Report Exxon

7/24/2019 Report Exxon

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NOVA SCHOOL OF BUSINESS ANDECONOMICS

EXXON MOBIL CORP.

REPORT I: RISK AND RETURN ANALYSISFINANCIAL MANAGEMENT

2ND SEMESTER | 2014/2015| GROUP 38 |

| Ana Preto #2244 | Martim Moreira #2293 | Jos Loureno #2249 | Omar al Fannoush #1949 |

INTRODUCTION:

Exxon Mobil Corp. is an American multinational oil and gas corporation headquartered inIrving, Texas, United States. It is a direct descendant of John D. Rockefeller's StandardOil Company, and was formed on November 30, 1999, by the merger of Exxon and Mobil(formerly Standard Oil of New Jersey and Standard Oil of New York). The world's 5thlargest company by revenue, ExxonMobil is also the second largest publicly tradedcompany by market capitalization. The company was ranked No. 6 globally in ForbesGlobal 2000 list in 2014.Exxon Mobil Corp., coded as XON by the NYSE and publiclytraded for the first time in the 2th of January 1970. Briefly, in this first report on Exxon, itis intended to evaluate the risk and return of the companys stock.


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Q1: The Historical Return since IPO

The study of expected returns normally is based on past performances of a security or index, fundamental tool thallows managers and investors to choose which stocks and projects to invest. Analysts usually review historicreturn data when trying to predict future returns or to estimate how much a security might react to a particulasituation, such as a drop in consumer demand. The most common method used is the computation of cumulativand annualized average returns. Historical returns can also be useful when estimating where future points of damay fall in terms of standard deviations. Therefore, in this section of the report, we are going to assess ExxoMobil Corp. returns through an historical perspective (since August 1980 until the end of February 2015) andiscuss the utility of this method.

First of all to perform the return analysis is necessary to calculate the percentage return (investor would earn pmonth by investing in Exxon Mobil Corp.). We extracted monthly data about the gross return (capital gains dividends) through Bloomberg. We assumed that this assembly of data was the most suitable mainly becausprovides information with less variability than diary and in sufficient number of observations for a substantistatistical analysis. The other reason is because both capital gains and dividends are included (as mentionebefore). Therefore, we computed monthly percentage returns and growth rates based on the monthly variation gross returns.

In order to do a comparative analysis of data, we took monthly data too from the market S&P500 index (SPX) anone month US Treasury Bills (T-bills). Additionally the method for calculating rates of return for the market waidentical to the one described above, except on the T-Bills because the risk-free rates were already available. Thuarithmetic and geometric average annualized returns were calculated assuming that returns are independent anidentically distributed. The annual arithmetic average of the returns was obtained by multiplying the arithmetaverage of the monthly percentage returns by 12 and the annual geometric average of the returns was determineby computing the geometric average of 1 plus the monthly rates of return, subtracting the result by 1 and finalmultiplying it by 12 (see Appendix 1 Table 1, Table 2, Table 3 for monthly and annual arithmetic angeometric average returns). Compounded returns were also determined using 100% as a base value for all data setallowing comparisons among securities, between Exxon Mobil Corp., S&P500 and T-Bills (see Appendix 1Figure 1for compounded returns from 1980 to 2015), through the following formula:

Through the analysis of the appendixes it is possible to observe that the geometric average annualized returns alower than the annual arithmetic average returns, for the Exxon Mobil security example. This inequality is totallexpected because arithmetic average is the sum of a collection of numbers divided by the number of numbers in thcollection thus considering each return as being independent from the others however, the geometric averagindicates the central tendency or typical value of a set of numbers by using the product of their values therefotaking into account the effect of compounding. In other words, investment returns are not independent of eacother, so they require a geometric average to represent their mean. Based on the previous information and througempirical studies its demonstrated that geometric average is more reliable and representative on measuring of thaverage returns, therefore we can conclude that an investor who decides to invest in Exxon Mobil stock in the en

of 1980 would have earned an average of 1.07% per month and 12.9% on an annual reference, instead of 1.19and 14.33% respectively in an arithmetic average, considering the investor held the stock until now. Considerinthe same logic, it is possible to assume that investors earned, on average, 8.14% per year with the S&P50portfolio and 4,49% with one month US Treasury Bill (T-Bills).

