WMT & CASY Simple Regression Analysis of Returns

Linear Regression--attempting to find those few variables that drastically help explain another factor's outcome, providing a perceived edge over the competition. A simple model usually includes less than a handful of independent variables, but finding those variables is quite the adventure. Run after run, more or less multicollinearity each time in a time series, plugging in another lag, possibly running into serial correlation, so on and so forth--quite the rigorous process. If one can however come upon interesting data that can explain 80%+ of the S&P 500 returns over the past 10 years, for example, with a significant adjusted R squared, indicating significant independent variables, one might have his hands on a new model that other market participants are not considering. You could begin to explain flaws in a plethora of current securities valuations. This is the beauty of statistics in securities analysis.

I regressed monthly returns over the past five years for Casey's General Store (CASY) and Walmart (WMT).?Considering these are both non-small-cap, public, US companies, returns were regressed against the S&P500.?For CASY,?I computed a beta of 0.67 and some change.?This is compared to the Yahoo Finance and Guru Focus betas of 0.69 and 0.82, respectively.?For WMT,?I computed a beta of 0.28.?This is compared to the Yahoo Finance and Guru Focus betas of 0.28 and 0.44, respectively.?The Guru Focus betas often regress against computer-generated custom benchmarks, as opposed to the S&P 500 which is often a standard market representative. This can explain the large deviation in Yahoo and Guru Focus calculations.

The calculated R squared for CASY was 0.19, which is low.?Given a 0.19, I would probably move on to a multi-factor model in an attempt to find better factor representations, while holding onto a significant F, or I could exclude large outliers.?If you look at the slope on the plot, you'll notice quite a few large outliers.?My regression F statistic was 13.61 with a p value of .0005-- very significant, considering anything below 0.005 at the 95% level is typically acceptable.?That shows no concern.?My independent variable, S&P 500, is associated with a t-stat of 3.69-- significant as well.?That raises no concern.?At a glance, heteroskedasticity does not seem to be a concern, and neither does multicollinearity.?Autocorrelation concerns seem to be ok as well, given my F statistic is highly significant along with the S&P 500 t-stat. The F is expected to be significant, given my single variable is significant.?As I mentioned though, the R square is pretty low, and I would not recommend using this simple model to help explain CASY returns.??

My R square for WMT is 0.05, about as low as it gets.?My WMT/S&P 500 beta's t-stat is 1.78,?insignificant at the 95% level, so it can be assumed to be zero (so worthless).?In turn, my F statistic of 3.17 is also insignificant, clocking in at a p value of 0.08; remember, needs to sit below 0.05.?In a nutshell, Walmart's beta of 0.28 theoretically means it will move up 0.28% for every 1% move of the market, but in reality, we do not have much evidence of this. Do note the significant outliers associated with WMT though. It seems as if the slope would be slightly more positive if we adjusted for this, but it is my opinion that there is no need to move forward with the CAPM discussion for WMT, given the significant issues so far with the market beta... I frankly don't take much away from the CASY market beta either, considering its low R square.?I much more prefer meaningful, researched, proven, multifactor models specific to particular securities.?Many investors today do not realize how insignificant a regular market beta is for the majority of shares.

To offer a little more perspective of Walmart's beta, consider the following: The S&P 500 is down 11% since February 24, approximately when the market began to crash in response to COVID-19... Walmart is up nearly 14%. Beta says WMT should have decreased with the market.

If I had regressed this with daily returns as opposed to monthly, I do believe the results would be different.?CASY exhibits a stronger standard deviation, while the S&P attempts to mitigate this with large diversity.?CASY standard deviation at a glance has been much higher than the S&P, but WMT has been a lot more consistent with the S&P.?I believe this is due to Walmart's role as a consumer staple/defensive company. This almost acts as a diversifier;?in recessions, defensive goods (guns and non discretionary items, both of which Walmart carries) remain strong in sales. Over the COVID-19 bear market, WMT has made a fantastic performance.?It just today hit its all-time high of $129.?I actually sold WMT last week at a very attractive price. I did hold on to half my position though, so hopefully we will see the momentum continue.?

Casey's also handles defensive, consumer staple goods, but Casey's operates in predominantly lower-income, farm-driven communities and handles gasoline.?As we are all aware, oil prices have been falling drastically, and this is leading the a perfectly competitive c-store industry to drop gasoline prices to the floor.?With a historically constant fuel margin over the past several years, this will mean less fuel income during this oil war for Casey's, and fuel is their largest revenue driver.?Well due to the quarantining, traveling is also decreasing, further hindering Casey's fuel sales. In recessions, historically, Casey's has not performed as well as competitors such as 7/11 and Murphey USA.?US farm revenues and net income have significantly dropped off over the last decade, and this is not a good sign for Casey's, although Casey's is consistently acquiring and building new stores.?Their same-store sales growth has been consistently dropping off year-to-year.?Casey's has experienced large price movements, fluctuating from $130 to $180 over the past year alone.?It sat at $175 in November, moving to nearly $150 in February, and back up to $180 pre-COVID bear market-- much more volatility than WMT and S&P 500.

I also regressed three years instead of five.?For Casey's, the only significant difference is the R square; it increased to 0.29, from a five-year R square of 0.19.?This is an improvement!?For WMT, I have some interesting findings.?R square increased from 0.05 to 0.13-- still not good, but better.?The F statistic p value also decreased from 0.08 to 0.029, and this is significant at the 95% level!?This is due to the t-stat of S&P 500 returns increasing from under 2 to 2.28.?It seems that we have a valid beta for a CASY CAPM now; although I would still suggest a multi-factor model, considering such a low R square. Three years is also not a very significant period of returns, just barely surpassing the "n > 30" rule to use the T distribution.?I believe as Casey's increases in size, it will perform closer with the S&P though.?In fact, Casey's moved from small-cap into the mid-cap territory surpassing the $2 billion mark in just 2012, and management expects to operate 350 new stores in the next three years.

I was curious what would happen in a multi-factor model such as the Fama-French 5-factor.?I pulled the necessary data, and did a Fama-French 5-factor regression on CASY and WMT, and both models were trash.?I noticed the HML t-stat was significant though.?I regressed CASY on S&P and HML (though I can imagine these independent variables could possibly represent autocorrelation) with five years of monthly data.?I still had a significant F at 95%, but HML was an insignificant coefficient in the model.?I would like to possibly perform some regression analysis based on important quarterly financial line items, and I even think a multiple macro-economic regression with an S&P 500 dependent variable and dependent variables such as GDP, unemployment rates, and other possibly significant variables would be very interesting.

So there are obviously not a whole lot of meaningful finds here, but it lays out my understanding. I am working on a masters of investment management and financial analysis at Creighton University in the heart of Omaha, so I am looking for as much practice with practical multiple regression analysis as I can find; anybody interested in touching base can shoot me an email, LinkedIn message, or simply comment below.