The document is an investment proposal prepared by Samantha Hoffer of SHH Wealth Management for John A. Bryant, outlining a tailored wealth management strategy. It features a detailed analysis of a diversified portfolio of ten selected stocks from various industries, emphasizing the importance of low correlations for risk mitigation and higher returns, and includes statistical analyses like beta and Sharpe ratio calculations. The proposal concludes with insights into the expected performance of the selected stocks against market benchmarks, demonstrating potential for steady returns aligned with the client's financial goals.

1. Apple Jack
Investment Proposal
Prepared by
Samantha Hoffer
Wealth Management

2. Table of Contents
Client Letter
Stock Information
Apple
Bristol-Myers Squibb
Dominion Resources
Jack in the Box
Southwest Airlines
Summary of Portfolio Findings
Pairwise Correlations
Statistical Analysis
Variability of Beta
Capital Asset Pricing Model
Appendices
Appendix A: Rate of Return Graphs
Appendix B: Statistical Analysis Data
Appendix C: Capital Asset Pricing Model Graph
Appendix D: Variability of Beta
Appendix E: Data for 10 Stocks
Appendix F: Data for S&P 500
Appendix G: Data for Treasury Bill
Appendix H: Data for Pairwise Correlation of 10 stocks
Appendix I: Data for Pairwise Correlation of 5 Stocks
Appendix J: Data for Rate of Return Graphs
Reference List

3. Samantha Hoffer
SHH Wealth Management
4492 Diamond Street
West Long Branch, NJ 07764
June 29, 2015
John A. Bryant
Kellogg Company
One Kellogg Square
Battle Creek, MI 49016
Dear Mr. Bryant:
I am writing you to follow up on the meeting we had last month - I appreciate your
time and willingness to sit down with me to discuss your current financial position, as
well as your future aspirations. Upon reflecting about our conversation, I have
determined that you are in need of a proper wealth management strategy to help attain
your financial goals.
Multiple statistical analyses were performed in an effort to compile an investment
portfolio that will best suit your requirements. This proposal will provide you with: a
detailed record of portfolio securities and the criteria used to select them, an analysis of
risk factors, as well as a comparative assessment to S&P 500 and 13-week Treasury
Bill returns.
I have outlined your primary objectives and portfolio expectations, based on what
we have previously discussed, as the following:
• Stocks with less risk than the market
• Portfolio Diversification
• Capital Preservation
Given these investment goals, I chose to select ten stocks listed on the S&P 500,
for the sake of simple market comparison. All ten of the chosen stocks belong to
different industries to help diversify the portfolio adequately enough to mitigate risk
factors.
Wealth Management

4. The following table includes these ten stocks with the sector and industry classifications:
Company (Ticker) Sector Industry
Apple Inc. (AAPL) Consumer Goods Electronic Goods
Bristol-Myers Squibb (BMY) Health Care Biotech & Pharma
Dominion Resources (D) Utilities Integrated Utilities
General Electric (GE) Industrials Electrical Equipment
Jack in the Box (JACK) Services Restaurants
Southwest Airlines (LUV) Consumer Discretionary Passenger Transportation
United Pacific Corp. (UNP) Industrials Transportation & Logistics
United Parcel Service (UPS) Services Express Delivery Services
Ventas (VTR) Services Real Estate Operations
Verizon Communications (VZ) Communications Telecom Carriers
The next step I took in evaluating these securities was to calculate the average
returns of the stocks (Appendix E) using the monthly adjusted closing prices for the past
ten years and one month (April 2005 to May 2015). This was done using the following
formula: P1-P0/P0 x 100.
Once these rates were determined, I was then able to perform a Pairwise Correlation
Analysis, as detailed in Appendix H, between these ten stocks, as well as the S&P 500,
and 13-week T-Bill. The ultimate goal when determining correlations between stocks for
a portfolio is to choose securities that have a low correlation to the market. This is
because the lower the correlations, the higher the diversification of the portfolio.
Conversely, the larger the correlation, the lower the advantage of diversification.
For your particular portfolio, I selected the decision rule of removing one of the
two stocks involved in the correlation calculation if the pairwise correlation is greater
than or equal to 0.3. The purpose of this step in the process is to ensure the portfolio is
well diversified. This eliminated exactly half of the stocks, leaving the following five low-
correlated stocks to comprise the portfolio:
Company (Ticker) Sector Industry
Apple Inc. (AAPL) Consumer Goods Electronic Goods
Bristol-Myers Squibb (BMY) Health Care Biotech & Pharma
Dominion Resources (D) Utilities Integrated Utilities
Jack in the Box (JACK) Services Restaurants
Southwest Airlines (LUV) Consumer Discretionary Passenger Transportation
Wealth Management

