RESEARCH Returns on Small Cap Growth Stocks, or the Lack Thereof: What Risk Factor Exposures Can Tell Us The small cap growth space has been noted for its underperformance relative to other investment styles. Is there something inexplicable happening, or can this phenomenon be attributed to fundamental factor exposures? Abstract This paper examines the historical performance of small cap growth stocks through the lens of the Fama-French three-factor model and the use of quantitative measures, such as the Sharpe ratio, seeking to shed light on why this investment style has historically given investors so little to cheer about. Through multi-factor regression analysis, we determine that the majority of small cap growth underperformance comes from the growthiest of growth stocks in the index. We conclude with simulations that suggest that investors can enhance their US small cap growth risk-adjusted returns by employing strategies that seek to minimize or even eliminate exposure to the highest-growth quintile of the small cap growth universe. Background In the early 1990s, Eugene Fama and Kenneth French (1) analyzed the returns of all US equities over different independent time periods and identified three systematic sources of risk that explain over 90% of portfolio performance: 1 1. Mkt (Market): This represents the exposure to the equity market. It is similar to beta but differs because of the presence of two additional factors: 2. SmB (Size): Small (market capitalization) minus Big represents the exposure to smaller market capitalization relative to the market. The greater the SmB factor exposure, the more the company behaves like a smaller company. 3. HmL (Value): High (book to price) minus Low represents the value/growth characteristics of the stock. The higher the book to price ratio of the company, the more value oriented it is. The ideas that were statistically and theoretically represented by this three-factor model, however, were not new ones. Investors have applied the principles of value investing for decades. Value investing was introduced by Benjamin Graham in 1928, further refined with the assistance of David Dodd, and made broadly famous by the so-called Sage of Omaha, Warren Buffett. Investors had also reaped the benefits of investing in small companies that had great potential to grow. What Fama and French s three-factor model did was to quantify the risk-return relationship by attributing the performance that fund managers and individual investors produced to specific risk factors as opposed to their stock picking genius. As successful as this model has been in explaining stock and portfolio returns, it still is not 100% accurate. By definition, models are imperfect because they are only approximations of actual phenomena. In practice, when returns are dissected and attributed to Fama and French s three distinct factors, there is a component of the returns that can t be explained by the factors. In this paper, we will refer to this component as alpha 2. A quick look at historical data shows that premiums do exist for the three factors in the Fama-French model. First, there is a return premium for being invested in smaller companies; small companies are inherently riskier than larger, more established companies, and investors need to be compensated for that additional level of risk. Exhibit 1 shows the returns of small cap stocks versus large cap stocks by comparing the performance of the Fama-French Large Cap Index with that of the Fama-French Small Cap Index 3. 1 Common Risk Factors in the Returns on Stocks and Bonds. Fama, Eugene F. and French, Kenneth R. Chicago : Journal of Financial Economics, 1992, Vol. 33, pp. 3-56. 2 It is important to distinguish this definition of alpha from the other popular interpretations of the term: for example, alpha is commonly used to refer to the return over and above a benchmark that is not attributable to market performance and is instead chalked up to manager skill. By our definition, even an index can have an alpha; in this case it represents whatever portion of the index s return that cannot be accounted for by Fama and French s three factors. 3 The Fama-French domestic indexes are created using the CRSP (Center for Research in Security Prices) database.
