
3077
%17
Jan
12
, 201
5-0
.854
0%-1
.161
7%-5
.750
6%-6
.058
3%
Wee
k 18
23/1
/201
50.
3077
%18
Jan
20
, 201
5-1
.771
2%-2
.078
9%1.
3499
%1.
0422
%
Wee
k 19
30/1
/201
50.
3077
%19
Jan
26
, 201
5-2
.019
9%-2
.327
6%-4
.066
8%-4
.374
5%
Wee
k 20
6/2/
2015
0.26
92%
20F
eb
2, 2
015
0.96
54%
0.69
62%
6.46
06%
6.19
13%
Wee
k 21
13/2
/201
50.
2692
%21
Fe
b 9,
201
5-1
.464
1%-1
.733
4%3.
0777
%2.
8085
%
Wee
k 22
20/2
/201
50.
2692
%22
Fe
b 17
, 20
151.
3444
%1.
0752
%0.
2193
%-0
.049
9%
Wee
k 23
27/2
/201
50.
2692
%23
Fe
b 23
, 20
152.
2442
%1.
9749
%2.
4743
%2.
2051
%
Wee
k 24
6/3/
2015
0.30
77%
24M
ar 2
, 201
5-2
.341
2%-2
.648
9%-0
.640
6%-0
.948
3%
Wee
k 25
13/3
/201
50.
3846
%25
Mar
9, 2
015
-0.8
990%
-1.2
836%
0.18
18%
-0.2
028%
Wee
k 26
20/3
/201
50.
5000
%26
Mar
16,
20
153.
2154
%2.
7154
%1.
2211
%0.
7211
%
Wee
k 27
27/3
/201
50.
4615
%27
Mar
23,
20
15-2
.011
7%-2
.473
3%-3
.554
0%-4
.015
5%
Wee
k 28
3/4/
2015
0.46
15%
28M
ar 3
0, 2
015
1.20
59%
0.74
44%
2.36
65%
1.90
49%
Appendix 17
Page 39 of 49
Th
e A
ES
Co
rpo
rati
on
S&
P 5
00E
qu
ally
We
igh
ted
Po
rtfo
lio
We
ek
Dat
eD
iscr
ete
Re
turn
Ex
cess
Re
turn
sD
iscr
ete
Re
turn
Ex
cess
Re
turn
sD
iscr
ete
Re
turn
Ex
cess
Re
turn
s
1S
ep 2
2, 2
014
2S
ep 2
9, 2
014
-0.5
735%
-0.7
273%
-0.7
540%
-0.9
078%
-0.7
276%
-0.8
815%
3O
ct 6
, 201
4-6
.272
5%-6
.464
8%-3
.138
9%-3
.331
2%-4
.310
2%-4
.502
5%
4O
ct 1
3, 2
014
0.23
08%
0.03
85%
-1.0
162%
-1.2
085%
-2.0
788%
-2.2
711%
5O
ct 2
0, 2
014
3.37
68%
3.14
61%
4.12
45%
3.89
38%
4.12
94%
3.89
86%
6O
ct 2
7, 2
014
2.82
11%
2.59
03%
2.72
17%
2.49
09%
3.43
26%
3.20
18%
7N
ov 3
, 201
4-4
.332
1%-4
.562
9%0.
6873
%0.
4565
%-0
.773
9%-1
.004
6%
8N
ov 1
0, 2
014
0.07
55%
-0.1
938%
0.38
88%
0.11
96%
-0.6
301%
-0.8
993%
9N
ov 1
7, 2
014
4.67
57%
4.40
65%
1.16
09%
0.89
17%
1.77
86%
1.50
94%
10N
ov 2
4, 2
014
-1.6
571%
-1.9
263%
0.19
68%
-0.0
725%
-0.5
929%
-0.8
622%
11D
ec 1
, 201
4-1
.318
7%-1
.626
4%0.
3777
%0.
0700
%1.
0500
%0.
7423
%
12D
ec 8
, 201
4-2
.895
3%-3
.279
9%-3
.519
4%-3
.904
0%-3
.637
1%-4
.021
7%
13D
ec 1
5, 2
014
1.60
55%
1.18
24%
3.41
20%
2.98
89%
1.94
68%
1.52
38%
14D
ec 2
2, 2
014
5.34
24%
4.80
39%
0.87
51%
0.33
66%
1.95
74%
1.41
89%
15D
ec 2
9, 2
014
-3.6
429%
-4.1
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16Ja
n 5,
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5-5
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n 12
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53.