5. Once the stocks were established using the Pairwise Correlation Method, the
average rates of return are then calculated. The monthly-adjusted rates for each stock,
the S&P 500, and the 13-week Treasury Bill were individually totaled then divided by
120, the number of monthly returns for the ten year time period, to get the average rates
of return (Appendix B).
To determine the portfolio’s average rate of return, these five rates are added
together and divided by five. The average rate of return on the portfolio is 1.54. Using
the same calculation method as with the stocks, the average rate of return on S&P 500
comes out to 0.59, and the average rate of return on the 13-week T-Bill equals 0.11.
Beta measures the responsiveness of a security to movements in the market; in
this case, S&P 500 data is used as a proxy for the market portfolio. The formula to
calculate beta is as follows:
βi = Covariance (Ri, Rm) / Variance (Rm)
Covariance (Ri, Rm) is the covariance between the return on a particular stock
and the return on the market. The denominator is then equal to the variance of the
market, in this case the S&P 500. Using this formula, I determined the betas, as seen in
Appendix B.
The Sharpe ratio is the risk premium of the asset, relative to Treasury Bills,
divided by the standard deviation. It provides a reward-to-risk ratio, the larger the ratio,
the better the investment. Expressed algebraically the formula reads:
Sharpe Ratio = (Rav – T-billav)/standard deviation
The Sharpe Ratio calculations for the stocks and the portfolio can be found in
Appendix B.
Wealth Management

6. The Capital Asset Pricing Model (CAPM) is an equilibrium asset pricing theory
that illustrates that the equilibrium expected return on all risky assets is a function of
their covariance in a market portfolio. This formula implies that the expected return on a
security is linearly related to its beta.
This relationship between expected return and beta can be represented as follows:
E(Ri) = Rf + βi (Rm - Rf)
Rf is the risk-free rate, as determined by the 13-week Treasury Bill, and Rm is the
expected return on the market, as determined by the S&P 500. Appendix B shows the
expected returns, calculated using the CAPM.
Using these expected returns as Y-variables, and the corresponding betas as X-
variables, I constructed the CAPM Graph, which can be found in Appendix C. When
comparing the CAPM rates of return with historical average rates of return, it is clear
that the average rates of return are greater than the CAPM rates of return. This signifies
that I was able to create a portfolio that beats the market with the five low-correlation
stocks individually, as well as together, in this well-diversified portfolio.
In the end, I have created this portfolio specifically for your unique set of
investment objective and long-term financial goals. The low-correlation among the five
stocks that make up the portfolio allows for risk to be lower, while still realizing steady
returns on your capital over time. I appreciate your trust and consideration in building a
wealth management portfolio with me. If you have any questions or concerns, please do
not hesitate to contact me. I plan to call you next month to schedule a meeting to
discuss, after you have had sufficient time to look over the contents of this proposal.
Sincerely,
Samantha H. Hoffer
SHH Wealth Management
Wealth Management

7. Stock Information
Apple (AAPL)
Bristol-Myers Squibb (BMY)
Dominion Resources (D)
Jack in the Box (JACK)
Southwest Airlines (LUV)

8. Apple Inc.
Apple Inc. (Apple) is a technology company that provides personal
communication devices and related software and solutions. The company designs,
manufactures, and markets its mobile communication and media devices, personal
computers, and digital music players. Apple’s products and services include iPhone,
iPad, iPod, Mac, Apple TV, along with a number of consumer and professional software
applications. The company also sells a variety of Apple-brand and third-party Mac- and
iOS- compatible products. Apple has operations in North America, South America,
Europe, and Asia Pacific regions. The company deals with sales to consumers, to
small- and medium-sized businesses, as well as to education, enterprise, and
government entities.
For the financial year ending September 2014, Apple reported annual revenues
of $182,795 million, which is a 7% increase from revenues in the previous year. The
company generates these revenues through six primary product lines: iPhone (55.8% of
total revenues in FY14), iPad (16.6%), Mac (13.2%), iTunes (9.9%), accessories
(3.3%), and iPod (1.3%).
• iPhone is Apple’s line of smartphones that combine a phone, digital music
player, and internet device in one product.
• iPad is the company’s line of tablets, which include iPad Air and iPad mini.
• Mac is Apple’s line of desktop and laptop computers, which include
MacBook Pro and MacBook Air.
• Apple’s iTunes Application keeps users’ music, movies, and television
shows all organized together.
• Accessories include Apple TV, headphones, cases, displays, and storage
devices.
• iPod is Apple’s line of portable music and media players, which include
iPod Touch, iPod Nano, iPod Shuffle, and iPod Classic
Upcoming opportunities for Apple include the growth potential of Apple Pay, a
new mobile payment service that launched in September 2014. The steady growth of
the market for smart wearable devices also offers the corporation an abundance of

9. potential opportunities. Apple’s newest product, Apple Watch is a personal electronic
device that enables customers to communicate in new ways by combining an iOS-
based interface created uniquely for a small device with watch technology. Apple has
strategically positioned itself to benefit from these growing markets and effectively
generate continued revenue growth.
Bristol-Myers Squibb Company
Bristol-Myers Squibb (BMS) is involved in the discovery, development, licensing,
manufacturing, marketing, distribution, and sale of biopharmaceutical products. These
products are sold around the world to wholesalers, pharmacies, hospitals, government
agencies and medical professionals. BMS operates in North America, South America,
Europe, Asia, Australia, Africa, and the Middle East. The company has only one
reportable business segment, which is biopharmaceuticals. The biopharmaceutical
segment focuses on innovative medicines for serious diseases. BMS’ products include
chemically synthesized drugs as well as biologically processed products. The
company’s primary focus areas include cardiovascular drugs, virology drugs, oncology
medicines, neuroscience, immunoscience, and metabolic drugs.
As of January 2014, BMS and the California Institute for Biomedical Research
signed a worldwide research collaboration to develop anti-fibrotic therapies, and an
exclusive license agreement that allows BMS to develop, manufacture, and
commercialize preclinical compounds resulting from this collaboration. In early 2014,
both Five Prime Therapeutics and CytomX Therapeutics signed agreements with BMS
that will help advance the company’s immuno-oncology portfolio. The company’s
alliance and collaboration network for drug development and commercialization allows
BMS to mitigate risk while continuing to drive steady revenue generation.

10. Dominion Resources Inc.
Dominion Resources, Inc. (Dominion) is an integrated energy company that
engages in power generation, electricity transmission and distribution, natural gas
transmission, gathering, and storage and gas distribution services. Dominion operates
within 15 states in the US, making it one of the nation’s largest producers and
transporters of energy.
Dominion operates through three primary segments: Dominion generation,
Dominion energy, and Dominion Virginia Power (DVP).
• Dominion generation includes Virginia Power’s generation facilities and its
related energy supply operations. Also includes the generation operations
of the company’s merchant fleet and energy marketing.
• Dominion energy includes regulated liquefied natural gas operations and
producer services. Dominion energy’s gas distribution network harnesses
approximately 21,900 miles of pipe, which has approximately 10,900 miles
of gas transmission, gathering, and storage pipelines in Maryland, New
York, Ohio, Pennsylvania, Virginia, and West Virginia.
• DVP includes Virginia Power’s electric transmission and distribution
operations, and Dominion’s retail energy marketing operations. DVP’s
electric distribution network includes 57,000 miles of distribution lines in
North Carolina and Virginia.
Dominion has taken on numerous initiatives to help develop its renewable energy
business. Over the past year, the company has made several solar farm acquisitions
due to the increasing environmental concerns as well as rising energy prices. This shift
towards solar energy production enables Dominion to strengthen its renewable portfolio.