Looking now for the representation of compounded returns allows the identification of strong moves andisparities among the securities, namely concerning the positive growth of Exxon Mobil Corp. returns over th

Compound Returns(t) = Compound Returns (t-1) x [1 + Monthly Returns(t)]


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years, as well as the returns of the S&P500, however much lower. In general terms, Exxon Mobil Corp. returnhave been much higher relatively to the market and to the risk-free security. Moreover, there was a continuougrowth from 2003 to 2008, instability from 2008 to 2010, due to the financial and economic crisis and a shargrowth from 2010 to 2011 demonstrating a very effective recover from the economic crises. In 2014, Exxon Mobreturns have reached the highest compounded return, meaning that for each dollar invested in August 198investors would have earned $79, 75 in January 2015. The risk-free security has proved to be way beyond ExxoMobil Corp. and markets performance over the years.

As already mentioned, historical performance of a security may be used to predict future returns and the cost capital of an investment. However, this approach has some disadvantages: firstly, the future behavior of a securimay not be the same it was in the past, secondly the older historical data on returns is not very useful whepredicting future returns. This happens because the constant changes in the financial markets reality, thirdinvestors future expectations may not correspond to past estimations. Additionally expected returns obtained frohistorical data are subject errors and volatility distorts results even when expectations and market circumstanceare similar. As a conclusion, despite being helpful, the average return that the investors earned in the past is notvery reliable estimate of a securitys current and future expected returns. Instead, an alternative strategy based othe Capital Asset Pricing Model (CAPM) should be used. In the following questions, techniques to estimate a moreliable value of Exxon Mobil expected return will be properly studied.

Q2: Exxon Mobil (Systematic) Risk AnalysisIn the sequence of what was previously referenced, in this section of the report its supposed to elaborate method

that allow the calculation of the Exxon expected returns. Therefore, analyzing and quantifying the risk of the stocis a fundamental procedure to keep in mind. All over the world, investors face uncertainty related to stockperformance, since companies returns are subjected to risk. Thus, to obtain Exxon risk profile is crucial to calculathe firm volatility and its beta. The first objective is to elaborate the company beta defined by the standardeviation of the returns. The second goal is to elaborate the volatility in order to have all requirements to calculathe systematic and unsystematic risk. Seeing the fact that the stocks annual volatilities are calculated by using thexcel formula (=STDEV(Monthly Return) x SQRT(12)), it is now required to calculate the Beta. According the model, the Security Market Line (SML) equation, which relates the market risk premium, the stocks beta an

the risk-free rate with the companys expected return, must be verified for all stocks, assuming the followinformula: E(re)-rf=+e(E[rm]-rf).In that sense, by using historical data, it is possible to run a regression of thexcel add-in Data Analysis between the values for the excess return of the stock in relation to the risk-free rate (Variable) and the values for the excess return of the market in relation to the risk-free rate (X Variable). All thnecessary data to compute risks was collected in the previous section of the report, except for the industry totreturns necessary to compare Exxon risk with its industry risk. Thus, the data set for total gross returns wobtained in monthly percentage returns were calculated as before. Nonetheless, only 5 years of data were used, order to capture the more recent market circumstances.

After performing all the calculations and running the regressions (see Appendix 2Table 1, Figure 1, Table Figure 2for regression results and risk analysis), some final conclusions can be drawn on Exxon risk. An annu

volatility of 16.36% was obtained for Exxon stock, comparing with a markets annual volatility of 12.99%Therefore, it is possible to assume that the companys stock is riskier than the market proxy considered (S&P50

Index). Moreover, the stock has a beta of approximately 0.0427 (C.I. [-0.28; 0.39]) while its industry has a beta nearly -0.17 (C.I. [-0.57; 0.22]), which means that Exxon systematic risk is higher than that of the industry and ththeir returns (both Exxon and the industry) vary less than those of the market (that, in this case, has a beta equal 1). The market portfolio of all investable assets has a beta of exactly 1. A beta below 1 can indicate either ainvestment with lower volatility than the market, or a volatile investment whose price movements are not high


