Portfolio Group Assignment Report 2015.docx

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.

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ReferencesAnalyst Notes 2015. "CFA Exam: Study Notes, Practice Questions and Mock

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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

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

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

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

of 49

Appendix 5

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-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)

of 49

Appendix 8

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

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

of 49

Appendix 11

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

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

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

of 49

Appendix 15

of 49

Appendix 16

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

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

044%

-1.4

635%

-1.9

251%

-1.2

031%

-1.6

647%

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n 5,

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ar 1

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015

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7.19

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25%

27M

ar 2

3, 2

015

-2.7

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28M

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78%

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0.76

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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

of 49

Appendix 19

SUMMARY OUTPUT





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

of 49

Appendix 20

SUMMARY OUTPUT



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

of 49

Appendix 21

SUMMARY OUTPUT





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

of 49

Appendix 22

of 49

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