11. Development of the renewable energy business allows the company to leverage its
expertise to serve growing demands among renewable energy clients.
Jack in the Box Inc.
Jack in the Box Inc. (JACK) is a restaurant company that operates and
franchises Jack in the Box quick-service restaurants and Qdoba Mexican Grill (Qdoba)
fast-casual restaurants. JACK is one of the largest hamburger chains in the United
States, with over 2,888 Jack in the Box and Qdoba restaurants throughout the country.
The company generates revenues through two business segments: Jack in the Box
restaurant operations (76% of total revenues), and Qdoba restaurant operations (24%).
• Jack in the Box restaurants serve products targeted at the adult fast-food
consumer. During the financial year ending September 2014, Jack in the
Box operated 2,250 restaurants in 21 states, plus Guam. 431 of these
locations were company-operated, while 1,819 were franchises.
• Qdoba restaurants offer Mexican food in a fast-casual setting. During
FY2014, the Qdoba sector operated 638 restaurants in 47 states, plus the
District of Columbia and Canada. 310 of these locations were company-
operated and 328 were franchises.
In FY2014, the Jack in the Box segment recorded revenues of $1,127 million, a
decrease of 4.4% compared to FY2013. The Qdoba segment recorded revenues of
$357 million in FY2014, an increase of 14.9% over FY2013. During FY 2014, JACK
recorded revenues of $1,484 million, a decrease of 0.4% compared to FY2013. Its
operating profit was $162.3 million in FY2014, an increase of 17.4% over FY2013, and
net profit was $89 million in FY2014, an increase of 73.9%. Based on this data, it is
clear that the Qdoba restaurant segment is flourishing, resulting in a high profit margin
for the company as well as an increase in shareholder value.

12. Southwest Airlines Company
Southwest Airlines Company (Southwest) is a low-fare passenger airline that
provides air transportation in the United States and near-international locations
including Mexico, Jamaica, The Bahamas, Aruba, and the Dominican Republic.
Southwest operates primarily through one business segment, which is providing
scheduled passenger and freight transportation. Further, the company operates through
two subsidiaries: Southwest Airlines and AirTran Airways (AirTran).
• Southwest Airlines offers point-to-point service, rather than the hub-and-
spoke system used by the majority of US Airlines. This strategy increases
the company’s revenues.
• AirTran Airways operates through a hub-and-spoke network system - half
of its flights start or end at its largest base in Atlanta. Additionally, AirTran
serves multiple markets with non-stop service from smaller bases of
operation in Baltimore, Milwaukee, and Orlando.
The total fleet operated by both Southwest and AirTran during FY2013 consisted
of 680 aircraft, 516 owned and 164 leased under operating and capital leases. In that
same year, both segments carried 108 million passengers with combined revenue
passenger miles of 104.3 billion.
Southwest Airlines generates revenues through three business segments:
passenger (94.5% of total revenues FY2013), freight (0.9%), and other (4.6%). The
growth present in the global tourism industry may aid Southwest in increasing its market
position. A strong recovery in the tourism industry has occurred since the 2008
recessional period. This industry is forecasted to continue growing into future years. The
company’s integration of the networks and operations of Southwest and AirTran has
greatly improved the route network. Customers have the ability to fly between any of the

13. 96 Southwest and AirTran destinations on one itinerary. This integration improves the
customer experience and will contribute to increased efficiencies for Southwest Airlines.

14. Summary of
Portfolio Findings
Pairwise Correlations
Statistical Analysis
Variability of Beta
Capital Asset Pricing Model

15. Pairwise Correlations
(Appendix H & I)
A pairwise correlation between stocks is a useful method to determine the
degree to which prices of stocks move together. In order to ensure a well-diversified
investment portfolio, it is important to first determine this relationship between the
historical returns of potential stocks and the market return. Both covariance and
correlation are figures used to evaluate how two variables are related. To calculate the
pairwise correlations, as shown in Appendix H, the covariance between each stock’s
returns and the S&P 500’s returns must be determined using the Excel formula. This
covariance is then divided by the standard deviations of the stock and the market to get
the correlation. The correlation will always be between +1 and -1.
The ultimate goal when determining correlations between stocks for a portfolio is
to choose securities that have a low correlation to the market. This is because the lower
the correlations, the higher the diversification of the portfolio. Conversely, the larger the
correlation, the lower the advantage of diversification. For this particular portfolio, the
decision rule was to remove one of the two correlated stocks if the pairwise correlation
was calculated to be greater than or equal to 0.3. The Pairwise Correlation Matrix of
Ten Stocks (Appendix H) highlights in red the pairwise correlations that exceed this 0.3
mark.
Stocks removed during this step establish the remaining five securities that will
be held in the portfolio. The outcome of this process can be seen in Appendix I,
Pairwise Correlation of Five Stocks, in which none of the correlations are greater than or
equal to 0.3. These resulting securities represent a set of five low correlated stocks.

