As an asset class, can we say with confidence that small-cap stocks outperform larger ones? Investors who were lucky to invest in Apple (NASDAQ:AAPL) when it was still a small-cap stock and managed to stay the course were certainly rewarded handsomely. However, can these one-time events be generalized for the performance of small-cap stocks as a whole? It is not very often that the average small-cap company witnesses such a phenomenal rate of growth. Therefore, in order to test this, I decided to conduct a regression analysis of 30 companies in total across three separate industries to examine the elasticity of returns across these two asset classes. Based on my findings, there is no evidence that small-cap companies in the airline or energy sectors outperform large-cap companies. However, there are indications that **small-cap financial stocks could have the ability to outperform their larger rivals.**

**Methodology**

My study examines large and small market capitalisation company returns across the **airline**, **financial**, and **energy** sectors for the period 26th May 2011 to 16th June 2014. The companies considered in the study are as follows:

**Airlines**

**Energy**

**Financials**

Using the double-log model, I examine the elasticity of small and large cap returns for each industry and across large and small-cap classes. I use the 10% level of significance. Using large cap returns as the independent variable (X) and small cap returns as the dependent variable (Y), my null and alternative hypotheses using a two-sided t test are as follows:

**Null Hypothesis:** Beta is equal to 0; i.e. a percentage change in the returns of large-cap companies do not correlate with a change in the returns of small-cap companies.

**Alternative Hypothesis:** Beta is not equal to 0; i.e. a percentage change in the returns of large-cap companies correlate with a change of a certain magnitude in the returns of small-cap companies.

My rationale for using these hypotheses are to test how the companies in each size bracket would perform during periods of industry up-trends which are in many ways fuelled by larger companies, and given the period 2011 to the present has witnessed general uptrends in these three industries, the selection of this time period for the study is deemed appropriate. If we suppose large cap companies changed by 1% while small cap companies changed by 1.5%, then we see that small-cap returns are elastic; i.e. when large-cap companies change, small-cap companies change with an even higher magnitude. On the other hand, if small-cap returns are inelastic, then the change in small-cap returns will be of a lesser magnitude than large-cap returns.

In order to facilitate comparisons between small and large cap companies in each industry, I create an equally weighted price index for five companies, segmented across industry and size. I assume a 0.2% weighting for each company, and create a weighted price for both large and small cap stocks for each industry.

**Price Of Index =***(Price of Company A*0.2) + (Price of Company B*0.2) + (Price of Company C*0.2) + (Price of Company D*0.2) + (Price of Company E*0.2)*

I then create a double-log function using the natural log of returns for each of the indexes across the three price baskets for each industry. The resulting regression equations allows us to determine the elasticity of returns between small and large cap companies, and the t-test allows us to use the results in either proving or disproving the null hypothesis as outlined above.

**Airlines**

The below regression equation indicates that for every 1% change in large-cap returns, there is a 0.58% change in the returns of small cap companies. With a p-value of 0.0655, our results are significant at the 10% level. This means that at the given significance level, small-cap returns are inelastic - in this case when large-cap returns increase, small-cap returns also increase but not by as much. This may suggest that during periods of market upturns, large-cap airlines are in a better position to capitalise on growth than small-caps. In addition, note that I have not tested the models in this study for serial correlation between returns; this means that the p-value may be higher as stated and it is still possible we cannot reject the null hypothesis. However, this would not change the underlying conclusion that there is no evidence that small-cap airline companies outperform larger ones.

**Energy**

For energy stocks, our regression equation indicates that for every 1% change in large-cap returns, there is a 1.18% change in small-cap returns. However, note that our p-value is 0.124 which means our p-value is insignificant at the 10% level. This means that we cannot reject the null hypothesis that small-cap returns in fact have a slope of zero and are inelastic with respect to large-cap returns, i.e. when large-cap returns change, this means there is no corresponding change in small-cap returns. Given we have an average small-cap return of 0%, this would appear to support the null hypothesis - there is no evidence to support that small-cap energy stocks can outperform larger firms.

**Financials**

In the case of financials, the regression equation indicates that for every 1% change in large-cap returns, there is a 0.6238% change in small-cap returns. However, note that the p-value is 0.199 which means our p-value is highly insignificant at the 10% level. However, also note that the mean return of 0.08% for small-cap companies are double that of the mean return of 0.04% for large-cap companies. This would suggest that small-cap returns are inelastic with respect to large cap returns, but more specifically **are inelastic with regards to losses**. The data would appear to support this hypothesis. For the period of 2011 being examined, the firms in the large-cap basket sustained a cumulative loss of 33.74%, while the basket of small-cap firms actually gained 8.38%. Given that we cannot reject the null hypothesis, the outperformance of small-cap financial stocks may actually suggest that they are more immune to the losses that are experienced by larger firms in the banking sector, and therefore generate higher returns overall.

**Investment Considerations**

Overall, in terms of possible investment considerations based on the above data, investors interested in the above sectors would do well to consider large-cap names from the airline and energy sectors as these companies seem to be in a better position to capture growth. However, in terms of a play on the financial sector, the returns from small-cap financial firms seem quite attractive and the downside risk seems to be lower than that of large-cap firms in the industry. Ultimately, if I were to pick the three companies that I believe offers best exposure to growth in the above industries, I would go with these three:

**Delta Airlines (NYSE:DAL):** With a cumulative return of 159.84% and a current P/E ratio of 159.84%, Delta Airlines seems incredibly cheap both relative to its historical P/E ratios and relative to its competitors, with the P/E ratios of Spirit Airlines (24.93), Southwest (22.32), United (43.37) and JetBlue (21.80) being far higher. Given the increase in passenger numbers and higher fares coupled with the current upturn in the airline industry, Delta Airlines could be a great value play in this regard.

**Chevron (NYSE:CVX):** Having hit an intraday high of 130.50 today with a current P/E of 12.69, the stock still appears to be a bargain at the 52-week high. In addition, investors looking for dividend income would find it hard to go wrong with Chevron given its track record as a dividend aristocrat and a current yield of 3.40%. Given Asia's projected increase in LNG demand through to 2020, CVX appears to be in a better position than its competitors to capture such growth through its current investment in the Gorgon LNG Project.

**Eagle Bancorp (NASDAQ:EGBN):** While the company trades at a slightly higher P/E ratio of 18.16 compared to its peers (FFIC - 14.76, WASH - 15.99, SBSI - 12.96, CHCO - 13.47), the firm has amongst the best track records in terms of showing the sharpest percentage increase in earnings performance, with vibrant growth and an estimated 3-5 Year Earnings growth rate of 37.7% according to CNBC which is the highest of the five firms in question. While it may trade at a slight premium on a P/E basis, it still appears to be the best contender for an earnings play.

Ultimately, my study has focused on thirty firms across three industries, and more data would be needed to determine small cap vs. large cap returns as a whole. However, the out-performance of small-cap financial stocks certainly offers some food for thought. If their returns are inelastic, then this may mean that they are able to withstand a downward cycle in the banking sector while taking full advantage of good market performance. This, coupled with large-cap plays from the oil and airline sector, would have seen an investor do very well in the past and in my opinion, would do very well in the future.

**Disclosure: **The author is long WFC, CVX. The author wrote this article themselves, and it expresses their own opinions. The author is not receiving compensation for it (other than from Seeking Alpha). The author has no business relationship with any company whose stock is mentioned in this article.