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correlated with the market. Negative betas are possible for investments that tend to go down when the market goe

up, and vice versa. In finance, systematic risk is measured by ^2_e^2_M, while unsystematic risk

calculated by ^2_e-^2_e^2_M. After the calculations, it is possible to decompose Exxon risk systematic risk (0,003%) and unsystematic risk (2,675%).Finally, one may argue on the performance of the company relative to the use of CAPM, using the estimated alph() of the regression as indicator. Since the estimated value of alpha for Exxon stock is positive 0.006, the ass

outperforms the expected return implied by the CAPM and is, therefore, undervalued. This is a conclusion that caalso be easily verified by representing the SML that illustrates the relation between expected returns and systematrisk. Since investors only take additional risks if expected returns increase and a beta of 1 corresponds to thexpected return of the market proxy (risk-free asset), therefore it is possible to plot the upward-sloping line of thSML, using historical data (see Appendix 3-Table 2, Table 3 for the Security Market Line graph). In fact, thstock is positioned above the SML, confirming the fact that it is undervalued - for its level of systematic risk, threturn is expected to be very high, so investors will buy the stock and the price will gradually increase at the samtime that return decreases until equilibrium is reached.

Q3: Exxon Mobil Expected ReturnIn order to estimate, in the most reliable and accurate way, Exxon expected return (also called cost of equity), onshould apply CAPM widely known and used techniques. As already mentioned, according to this theory, all stockmust lie on the SML. For that reason, by relying on a forward-looking (not historical) approach, its intended adjust SMLparameters to solve for a Forward-Looking SML: the one Month US Treasury Bill was replaced by1,97% 10 years US Treasury Bill (for a medium term approach), the betas were those determined in the previousection of this report (Exxon beta - e 0,043 - and Exxon industry beta - I -0,173 - to account forcomparable approach, since considering the entire industry is more accurate than considering only a fecompetitors) and the forward-looking expected return of the market (E[rM])still had to be calculated.

In order to determine a forward-looking expected market return (S&P500 Index as the market proxy), its supposeto collect the market value index and total yields between 2001 until 2014 (dividends in 2014 equal the produbetween the market value index and the total yield of that year). Moreover, dividends were assumed to grow 7.70% in the next five years and from 2013 to 2014 (assuming dividends will grow in a similar way, since there no data on this value), to after continue to grow at 8.14% forever (an estimate based on the average earninggrowth made available by the professor) and to be discounted by the expected market return. Thus, the forwardlooking expected market return was determined using the excel add-in Solver, so that the present value of futucash flows (dividends), that is, the present value of the 5 years growing annuity and growing perpetuity, in 201would equal the market value index in that same year, that is, $2058.9 (see Appendix 3-Table 1 for data on thestimation of the forward-looking expected market return). This resulted in an expected market return of 13.12%Exxon cost of equity was, then, calculated by simply solving the SML equation with the previous values (sAppendix 3-Table 2, Table 3 for the estimation of Exxon expected return). A forward-looking expected return o2.45% was obtained using Exxon beta, a higher value than the 0.04% obtained using Exxon industry beta, since thbeta is also lower. These costs of equity are lower comparing with the return determined using historical da(12.99% annual geometric average return). Therefore, it is possible to confirm what was previously stated on thdangers of using historical data to estimate stocks expected returns. In fact, there is a difference of 10.54% an12.94% in the cost of equity from using the historical data and not a forward-looking approach. This misleadininformation may cause managers to not invest in a project that actually creates value (in this case, future cash flowwould be heavily discounted if an historical approach is followed) or deceive investors that buy companies stock

Nevertheless, it is worth to mention that betas were also obtained with historical, despite more recent, data and alhave an impact on the estimates of Exxon cost of equity.


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Finally, despite being advisable the use of forward-looking approaches, it can be easily conclude that estimatinexpected returns with different methods is important to allow financial and management agents to simuladifferent scenarios, with more optimistic and pessimistic estimations, when evaluating investment opportunities.

Q4: Mean-variance Portfolio Choice

For what was previously stated, in this section of the report it is intended to conclude Exxon risk and returanalysis by combining other stocks with Exxon, determining the most efficient portfolios, in an attempt approach this study to what actually happens in the financial markets. In addition to the data previously collecteon Exxon and on one Month US Treasury Bills monthly returns, data on Apple Inc. (AAPL)s and onNike in(NKE)s monthly returns was gathered (using the same total return index available in Bloomberg), so that minimum matching sample period of over 10 years was ensured. Excluding the risk-free asset that has a 0 covariance with all companies, annualized co-variances between companies were obtained. Exxon is a considerabstable company, ranked in S&P 500 as AAA level company. Given the company rating, it is expected that thcompany has low risk exposure. In order to assess this information the companies monthly rates of return wer

used to compute the annual arithmetic average returns and volatilities (standard deviations). The results were 67for volatility and 15.1% for stocks' arithmetic average return. In order for a portfolio be profitable is important tcombine as much stocks from different industries as possible in one portfolio so that risk is eliminated. Evethough diversification benefits always exist, the amount of eliminated risk depends on the degree to which stockare exposed to common risks and their returns move together (measured by co-variances and correlationTherefore we chose companies from different industries and with different behaviors (regarding the volatility anarithmetic average return), to have a diversified portfolio.

The companies selected to include the portfolio were Nike (22.63% for arithmetic average return and 35.29% fovolatility) and Apple. (28.49% for arithmetic average return and 46.47% for volatility). Companies monthly ratof return and annual arithmetic average returns and volatilities (standard deviations) were computed according the procedures described in the second section of this report, except the risk-free assets volatility that was sequal to 0% (see Appendix -Table 1 for stocks annual arithmetic average returns, volatilities and co-variances).

In this report, three different sets of stocks are analyzed: Portfolios I (Exxon & Nike), Portfolios II (Exxon Apple) and Portfolios III (Exxon, Apple and Nike), (see Appendix - Table 2; 3; 4). Since the correlation and thco-variances between stocks returns are positive, one expects diversification benefits to exist.

Mean-variance frontiers are quite helpful in decisions regarding portfolios given that it establishes a relatiobetween the returns and risk. Through the use of this tool is possible to adjust the weight of each stock in thinvestment, in order to achieve the most desirable ratio risk-revenue. The most desirable condition to an investor to have the highest revenue at the smallest risk. If a portfolio combines different stocks, its possible to associa

them in order to achieve this scenario. Therefore the most diversified (more stock thus more relationoptionbest scenarios are achievable. In our work, we could conclude that the portfolio with more stocks (Portfolio IIactually present the most benefits of the diversification. Portfolio III (see Appendix 4 Figure 1) is the onlocated to the left, meaning that is possible to obtain higher expected returns for any level of risk, comparin

with the other two frontiers. It is also presented the frontiers when the investor cannot take a short position, and wcan verify that if the investor cant borrow from one side to invest on the other(expanding his horizons), thmean variance frontier gets flatter (see Appendix 4-Table 2). If we were to compare our portfolio option to aequally weighted portfolio, as a matter of fact, the mean variance frontier of portfolio III already has a point witsimilar characteristics (weights of 33,35%; 34,28%; 32,37%, consult Appendix 4-Table 4). Since this line has thbest options to invest, this may mean that an equally weighted portfolio is close to the portfolio best options(depending on the risk sensibility of the investor). Additionally this could mean that the companies do not diff


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that much between them (the same portion is a good option) or compensate each other weaknesses.Summinup, since we have already a point in the mean variance frontier similar to the equally weighted option, we caassume that it may be a good option for the less risk adverse investors.

Short-selling (transaction in which you sell a stock today that you do not own, with the obligation to buy it back ithe future) involves a short position (negative investment) in a stock and on the other hand a long position another stock (positive investment). This opens the opportunity given that is possible to sell a less profitabstock to purchase a more rentable one. This process is profitable as long as the investment is applied in a stock wihigher expected return. Hence, stocks with lower expected return are the ones in which investors hold a shoposition, to invest in other of higher return (in this case, Exxon stock is the first to be short-sold). Portfolios wimore than two stocks and with no short-selling will result in exactly the same expected returns and volatilities as short-selling was allowed for expected returns between the lower and the higher expected returns of the individustocks (you can reduce the investment in the one with lowest return and look for other options). This happenbecause within this range short-selling is not necessary.1