16. Statistical Analysis
(Appendix B)
Once the portfolio holdings have been established using the pairwise correlation
method, the average rates of return are determined. The monthly-adjusted rates for
each stock, the S&P 500, and the 13-week Treasury Bill are individually totaled and
then divided by 120, the number of monthly returns for the ten year time period, to get
the average rates of return. As shown in Appendix B the average rates of return are as
follows: AAPL = 3.2; BMY = 0.95; D = 0.63; JACK = 1.64; LUV = 1.28.
To determine the portfolio’s average rate of return, these five rates are added
together and divided by five. The average rate of return on the portfolio is 1.54. Using
the same calculation method as with the stocks, the average rate of return on S&P 500
comes out to 0.59, and the average rate of return on the 13-week T-Bill equals 0.11.
Sharpe Ratio
The Sharpe ratio is the risk premium of the asset, relative to Treasury Bills,
divided by the standard deviation. It provides a reward-to-risk ratio, the larger the ratio,
the better the investment. Expressed algebraically the formula reads:
Sharpe Ratio = (av. R – av. T-bill)/std. dev.
As seen in Appendix B, the Sharpe ratios are as follows: AAPL = 0.32; BMY =
0.14; D = 0.11; JACK = 0.19; LUV = 0.11; Portfolio = 0.31.

17. Variability of Beta
(Appendix B & D)
Beta measures the responsiveness of a security to movements in the market; in
this case, S&P 500 data is used as a proxy for the market portfolio. The formula to
calculate beta is as follows:
βi = Covariance (Ri, Rm) / Variance (Rm)
Where Covariance (Ri, Rm) is the covariance between the return on Stock I and the
return on the market, and the denominator is equal to the variance of the market. Using
this formula, I determined the betas, as seen in Appendix B, to be: AAPL = 1.22; BMY =
0.54; D = 0.43; JACK = 0.78; LUV = 1.13; Portfolio = 0.82.
The portfolio beta can be calculated alternatively as a weighted average of the betas of
the 5 stocks:
βp =w1β1 +w2β2+w3β3+w4β4+w5β5
Where wi are the weights of each stock, in this case, the weight is 0.2 for each stock
because of the assumption that an equal amount of each stock in the portfolio will exist.
Additionally, the beta of the market will always be equal to 1, because if all securities
were weighted by their market values, the resulting portfolio is the market.
Appendix D outlines the variability of beta during the ten years of observation.
Beta calculations during the first 60 months and the last 60 months of the total 120-
month time period vary significantly from each other as well as the previously calculated
betas. During the first 60 months, the betas for all five stocks and the portfolio are
greater than their 10-year betas. During the last 60 months, the betas are lower than
their 10-year betas and first 60 months betas. I would consider these beta figures to be
significantly different from betas calculated for the 10-year period.

18. Capital Asset Pricing Model
(Appendix B & C)
The Capital Asset Pricing Model (CAPM) is an equilibrium asset pricing theory
that illustrates that the equilibrium expected return on all risky assets is a function of
their covariance in a market portfolio. This formula implies that the expected return on a
security is linearly related to its beta.
This relationship between expected return and beta can be represented as follows:
E(Ri) = Rf + βi (Rm - Rf)
Where Rf is the risk-free rate, as determined by the 13-week Treasury Bill, and Rm is the
expected return on the market, as determined by the S&P 500. Appendix B shows the
expected returns, calculated using the CAPM, to be as follows: AAPL = 0.7; BMY =
0.37; D = 0.32; JACK = 0.49; LUV = 0.66; Portfolio = 0.51.
Using these values as Y-variables, and the appropriate betas as X-variables, I
constructed the CAPM Graph, which can be found in Appendix C. It includes the
Security Market Line (SML) by adding a line connecting the average market rate of
return with its beta of 1, and the average risk-free rate of return with its beta of 0.
Comparing the CAPM rates of return with historical average rates of return, it is
clear that the average rates of return are greater than the CAPM rates of return. This
signifies that I was able to beat the market with my five low-correlation stocks,
individually, as well as together in this well-diversified portfolio.

19. Appendices
Appendix A: Rate of Return Graphs
Appendix B: Statistical Analysis Data
Appendix C: Capital Asset Pricing Model Graph
Appendix D: Variability of Beta
Appendix E: Data for 10 Stocks
Appendix F: Data for S&P 500
Appendix G: Data for Treasury Bill
Appendix H: Data for Pairwise Correlation of 10
Stocks
Appendix I: Data for Pairwise Correlation of 5 Stocks
Appendix J: Data for Rate of Return Graphs