• Analyzed the weekly stock prices of a portfolio of 5 companies over 3 years using statistical methods such as Correlation, Sharpe ratio, Covariance matrix etc. • Identified optimal portfolio return using equal weight portfolio and different portfolio weight with highest Sharpe ratio by diversifying between uncorrelated stocks.

1. FIN 6306 – Project 1
Marks, Dustin (drm160130@utdallas.edu)
Burger, Stephen (srb171130@utdallas.edu)
Yang, Jingxue (jxy130530@utdallas.edu)
Wang, Boyu (bxw161730@utdallas.edu)
Ranjan, Rajat (rxr167030@utdallas.edu)
HAL (Halliburton Company): Halliburton Company was founded in 1919 and is based in
Houston, Texas. It is one of the largest oilfield services company in the world and provides a
range of services and products to the upstream oil and natural gas industry worldwide. Its $46B
company and its last year annual revenue was $23B and last 5 year CAGR is 5.6%. Last year, it
has reported a negative net income of $671M and the negative return on equity of 4.2%.
Mean 0.0783%
Standard Deviation 4.2455%
Skewness -0.9208
Kurtosis 2.8826
Table 1 - HAL Statistics
HAL has an average return of .0783% with a standard deviation of 4.2455%. It holds the
minimum return in our portfolio on average, but it also carries more risk on average at it has the
lowest sharpe ratio among portfolio stocks. This stock has the most negatively skewed
distribution in our analysis. The return distribution carries much of its weight in its tails, which is
evidenced by it holding the highest excess kurtosis out of our chosen stocks.
TXN (Texas Instruments): Texas Instruments is a leading semiconductor manufacturer
headquartered in Dallas, TX. It is a $76.8B company with steady revenue and steady growth in
profit. TI’s stock value has doubled in the last three years due to stockholder confidence in the
strength of the company. Last year, it has reported a net income of $3.6B and the return on
equity of 29.4%.
Mean 0.3854%
Standard Deviation 3.0707%
Skewness -0.2419
Kurtosis 1.7147
Table 2 - TXN Statistics

2. TXN has an average return of 0.3854% with a standard deviation of 3.0707%. It has a higher
average return than HAL, and it carries the lowest less risk on average out of the five stocks
analyzed. The TXN returns are fairly close to a normal distribution. It is negatively skewed with a
higher peak than the normal distribution, so it carries more weight in its tails, mainly on the left
side. As it is slightly negatively skewed, so it holds a slightly lesser chance of achieving an
abnormally high negative weekly return.
IBTX (Independent Bank Group Corp.): IBTX operates as the bank holding company for
Independent Bank that provides a range of commercial banking products and services to
businesses, professionals, and individuals in the United States. Its $1.2B company and its last
year annual revenue was $198M and last 5 year CAGR is 5.6%. Last year, it has reported a net
income of $53.5M and the return on equity of 8.2%.
Mean 0.1654%
Standard Deviation 4.6633%
Skewness 0.2874
Kurtosis 1.9260
Table 3 - IBTX Statistics
IBTX has an average return of .1654% with a standard deviation of 4.6633%.
LUV (Southwest Airlines Co.): Southwest Airlines Co. operates a passenger airline that
provides scheduled air transportation services in the United States and near- international
markets.
Mean 0.619%
Standard Deviation 4.3153%
Skewness -0.2558
Kurtosis 1.5410
Table 4 - LUV Statistics
AMZN (Amazon.com, Inc.): Amazon.com, Inc. engages in the retail sale of consumer products
and subscriptions in North America and internationally. It sells merchandise and content
purchased for resale from vendors, as well as those offered by third-party sellers through its
retail websites.

3. Mean 0.4085%
Standard Deviation 4.1884%
Skewness -0.0405
Kurtosis 2.4432
Table 5 - AMZN Statistics
Correlation Matrix
HAL IBTX TXN LUV AMZ SP500
HAL 1.00 0.37 0.40 0.26 0.18 0.54
IBTX 0.37 1.00 0.31 0.22 0.19 0.44
TXN 0.40 0.31 1.00 0.34 0.31 0.74
LUV 0.26 0.22 0.34 1.00 0.26 0.44
AMZ 0.18 0.19 0.31 0.26 1.00 0.44
SP500 0.54 0.44 0.74 0.44 0.44 1.00
Table 6 - Correlation Matrix
Covariance Matrix
Equal Weight Portfolio
EQUAL WEIGHT PORTFOLIO
Stock Symbols HAL IBTX TXN LUV AMZ
Weight 0.2 0.2 0.2 0.2 0.2
Portfolio Return 0.3314%
Variance 0.00071
Stdev 2.67%
Sharpe Ratio 0.1136
HAL IBTX TXN LUV AMZ SP500
HAL 0.001803 0.000726427 0.000516 0.00048 0.000314 0.000394
IBTX 0.000726 0.002174342 0.000447 0.000441 0.000381 0.000352
TXN 0.000516 0.000447123 0.000943 0.000451 0.000398 0.000391
LUV 0.00048 0.000440977 0.000451 0.001862 0.000465 0.000329
AMZ 0.000314 0.000380523 0.000398 0.000465 0.001754 0.000319
SP500 0.000394 0.000351866 0.000391 0.000329 0.000319 0.000295

4. Table 6 - Equal Weight Portfolio
By allocating equal weight to each of the stocks, we compute the portfolio expected value
(0.3314%), standard deviation as a measure of risk (2.67%), and the Sharpe ratio (0.1136).
Comparing to SP500 units of measurement of expected value, standard deviation, and Sharpe
ratio, we have.
Optimal Portfolio
OPTIMAL PORTFOLIO
Stock Symbols HAL IBTX TXN LUV AMZ
Weight 0 0 0.39 0.42 0.18
Portfolio Return 0.4885%
Variance 0.000818
Stdev 2.86%
Sharpe Ratio 0.16008
Table 7 - Optimal Portfolio
In creating the optimal portfolio, we chose to isolate the stock choices down to HAL, IBTX, TXN,
LUV and AMZ for the portfolio. This was done by calculating the Sharpe Ratio for the portfolio
with different weights assigned to each stock and choosing the highest Sharpe Ratio received.