All the portfolios with an expected return lower than the one of the minimum variance portfolio arinefficient. Reversely, all the portfolios that have an expected return equal or higher than the one of thminimum variance portfolio are efficient, given that for their level of risk it is not possible to earn higher return(See Appendix 4 - Figure 3). Every investment has its risks, and usually with higher risks comes a higher returThe choice of a portfolio depends on investors risk susceptibility. So, investors that are completely risk-averchoose the minimum variance portfolio of the mean-variance frontier and risk-loving investors opt for an efficieportfolio in which their risk preferences are satisfied (ultimately, risk-loving investors may even short-sale).2

Considering a risk free asset is absolutely important to consider the Capital Market Line. By combining a risfree asset with a portfolio on the efficient frontier, it is possible to achieve portfolios even more lucrative than thones in the efficient frontier.3To achieve the best solution, the risk free asset should be tangent to the portfolio (SAppendix 4 - Figure 3) and thus the Sharpe Ratio should as steepest as possible. From what have been mentioneand the (See Appendix 4 - Figure 3), one can conclude that investors are in a best position if they invest-fresecurity with risky investments, since portfolios with the maximum expected returns, given any level of risk. Thefficient frontier turns to be the steepest line that links the risk-free and the risky investments (and no longer thportfolios above the minimum variance portfolio) and all the previous mean-variance frontiers becominefficient. Given the special scenario that a risk free asset provides, with the Capital Market Line, one caassume that is always the best option given that it provides highest return per unit of volatility of any portfoliavailable.

1https://books.google.pt/books?id=pwXWZzxXxfwC&pg=PA207&lpg=PA207&dq=which+portfolios+are+efficient+for+short+selling&so

ce=bl&ots=a7O_rdWf21&sig=9C8gqof-1c0x0lwv0YfqHl3HvAU&hl=en&sa=X&ei=ykUMVcWVLIO1Ue3rgJgB&ved=0CCwQ6AEwAA#v=onepage&q=which%20portfolios%20are%0efficient%20for%20short%20selling&f=false2http://www.investinganswers.com/

3http://riskencyclopedia.com/articles/capital_market_line/


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Appendix:Appendix 1Question 1

Table 1:Exxon Mobil Corp. arithmetic and geometric average return and volatility

EXXON MOBIL CORP.ARITHMETIC AVERAGE

RETURNGEOMETRIC AVERAGE

RETURN VOLATILITY

MONTHLY 1,18% 1,07% 5,00%

ANNUAL 14,21% 12,79% 17,32%

Table 2: S&P500 Index arithmetic and geometric average return and volatility

S&P500 INDEXARITHMETIC AVERAGE


RETURNVOLATILITY

MONTHLY 1,00% 0,90% 4,36%

ANNUAL 11,98% 10,83% 15,10%

Table 3: 1 Month Treasury-bill arithmetic and geometric average return and volatility

1 MONTH TREASURY-BILLSARITHMETIC AVERAGE


RETURNVOLATILITY

MONTHLY 0,37% 0,37% 0,29%

ANNUAL 4,48% 4,48% 0,99%


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Figure 1: Cumulative Returns

0,00%1000,00%2000,00%3000,00%4000,00%5000,00%6000,00%7000,00%8000,00%9000,00%

10000,00%

08-0

8-1980

12-1

2-1981

04-0

4-1983

08-0

8-1984

12-1

2-1985

04-0

4-1987

08-0

8-1988

12-1

2-1989

04-0

4-1991

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8-1992

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2-1993

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4-1995

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8-1996

12-1

2-1997

04-0

4-1999

08-0

8-2000

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2-2001

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4-2003

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2-2005

04-0

4-2007

08-0

8-2008

12-1

2-2009

04-0

4-2011

08-0

8-2012

12-1

2-2013

CumulativeReturn

Data

Cumulative Return

Exxon

T-Bill

S&P500


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Appendix 2Question 2

Table 1: Exxons Risk Analysis

Exxon Mobile Regression

SUMRIO DOS RESULTADOS - EXXON MOBIL

Estatstica de regresso Montly Volatility Stock 4,725%

R mltiplo 0,03396572 Yearly Volatility Stock 16,366%

Quadrado de R 0,00115367Montly VolatilityMarket 3,752%

Quadrado de Rajust.

