University of California Riverside

Multiple Regression AnalysisDelta Air Lines, Inc. (DAL)

Lopez, David and Phan, Caesar

Delta Air Lines, Inc. (DAL)

Business 136: Securities Analysis and Portfolio Management

Section 001

Professor Kalcheva

November 17, 2016

Delta Air Line, Inc. Analysis

In order to analyze Delta Air Line, Inc. ( DAL), we decided evaluate it based on a multiple regression analysis. This analysis seeks to evaluate DAL based on both recent data (past year) and more historical data (past 5 years) relative to the S&P 500, Small-minus-Big (SMB, High-Minus-Low (HML), and Momentum. We will start by first evaluating the Monthly Regression’s data over the span of 60 months, followed by the Daily Regression Data generated from the most recent year’s returns, and conclude with an overall analysis.

Starting by evaluating the DAL’s monthly returns, as seen on figure 3, although the regression stated that DAL has an alpha 0.02, it does not mean that it is underpriced. It’s alpha’s p-value was 0.09 and the t-stat was 1.7. In order to disprove the null hypothesis, the p-value needed to be at least less than 0.05 and the t-stat needed to be at least over 1.96 to be statistically significant. Due to the fact that both the p-value and t-stat are both statistically insignificant and, as such, are unable to disprove the null hypothesis. Since we cannot disprove the null hypothesis, the stock is likely to be correctly priced. This regression also determined that the Beta is 0.809. According to the t-stat and p-value generated, beta is statistically significant since the t-value is 2.21 and the p-value is 0.03. Since both are statistically relevant, proving that the null hypothesis has been rejected. This beta also tells us that DAL’s movements are less volatile than the market’s. In other words, DAL can be considered a relatively defensive stock. Looking at R-Squared, we are given 0.1329. This means this regression accounts for 13.29% of the variance. In other words, only 13.29% of the variables are explained by the model. Although this does not significantly help us predict future movements, it does tell us that, to some extent, there is a relationship between DAL’s return and the benchmark variables. According to DAL’s monthly regression, the only statistically significant independent variable produced is Beta, since it was the only one which was disproved its null hypothesis. This of course does not mean that the other independent variables have no correlation to DAL; however, due to the fact that they failed the p test and t test, we cannot disprove the null hypothesis and, as such, should not base our analysis on data which are not statistically relevant. Relative to the Beta determined by Reuters and Morningstar, our regression’s Beta relatively close. Reuter argues that DAL’s Beta is 0.91 and Morningstar’s Beta to 0.82, both of which are roughly only 0.1 away from our regression beta (0.809). Reuter’s beta is slightly higher (1.3), and as such, our Betas are spread apart by roughly 0.5. Considering 2 of these three major sites have determined the alpha relatively close to ours, we believe our regression’s Beta to be accurate. Based on the regression, the total risk of generated is 0.511. The regression, or systematic risk, or undiversifiable risk is 0.068. The residual or firm specific risk is 0.443. However, due to the fact that the p-value associated is 0.09, and not less than 0.05, we are not able to disprove the null hypothesis. As such, the risks generated are statistically insignificant.

With regards to DAL’s Daily regression (figure 6) we see that alpha is -0.0002; however, due to the fact that the p-value determined was 0.78 and the t-stat is -0.26, the p-value and the t-stat are not significant. Unlike the data produced from the monthly regression, the momentum for the daily regression appears to be statistically relevant since it has a p-value of 4.639E-7 and a t-stat of 5.179. Positive momentum points out two significant aspects: DAL’s stock price last twelve month’s average excess returns are positive and it’s DAL’s stock price has a tendency to continue rising. This regression also determined that the Beta is 1.13. According to the t-stat and p-value generated, beta is statistically significant since the t-value is 11.14 and the p-value is 0.789. This beta tells us that DAL’s movements are more volatile than the market’s average. In

other words, DAL can be considered a cyclical stock. When we look at R-Squared, we are given 0.3985, meaning only 39.85% of the total variance is explained by the market’s volatility. Conversely, 60.15% is not explained by the volatility of the benchmarks. In other words, only 39.85% of DAL’s returns are explained by the independent variables. Although this does not significantly help us predict future movements, it does tell us that there is there is to some extent, a relationship between DAL’s return and the benchmark variables. Compared to Reuters and Morningstar, our beta is significantly higher. Reuters produced a beta of a beta of .91 and Morningstar is 0.82. Relative to the Beta determined by value line, our regression is slightly lower. Value line argues that DAL’s Beta is 1.3, which is slightly more from our daily regression’s Beta (1.13). The betas are spread apart by roughly 0.31.Based on the regression, the total risk of generated is 0.096. The regression, or systematic risk, or undiversifiable risk is 0.038. The residual risk, or firm specific, or diversifiable risk is 0.057.due to the fact that the p-value is less than 5%, we argue that the risks associated are statistically relevant and to a certain degree reflect DAL’s actual risks.

Conclusion: Based on the conclusion from the data listed above, we do not believe this regression to be considerably accurate in predicting DAL’s stock price, based on the given independent variables: SMB, HML, and momentum. As stated previously, in many of regression generated below, many independent variables were not statistically relevant enough to disprove the null hypothesis. Due to the fact that r-squared were so low, the data is not close enough to the regression line for good predictions of future stock price. However, by doing regressions of various variables, we were able to not only prove statistically relevant Betas, we were also able to discover that DAL has a positive momentum. According to the beta (0.8092) generated from the monthly regression from figure 3, the risk-free rate (0.0229) found from the ten-year bond (figure 10), and the given risk premium (4%), we were able to generate an expected return of 5.53%. In other words, investors should expect at least a return of 5.53% from investing in Delta Air Lines, Inc.

Figure 1Monthly Regression

Figure 2 Monthly Regression

Figure 3 Monthly Regression

Figure 4 Daily Regression

Figure 5 Daily Regression

Figure 6Daily Regression

Figure 7 Morningstar Beta http://www.morningstar.com/stocks/XNYS/DAL/quote.html

Figure 8 Reuters http://www.reuters.com/finance/stocks/overview?symbol=DAL

Figure 9 Value Line Beta https://research.valueline.com/research#list=recent&sec=company&sym=dal

Figure 10 10 Year Treasury Bond Return https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield