Essay: Justifications and Discussion Portfolio Analysis

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¶ … Justifications and Discussion

Portfolio Analysis for Six Discrete Weight Combinations

Analysis of VaR Compared to Actual Returns

Overall Correlation Coefficient

Correlation Coefficient Comparison

VaR Calculations over Different Sub-Periods

Two separate major U.S. indexes were evaluated over a period of time between the beginnings of 2007 until the beginning of 2010. The Dow Jones Industrial Index was selected as a broad indicator of the total U.S. economic health while a more specific indicator was also selected, the Dow Jones U.S. Tobacco Index, which represents a more targeted industry analysis. Six phases of calculation were conducted and contrasted with various macroeconomic trends that were also prevalent throughout this duration of this period. This provided evidence that the Dow Jones U.S. Tobacco Index was compiled of companies that sold goods that had a low price elasticity of demand, low income elasticity, or possibly some combination of both. Furthermore, a discussion was included that recommended future research be conduct over this period to further delineate factors and information that could potentially be used for future public health policy.

Part One -- Data Selection: Justifications and Discussion

The macroeconomic environment from the period between the beginnings of 2007 to the beginning of 2010 is an interesting period to study. While the National Bureau of Economics Research (NBER) "officially" declared that the U.S. entered into a recessionary period in December of 2007, the economy on a whole definitely showed signs of stress long before this date, to say the least (MSNBC, 2008). The NBER later declared that the recession officially ended in June of 2009 (Isidore, 2010). However, consideration of only the official beginning and end dates only paint a small portion of the total picture. In fact, since the official end date past, America saw a deterioration of over nine hundred thousand jobs as well as the slowest growth in the nine-month stretch following a post-war downturn (The Economist, 2010).

Unemployment rates in the beginning of the period being studied approximated about seven million people in the U.S. And the unemployment rate was under five percent (Bureau of Labor Statistics, 2007). By the end of the period being studied, unemployment had risen to ten percent and then dropped slightly to nine point seven percent (Hincha-Ownby, 2010). Both the unemployment rate as well as the total number of people unemployed more than doubled. Many economists believe that the high levels of unemployment have created demand side problems that will never be overcome by supply side initiatives (Krugman, 2011). One factor that underlined many of the subsequent problems that the U.S. economy faced during the time was the housing bubble climax which was estimated to occur in 2005 (Byun, 2010). This phenomenon resulted in a subsequent unemployment effect that was estimated to range from 1.2 million to 1.7 million jobs as well as cost U.S. homeowners billions in lost real estate wealth.

Indices pricing data was selected for the period extending from January 1st, 2007 to January 1st 2010. The first index that was chosen was the Dow Jones Industrial Index (DJI). The DJI represents a fairly broad economic indicator. It is composed of thirty stocks and is price-weighted of the largest blue chip organization traded on the New York Stock Exchange (NYSE) (Abbondante, 2010). While other indexes contain a compilation of stocks, such as Standards and Poor's 500 (S&P500) and the NASDAQ index, the DJI has been a good indicator of the United States overall economic health by most measures and is certainly the most widely recognized index. However, it should also be mentioned that there a sparse number of critics who also argue that since the companies included in the index are limited and subject to frequent changes that it may not be quit as reliable as most people are led to believe (Blodget, 2009).

An index that represents a more narrow industry segment was also chosen for analysis. Since the macroeconomic environment at the time represents a period fraught with volatility and uncertainty, including some considerations of systemic risk, it seemed as if the Dow Jones U.S. Tobacco index would serve as interesting subsidiary selection. Though there is little reporting on this industry index by the main stream press, however there has been a tremendous body of literature developed in journals over the last three decades concerning the price and income elasticity of tobacco products (Chaloupka, 2011). For example, in the late 1960s, researchers identified the price elasticity established by previous studies to range from -0.10 to -1.48 (Lyon & Simon, 1968).

Tobacco can serve as a classic example for price elasticity of demand as well as income since there is data readily available before and after state and federal tax policies have been implemented. Both the federal government along with a majority of state governments has issued tax policies that have subsequently increased the purchase price for all consumers at given intervals (Tanzi & Zee, 2000). Although there seems to be a relative consensus regarding the fact that demand undoubtedly diminishes under such policy initiatives, the extent to which however is highly contested. New models consider not only the basic underlying economic data such as information on price and income levels, but new research is also trying to connect macro-social influence, such as various marketing campaigns, to the total body of knowledge (Chaloupka, 2011).