-0,015775929

Yearly VolatilityMarket 12,999%

Erro-padro 0,047608937 Systematic Risk 0,003%Observaes 61 Systematic Variance 2,679%

Unsystematic Risk 2,675%

ANOVA

gl SQ MQ F

F de

significncia

Regresso 1 0,000154459 0,0001 0,068145157 0,794965Residual 59 0,133730041 0,0022

Total 60 0,133884499

Coeficientes Erro-padro Stat t valor P 95% inferior95%

superio

0,006170218 0,0063791 0,9672 0,337364788 -0,006594 0,0189

e 0,042754415 0,163780981 0,2610 0,794965879 -0,2849700,3704

9


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Figure 1: Exxons Risk Analysis

y = 0,0428x + 0,0062R = 0,0012

-15,00%

-10,00%

-5,00%

0,00%

5,00%

10,00%

15,00%

-10,00% -5,00% 0,00% 5,00% 10,00% 15,00%E(re)-rf

(E(rM)-rf)

ExxonMobil Regression


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Table 2: Industrys Risk Analysis

Industry Regression

SUMRIO DOS RESULTADOS -INDUSTRY

Estatstica deregresso

R mltiplo 0,11173112Montly VolatilityIndustry 0,05802884

Quadrado de R 0,01248384Yearly VolatilityIndustry 0,20101782

Quadrado de Rajust. -0,0042537Erro-padro 0,05815213

Observaes 61

ANOVA

gl SQ MQ F

F de

significnci

a

Regresso 1 0,0025222 0,00252 0,74585796 0,39128819Residual 59 0,1995185 0,00338

Total 60 0,2020408

Coeficiente

s

Erro-

padro Stat t valor P 95% inferior

95%

superior 0,0104666 0,0077917 1,34329 0,18432228 -0,0051246 0,02605

I -0,1727701 0,2000509 -0,8636 0,391288199 -0,5730712 0,22753


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Figure 2: Industrys Risk Analysis

Figure 3: Security Market Line

y = -0,1728x + 0,0105R = 0,0125

-20,00%

-15,00%

-10,00%

-5,00%

0,00%

5,00%

10,00%

15,00%

20,00%

25,00%

-10,00% -5,00% 0,00% 5,00% 10,00% 15,00%E(rI)-r

f

(E(rM)-rf)

Industry Regression

y = 0,011x + 3E-05

-4,000%

-2,000%

0,000%

2,000%

4,000%

6,000%

8,000%

10,000%

12,000%

14,000%

16,000%

-0,4 -0,2 0 0,2 0,4 0,6 0,8 1 1,2

E(r)

SML

SML

Expected Value of Stock

Real Value of Stock


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Appendix 3Question 3Table 1: Estimating ForwardLooking Expected Return

Estimating Exxon Mobile Return - Based on

Forward Looking Expected Return for Market

S&P500Market Growth rate ( Estimation for 5years) 7,70%Market Growth rate (Based on Past -Future Growth) 8,14%

Risk free rate (10 Years treasury Bill) 1,97%

DIV 2015 (2014 + 1 = 2015) 108,23

DIV 2020 (2014 + 5 + 1 = 2020) 169,59

PV OF THE MARKET VALUE IN 2013 2.058,90

Table 2: Historical Beta

Historical Beta's

Exxon's Beta (e) 0,042754415 E(re)-rf=+e(E(rM)-rf) 2,45%

Table 3: Estimated Beta

Estimated Beta =Industry Beta

Exxon's Beta (e) -0,172770156 E(re)-rf=+e(E(rM)-rf) 0,04%


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Appendix 4Question 4

Figure 1: Mean-Variance Frontiers (With Short-Selling)

0,00%

5,00%

10,00%

15,00%

20,00%

25,00%

30,00%

35,00%

40,00%

0,00% 10,00% 20,00% 30,00% 40,00% 50,00% 60,00% 70,00%

Portofolio I Portofolio II Portofolio III


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Figure 2: Portfolio III (Mean-Variance Frontier & Short-Selling Effect)