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n 20
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n 26
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23F
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3, 2
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9.06
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24M
ar 2
, 201
5-5
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1%-5
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, 201
5-2
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9%-1
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7%
26M
ar 1
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015
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4.04
25%
3.54
25%
27M
ar 2
3, 2
015
-2.7
473%
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088%
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333%
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948%
-2.7
707%
-3.2
322%
28M
ar 3
0, 2
015
2.01
78%
1.55
62%
1.22
37%
0.76
21%
1.86
32%
1.40
16%
Appendix 18
SUMMARY OUTPUT
Regression StatisticsMultiple R 0.776973446R Square 0.603687736Adjusted R Square 0.587174725Standard Error 0.01390956Observations 26
ANOVAdf SS MS F Significance F
Regression 1 0.00707315 0.00707315 36.55831 3.04063E-06Residual 24 0.004643421 0.000193476Total 25 0.011716571
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%Intercept -0.00318773 0.002730045 -1.167647604 0.254419 -0.008822266 0.0024468 -0.0088223 0.00244681Beta (β) 0.816522029 0.135043867 6.04634663 3.04E-06 0.537805186 1.0952389 0.53780519 1.09523887
RESIDUAL OUTPUT
Observation Predicted Residuals Standard Residuals1 -0.030387604 -0.008558227 -0.6279640512 -0.013055422 -0.013897691 -1.0197498133 0.028605692 0.01396236 1.0244949584 0.017151279 0.025651594 1.8821981245 0.000539921 0.001007945 0.0739584286 -0.002211463 -0.000855552 -0.0627765137 0.004092837 -0.003036668 -0.2228169638 -0.003779527 0.004728335 0.3469439049 -0.002615776 0.001957457 0.143629391
10 -0.035064651 -0.006457821 -0.47384571911 0.021217689 -0.014648073 -1.07480942712 -0.000439105 -0.009620191 -0.70588616913 -0.018906426 0.009115157 0.6688290814 -0.011326187 0.011911282 0.87399606215 -0.015838698 0.004221328 0.30974195216 0.007400346 -0.028189232 -2.06839853217 -0.028315611 0.005039654 0.36978705418 0.019367575 -0.01240582 -0.91028306319 0.01110749 -0.028441232 -2.08688917120 -0.000203436 0.010954978 0.80382678421 -0.007630208 0.027379552 2.0089878922 -0.018596847 -0.007892426 -0.57911057923 -0.013368882 0.000532617 0.03908103924 0.014480782 0.012673235 0.92990473425 -0.025191604 0.000459031 0.03368165426 0.003035209 0.004408406 0.323468944
Page 40 of 49
Page 41 of 49
Appendix 19
SUMMARY OUTPUT
Regression StatisticsMultiple R 0.790503376R Square 0.624895587Adjusted R Square 0.609266236Standard Error 0.02024028Observations 26
ANOVAdf SS MS F Significance F
Regression 1 0.016379459 0.016379459 39.98219 1.54772E-06Residual 24 0.009832055 0.000409669Total 25 0.026211514
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%Intercept -0.001085287 0.003972582 -0.273194393 0.787041 -0.009284294 0.00711372 -0.009284294 0.00711372Beta (β) 1.242542482 0.196506981 6.323146773 1.55E-06 0.836972007 1.64811296 0.836972007 1.648112958
RESIDUAL OUTPUT
Observation Predicted Residuals Standard Residuals1 -0.042476697 0.010983728 0.5538569662 -0.016101448 -0.025468443 -1.2842520423 0.047296356 -0.004354364 -0.2195697964 0.029865602 -0.002507893 -0.1264610645 0.004587266 0.009352948 0.4716245196 0.000400347 -0.022377309 -1.1283809177 0.009993917 -0.009829082 -0.495633698 -0.001985853 -0.005566518 -0.2806929469 -0.000214916 0.039408117 1.98716326
10 -0.049593995 0.003253092 0.164037911 0.036053662 -0.008728576 -0.44014042912 0.003097434 0.001496685 0.07547066413 -0.025005214 0.025896794 1.30585173314 -0.013469985 -0.040410368 -2.03770197215 -0.020336898 -0.040246386 -2.02943316716 0.015027119 -0.004605122 -0.23221430217 -0.039323643 -0.004421012 -0.2229305518 0.033238251 0.028675143 1.44595058419 0.020668466 0.007416483 0.3739778320 0.003456063 -0.003955388 -0.19945134721 -0.007845628 0.029896629 1.50754433422 -0.024534112 0.015051145 0.75895738723 -0.016578456 0.014550784 0.73372659824 0.025801773 -0.018590552 -0.93743282125 -0.034569684 -0.005585316 -0.28164084226 0.008384471 0.010664783 0.537774107
Page 42 of 49
Page 43 of 49
Appendix 20
SUMMARY OUTPUT
Regression StatisticsMultiple R 0.459210464R Square 0.21087425Adjusted R Square 0.177994011Standard Error 0.03757895Observations 26
ANOVAdf SS MS F Significance F
Regression 1 0.009056864 0.009056864 6.413404 0.018280294Residual 24 0.033892259 0.001412177Total 25 0.042949123
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%Intercept -0.00525321 0.007375662 -0.712236197 0.483186 -0.020475832 0.0099694 -0.02047583 0.009969405Beta (β) 0.923954086 0.36484307 2.532469881 0.01828 0.170954999 1.6769532 0.170954999 1.676953173
RESIDUAL OUTPUT
Observation Predicted Residuals Standard Residuals1 -0.03603185 -0.028616534 -0.7772071382 -0.01641922 0.01680384 0.4563817663 0.030723357 0.000737178 0.0200212924 0.017761855 0.008141291 0.2211123685 -0.00103511 -0.044593887 -1.2111420216 -0.0041485 0.002210906 0.0600468157 0.002985278 0.041079578 1.115695618 -0.00592287 -0.013340039 -0.3623070979 -0.00460601 -0.011657731 -0.316616662
10 -0.04132427 0.008524885 0.23153054511 0.022363294 -0.010539018 -0.28623311512 -0.00214294 0.050181955 1.36291046313 -0.02304006 -0.018003895 -0.48897449514 -0.01446247 -0.047560966 -1.2917260415 -0.0195687 0.052712253 1.43163176516 0.006727965 -0.06147662 -1.66966649117 -0.03368724 0.002565445 0.06967586518 0.020269756 -0.035328098 -0.95948900719 0.010922868 -0.031144391 -0.84586215320 -0.00187627 0.001732813 0.04706210921 -0.0102802 0.098265859 2.66883914722 -0.02268975 -0.037108229 -1.00783625823 -0.01677393 -0.012607647 -0.34241578324 0.014739994 0.057183083 1.55305670825 -0.0301522 -0.001935715 -0.05257280526 0.001788495 0.013773683 0.37408461
Page 44 of 49
Page 45 of 49
Appendix 21
SUMMARY OUTPUT
Regression StatisticsMultiple R 0.79294298R Square 0.62875857Adjusted R Square 0.61329018Standard Error 0.01606241Observations 26
ANOVAdf SS MS F Significance F
Regression 1 0.010487209 0.010487209 40.64796 1.36318E-06Residual 24 0.006192021 0.000258001Total 25 0.01667923
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%Intercept -0.00317542 0.003152586 -1.007242232 0.323866 -0.00968204 0.0033312 -0.00968204 0.0033312Beta (β) 0.99424044 0.155945217 6.375575046 1.36E-06 0.672385326 1.3160955 0.672385326 1.31609554
RESIDUAL OUTPUT
Observation Predicted Residuals Standard Residuals1 -0.03629542 -0.008729327 -0.554669862 -0.01519084 -0.007519876 -0.4778201423 0.03553794 0.003448128 0.2190973644 0.02159044 0.010427374 0.6625653735 0.00136357 -0.011409764 -0.7249873916 -0.00198666 -0.007006562 -0.4452037037 0.00568979 0.009403722 0.597521558 -0.00389602 -0.004725545 -0.3002656839 -0.00247898 0.009901642 0.629159835
10 -0.04199044 0.001773162 0.11266841611 0.02654191 -0.0113042 -0.71827971712 0.00017145 0.014017867 0.89070873713 -0.02231533 0.005668655 0.36019182514 -0.01308523 -0.025350833 -1.61081632515 -0.01857991 0.005561865 0.3534062316 0.00971718 -0.031420502 -1.99648895917 -0.03377246 0.001061284 0.06743499318 0.02428912 -0.006352243 -0.40362764819 0.0142312 -0.017387924 -1.10484545220 0.00045842 0.002910564 0.18494005921 -0.00858481 0.05184222 3.29410452822 -0.02193837 -0.009982148 -0.63427529523 -0.01557253 0.000825114 0.05242852424 0.0183387 0.017086698 1.08570520525 -0.0299685 -0.002353892 -0.14956855126 0.00440196 0.009614524 0.610916089
Page 46 of 49
Page 47 of 49
Appendix 22
Page 48 of 49
Dat
eE
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s R
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rns
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1.07
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ar 1
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015
2.71
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0.72
11%
7.19
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2.16
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3.54
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23,
201
5-2
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.015
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.694
8%-3
.232
2%M
ar 3
0, 2
015
0.74
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1.90
49%
1.55
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0.76
21%
1.40
16%
Page 49 of 49
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