This document summarizes an assignment analyzing the risk and return characteristics of Delta Airlines (DAL) and Linn Energies (LINE). Daily return data from 2014-2015 was analyzed, finding DAL had higher expected returns and lower risk than LINE. A correlation analysis showed the assets were imperfectly negatively correlated. Various portfolio allocations were considered in a mean-variance analysis, deriving an opportunity set. The minimum variance portfolio was found to be 73% in DAL and 27% in LINE. While DAL performed better, diversification across the negatively correlated assets reduced overall portfolio risk.

1. EC411 ASSIGNMENT
Name: Cian McDonnell
ID: 12476828
Intro:
The risk assets I have chosen for this assignmentare Delta Airlines (DAL) and
Linn Energies (LINE).
Delta Air Lines (NYSE: DAL) is the 2nd largestpassenger airline in the world by
available seat miles. Itcurrently has a fleet of nearly 600 owned and over 200
leased planes and an averageage of around 15 years. Delta has the 2nd largest
and 3rd oldest fleet in the American airline industry.The airline operates on a
hub-and-spokesystem, centred at airports in Atlanta, Cincinnati, New York JFK,
and Salt Lake City. Delta is attempting to offset weak U.S. consumer demand
by expanding heavily in international flights.
Linn Energy is an independent oil and gas company focused on the
development and acquisition of long life properties in the United States. From
inception through January 2008, they completed 24 acquisitions of working or
royalty interests in oil and gas properties and related gathering and pipeline
assets.In addition, they have more than 7,200 producing oiland gas wells and
over 4,100 drilling locations.

2. Reasonfor choosing these two:
The reason I chose these two assets was to obtain a low or negative
correlation. The purposeof this is to lower portfolio volatility. Combining
assets that have a low correlation reduces the volatility of the portfolio as a
whole and allows the portfolio manager to investmore aggressively. In other
words, a portfolio manager willing to accept a given amount of volatility can
invest in higher risk/return investments. This is because the volatility of the
overall portfolio is lower due to combining non-correlated assets. This is called
portfolio optimization. A maxim among investors is that airlines are the best
way to get exposureto falling oil prices. Over the pastfive years, when oil
prices declined by 15, the sector specific performanceof airlines has been
approx. +0.4. Giver the regularity of falling oil prices over the last year I
thought it was relevanthe do the assignmenton these two companies.
Analysis:
To carry out my analysis I downloaded the daily shareprice of both Delta
airlines and Linn energy from26/11/14 to 26/11/15 to excel and worked out
the daily returns.
dal line
Mean
returns
0.050% -0.388%
variance 0.039% 0.123%
Standard
deviation
1.972% 3.503%
Delta airlines is clearly the better performing assetas it offers the better
expected returns with less risk.

3. I then examined the relationship between the two assets and found the
covarianceand correlation.
covariance -0.00008
correlation -0.12187
These assets are imperfectly negatively correlated which reduces the volatility
of the portfolio and allows the investor to investmore aggressively.
Mean-Variance Analysis:
Using the results I obtained above I then analysed the relationship between
mean and varianceand derived a mean varianceopportunity set. To do this I
assigned different weights to both assets creating 11 different portfolios. I then
calculated expected return, varianceand standard deviation of these
portfolios.
portfolio dal line Expected returns variance St. Deviation
1 0% 100% -0.38811% 0.123% 3.5028044%
2 10% 90% -0.34435% 0.098% 3.1346083%
3 20% 80% -0.30059% 0.077% 2.7818579%
4 30% 70% -0.25683% 0.060% 2.4512304%
5 40% 60% -0.21306% 0.046% 2.1529425%
6 50% 50% -0.16930% 0.036% 1.9022685%
7 60% 40% -0.12554% 0.030% 1.7201520%
8 70% 30% -0.08178% 0.027% 1.6297405%
9 80% 20% -0.03801% 0.027% 1.6462134%
10 90% 10% 0.00575% 0.031% 1.7665833%
11 100% 0% 0.04951% 0.039% 1.9719148%

4. By plotting these values, with Expected Return on the y-axis and Standard
Deviation on the x-axis, I obtained a graphical representation of the mean
variancefrontier. It can be seen quite clearly that as one moves along the
frontier, one can select a specific amountof risk that they are willing to accept
and see the maximum return for that level of risk. Conversely, onemay also
see the minimum amount of risk available for a given level of return.
Given the low expected returns of these two assets the graph is mostly
downward sloping.
-0.45%
-0.40%
-0.35%
-0.30%
-0.25%
-0.20%
-0.15%
-0.10%
-0.05%
0.00%
0.05%
0.10%
0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0%

5. Minimum variance:
The variance formula forthe portfolio is:
𝜎2=𝑊𝐴2𝜎𝐴2+𝑊𝐵2𝜎𝐵2+2𝐶𝑜𝑣𝐴𝐵𝑊𝐴𝑊𝐵
By letting 𝑊𝐴=1− 𝑊𝐵 and then differentiating the variance formula with respect
to 𝑊𝐴 and setting equal to 0, I was able to find the optimum weights which
would give the minimum variance on the mean variance frontier.
min variance
portfolio
dal line returns var st.dev
73% 27% -0.06803% 0.026% 1.6231350%
-0.07%
-0.45%
-0.40%
-0.35%
-0.30%
-0.25%
-0.20%
-0.15%
-0.10%
-0.05%
0.00%
0.05%
0.10%
0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00%
minimum varianceopportunity set

6. This means that 73% of our investment must be in Delta and 27% in Linn for
our portfolio to contain the least risk possible. In this casethe investor would
have to take more risk to get a positive expected return. This shows that Delta
is clearly the better assetas there is a high weight assigned to it in order to
minimise volatility. Although it is telling me that Delta is the better assetit also
tells me that diversification is importantin a portfolio so that the investor can
invest in higher risk/return investments. This is due to the fact that the
portfolio volatility was minimised by combining negatively correlated assets.