Figure 3: Efficient Frontier with Risky Investments and a Risk-free Asset

0,00%

5,00%

10,00%

15,00%

20,00%

25,00%

30,00%

35,00%

40,00%

0,00% 10,00% 20,00% 30,00% 40,00% 50,00% 60,00%

With Short Selling Portofolio III Without Short Selling

0,00%

5,00%

10,00%

15,00%

20,00%

25,00%

30,00%

35,00%

40,00%

0,00% 10,00% 20,00% 30,00% 40,00% 50,00% 60,00% 70,00%

Portofolio III Risk Free Asset

Tangency point

Borrowing at the Risk-FreeInterest Rate to Invest onRisky Stocks

Long position on Exxon and Shortposition on Nike and Apple

Long position on Nike and Appleand Short position on Exxon

3.94

Long position on Nike and Apple

and Short position on Exxon

Long position on Exxon and Short

position on Nike and Apple Inefficient Portfolios

Efficient Portfolios


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Table 1: Expected Return, volatility, and covariance

Expected Return, volatility, and covariance

Stocks' ArithmeticAverage Return Stocks Volatility

Covariance

EXXON Nike Apple

Exxon 15,055% 16,676% 2,774% 1,005% 1,57%Nike 22,629% 35,291% 1,005% 12,422% 2,89%

Apple 28,489% 46,470% 1,565% 2,889% 21,54%

Risk free asset 3,943% 0,000% 0,000% 0,000% 0,00%


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Table 2: Portfolio I (Exxon & Nike)

Portfolio I (Exxon & Nike)

Investmenton Exxon's

Stock

Investment onNike's Stock

Portfolio ExpectedReturn

PortfolioVolatility

-20,00% 120,00% 24,14% 41,91%-15,00% 115,00% 23,76% 40,23%

-10,00% 110,00% 23,39% 38,57%

-5,00% 105,00% 23,01% 36,92%

0,00% 100,00% 22,63% 35,29%

5,00% 95,00% 22,25% 33,68%

10,00% 90,00% 21,87% 32,09%

15,00% 85,00% 21,49% 30,52%

20,00% 80,00% 21,11% 28,99%

25,00% 75,00% 20,74% 27,49%

30,00% 70,00% 20,36% 26,03%

35,00% 65,00% 19,98% 24,62%

40,00% 60,00% 19,60% 23,26%

45,00% 55,00% 19,22% 21,97%

50,00% 50,00% 18,84% 20,76%

55,00% 45,00% 18,46% 19,65%

60,00% 40,00% 18,08% 18,64%

65,00% 35,00% 17,71% 17,77%

70,00% 30,00% 17,33% 17,05%

75,00% 25,00% 16,95% 16,49%

80,00% 20,00% 16,57% 16,12%

81,19% 18,81% 16,48% 16,06%

85,00% 15,00% 16,19% 15,96%

86,59% 13,41% 16,07% 15,94%

90,00% 10,00% 15,81% 15,99%

95,00% 5,00% 15,43% 16,24%

100,00% 0,00% 15,06% 16,68%

105,00% -5,00% 14,68% 17,30%

110,00% -10,00% 14,30% 18,08%

115,00% -15,00% 13,92% 19,00%120,00% -20,00% 13,54% 20,05%


18/20

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Table 3: Portfolio II (Exxon & Apple)

Portfolio II (Exxon & Apple)

Investment onExxon's Stock

Investment onApple's Stock

Portfolio ExpectedReturn

PortfolioVolatility

-20,00% 120,00% 31,18% 55,19%

-15,00% 115,00% 30,50% 52,99%-10,00% 110,00% 29,83% 50,81%

-5,00% 105,00% 29,16% 48,63%

0,00% 100,00% 28,49% 46,47%

5,00% 95,00% 27,82% 44,32%

10,00% 90,00% 27,15% 42,19%

15,00% 85,00% 26,47% 40,08%

20,00% 80,00% 25,80% 37,99%

25,00% 75,00% 25,13% 35,93%

30,00% 70,00% 24,46% 33,90%

35,00% 65,00% 23,79% 31,90%40,00% 60,00% 23,12% 29,95%

45,00% 55,00% 22,44% 28,05%

50,00% 50,00% 21,77% 26,22%

55,00% 45,00% 21,10% 24,47%

60,00% 40,00% 20,43% 22,82%

65,00% 35,00% 19,76% 21,29%

70,00% 30,00% 19,09% 19,91%

75,00% 25,00% 18,41% 18,71%

80,00% 20,00% 17,74% 17,73%

81,19% 18,81% 17,58% 17,54%

85,00% 15,00% 17,07% 17,01%

90,00% 10,00% 16,40% 16,58%

94,28% 5,72% 15,82% 16,47%

95,00% 5,00% 15,73% 16,47%

100,00% 0,00% 15,06% 16,68%

105,00% -5,00% 14,38% 17,19%

110,00% -10,00% 13,71% 17,99%

115,00% -15,00% 13,04% 19,04%

120,00% -20,00% 12,37% 20,29%


19/20

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Table 4: Portfolio III (Exxon, Nike, Apple)