Daily frequencies of data were chosen to provide an accurate data set to analyze each index as a result of the heavy volatility that occurred in markets throughout this period. Thus each data set for the individual indices consisted of seven hundred fifty two data points. Two potential macroeconomic influences that was hypothesized to potentially impact the narrower industry focused index was that either the index would experience diminished returns due to the effects of an effective reduction of income in the economy or possibly that the resulting recession implications would have no effect due to the marginal rate of tobacco's income elasticity. The data suggested that overall the tobacco index outperformed the market during this period.

(^DJI)

(^DJUSTB)

Mean

-0.0002386

7.20632E-05

STD. DEV.

0.017249966

0.015367525

Variance

0.000297561

0.000236161

Table 1 - Descriptive Statistics

Part Two -- Portfolio Analysis for Six Discrete Weight Combinations

The daily returns for each index was calculated for each index based on the rate of continuously compounding interest that each index earned for each day. The returns were compiled and the overall performance of each index was identified in terms of the return as well as the risk. A combination of various potential portfolios for the period was constructed at six discrete weightings ranging from 0% to 100% of each index. The risk and return figures were calculated for each possible portfolio weighting by multiplying the factors by their relevant portfolio weighting. Below are the individual figures for each portfolio as well as the performance of the combined portfolio possibilities under the constructed model.

Portfolio Weight DJI

RTN

RISK

w*s2

90%

-0.00021474

0.01552497

0.00024102

70%

-0.00016702

0.01207498

0.00014581

50%

-0.00011930

0.00862498

0.00007439

30%

-0.00007158

0.00517499

0.00002678

20%

-0.00004772

0.00344999

0.00001190

10%

-0.00002386

0.00172500

0.00000298

Table 2 - Dow Jones Industrial Average Portfolio Contribution

Portfolio Weight DJUSTB

RTN

RISK

w*s2

10.00%

0.00000721

0.001537

0.0000024

30.00%

0.00002162

0.00461

0.0000213

50.00%

0.00003603

0.007684

0.0000590

70.00%

0.00005044

0.010757

0.0001157

80.00%

0.00005765

0.012294

0.0001511

90.00%

0.00006486

0.013831

0.0001913

Table 3 - Dow Jones U.S. Tobacco Index Portfolio Contributions

PORTFOLIO

RETURN

RISK

1

-0.000207534

0.016624472

2

-0.000145401

0.015621417

3

-0.000083269

0.015002016

4

-0.000021136

0.014814468

5

0.000009931

0.014889209

6

0.000040997

0.015074902

Table 4 - Total Portfolio Performance for Each Weighting Variation

The dominant portfolio that emerged in the comparisons of the various weighting combinations is the portfolio that included the heaviest weight for the tobacco index. Since the tobacco index outperformed the broader index on the whole, the portfolio with the most profitable outcome. The total returns for each portfolio combination is displayed in Table 5. As the illustration shows, the slope shifts slightly when the weights of the contribution of the DJUSTB are at 80% and 90%. This is due to the fact that these two figures only represent a 10% incremental difference while other combinations represent a 20% incremental increase. This shift also supports the fact that the dominant portfolio was the tobacco index.

Table 5 - Dominant Portfolio Graphical Representation

Part Three -- Analysis of VaR Compared to Actual Returns

For the period January 1st, 2007 to January 1st 2010 as sample portfolio was constructed that was based upon the portfolio consisting of $100M at the beginning of the period being studied. The sample portfolio consists of 80% of the DJUSTB index and contains 20% of the DJI index. The standard deviation for each index was identified and weighted appropriately to represent the scenario. The actual returns that the portfolio generated were calculated to be $745,781.39 give the weighted returns that each index provided. Also the value at risk (VaR) was calculated at the 95% confidence interval (1.64) by multiplying this figure by the total portfolio risk. The calculated VaR figure was nearly two and a… [END OF PREVIEW]

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