Portfolio III (Exxon, Nike, Apple)

Investmenton Exxon's

Stock

Investment onNike's Stock

Investment onApple's Stock

Total InvestmentPortfolioExpected

ReturnPortfolio Volatility

ReturnConstrain

235,20% -53,01% -82,19% 100,00% 0,00% 52,37% 0,00%

216,85% -45,08% -71,78% 100,00% 2,00% 46,65% 2,00%

198,50% -37,14% -61,36% 100,00% 4,00% 41,02% 4,00%

180,15% -29,21% -50,95% 100,00% 6,00% 35,53% 6,00%

161,80% -21,27% -40,53% 100,00% 8,00% 30,24% 8,00%

143,45% -13,34% -30,12% 100,00% 10,00% 25,29% 10,00%

125,10% -5,40% -19,70% 100,00% 12,00% 20,93% 12,00%

115,93% -1,43% -14,49% 100,00% 13,00% 19,09% 13,00%

106,75% 2,54% -9,29% 100,00% 14,00% 17,59% 14,00%

102,16% 4,52% -6,68% 100,00% 14,50% 16,99% 14,50%

97,58% 6,50% -4,08% 100,00% 15,00% 16,50% 15,00%

92,99% 8,49% -1,48% 100,00% 15,50% 16,15% 15,50%

88,40% 10,47% 1,13% 100,00% 16,00% 15,93% 16,00%

83,76% 12,48% 3,76% 100,00% 16,51% 15,85%

79,23% 14,44% 6,34% 100,00% 17,00% 15,91% 17,00%

74,64% 16,42% 8,94% 100,00% 17,50% 16,12% 17,50%

70,05% 18,41% 11,54% 100,00% 18,00% 16,46% 18,00%

65,46% 20,39% 14,15% 100,00% 18,50% 16,93% 18,50%

60,88% 22,37% 16,75% 100,00% 19,00% 17,52% 19,00%

56,29% 24,36% 19,35% 100,00% 19,50% 18,22% 19,50%51,70% 26,34% 21,96% 100,00% 20,00% 19,01% 20,00%

47,11% 28,32% 24,56% 100,00% 20,50% 19,88% 20,50%

42,53% 30,31% 27,16% 100,00% 21,00% 20,83% 21,00%

37,94% 32,29% 29,77% 100,00% 21,50% 21,84% 21,50%

33,35% 34,28% 32,37% 100,00% 22,00% 22,90% 22,00%

28,76% 36,26% 34,98% 100,00% 22,50% 24,01% 22,50%

24,18% 38,24% 37,58% 100,00% 23,00% 25,17% 23,00%

19,59% 40,23% 40,18% 100,00% 23,50% 26,36% 23,50%

15,00% 42,21% 42,79% 100,00% 24,00% 27,58% 24,00%

10,41% 44,20% 45,39% 100,00% 24,50% 28,83% 24,50%5,83% 46,18% 47,99% 100,00% 25,00% 30,10% 25,00%

1,24% 48,16% 50,60% 100,00% 25,50% 31,40% 25,50%

-3,35% 50,15% 53,20% 100,00% 26,00% 32,71% 26,00%

-7,93% 52,12% 55,81% 100,00% 26,50% 34,04% 26,50%

-12,52% 54,11% 58,41% 100,00% 27,00% 35,38% 27,00%

-21,70% 58,08% 63,62% 100,00% 28,00% 38,11% 28,00%


20/20

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-40,05% 66,02% 74,03% 100,00% 30,00% 43,67% 30,00%

-58,40% 73,95% 84,45% 100,00% 32,00% 49,35% 32,00%

-76,75% 81,89% 94,86% 100,00% 34,00% 55,11% 34,00%

-95,10% 89,82% 105,28% 100,00% 36,00% 60,92% 36,00%

33,33% 33,33% 33,33% 100,00% 22,06% 23,03% 22,00%

Documents

Report Exxon