Exhibit 1: Annualized Return and Annualized Standard Deviation Monthly Data: Jul. 1, 1926-Dec. 31, 2010 Ann. Return (%) Ann. Std. Dev. (%) Large Cap Stocks 9.67 18.48 Small Cap Stocks 11.93 26.59 The performance differential is stark, particularly when compounded over time. In addition to having greater return, small cap stocks also entail a higher level of risk (as measured by the annualized standard deviation). When we apply the Fama-French model to these indexes, however, we see that the extra return is a result of small caps having greater exposure to certain risk factors. Exhibit 2 shows the exposures of the two portfolios to each of the three factors: market, size and value. What we see is that on the basis of factor-adjusted returns, large cap stocks have actually done better given that they have a positive alpha of 0.02 compared to an alpha of -0.08 for small cap stocks. Exhibit 2: Fama-French Factor Exposures Monthly Data: Jul. 1, 1926-Dec. 31, 2010 Mkt SmB HmL Alpha Large Cap Stocks 0.99-0.07-0.01 0.02 Small Cap Stocks 1.06 0.91 0.30-0.08 Similarly, value stocks are expected to outperform their growth counterparts, which are perceived as less risky. Exhibit 3 compares the performance of the Fama-French Large Cap Value index with the performance of the Fama-French Large Cap Growth Index. Exhibit 3: Annualized Return and Annualized Standard Deviation Monthly Data: Jul. 1, 1926-Dec. 31, 2010 Ann. Return (%) Ann. Std. Dev. (%) Large Cap Growth Stocks 9.16 18.87 Large Cap Value Stocks 10.98 25.53 Once again, the results bear out this hypothesis, with value stocks having greater return and greater risk compared to growth stocks. The reason for the outperformance can again be attributed largely to the additional exposure that the Large Cap Value index has to the HmL (price) factor relative to the Large Cap Growth index, as can be seen in Exhibit 4. After adjusting for factor exposures, the Large Cap Growth index has better returns since it has a positive alpha (and one that is statistically significant) as compared to the negative alpha for the Value index. Exhibit 4: Fama-French Factor Exposures Monthly Data: Jul. 1, 1926-Dec. 31, 2010 Mkt SmB HmL Alpha Large Cap Growth 1.02-0.08-0.24 0.06 Large Cap Value 1.08 0.02 0.78-0.16 The general trend here is that the majority of the return difference can be explained by risk factor exposures with a small, and sometimes statistically insignificant, unexplained contribution called alpha. Previous research 4 has shown that because the Fama- French factors are constructed by equal-weighting the different groups of securities, the factor returns are overweight small and value companies. Since small cap and value stocks have outperformed large cap and growth stocks respectively, these factor returns are higher than what a market-weighted factor construction would have yielded. This results in a positive alpha bias for large cap and growth stocks/indices and a negative one for small cap and value stocks/indices. In other words, since these stocks/indices have a low (possibly negative) exposure to the size and/or value factor, the explainable part of their returns is underestimated relative to their alpha (the portion not explained by the factor exposures). Similarly, since small cap and value indices have a positive (usually high) exposure to the size and/or value factor, the explainable part of their return is overestimated and the unexplainable underperformance becomes negative alpha. This is why even passively managed benchmark indices tend to have positive or negative alphas even after adjusting for factor exposures, as seen in Exhibits 2 and 4. 4 Should Benchmark Indices Have Alpha? Revisiting Performance Evaluation. Cremers, Martijn, Pteaajisto, Antti and Zitzewitz, Eric. Atlanta : AFA 2010 Atlanta Meetings Paper; EFA 2009 Bergen Meetings Paper, January, 2010. 2 Gerstein Fisher
The Small Cap Growth Performance Anomaly Small cap growth stocks haven t had the greatest run as an asset class. Though one would expect the asset s negative value premium to be offset by its positive size premium, this segment of the market has not given investors much to be optimistic about historically, as can be seen in Exhibit 5. Exhibit 5: Annualized Return (%) Monthly Data: Jul. 1, 1926-Dec. 31, 2010 Size/Style Value Growth Large Cap 10.98 9.16 Small Cap 14.10 8.93 Interestingly, the majority of the underperformance can be explained by the growthiest of stocks within a growth index. This result would make sense from the Fama-French perspective the lower the value exposure, the lower the expected return and risk. To isolate the effects of the various factor exposures on the returns of these growthiest of small cap stocks, we divided the Russell 2000 Growth Index, a commonly used proxy for small cap growth stocks, into five quintiles using a measure of value. This measure of value was calculated by dividing the stock s book value as of the most recent fiscal year end by its market capitalization as of the day of calculation. The greater this ratio, the greater is the stock s value exposure. These quintiles were recreated each month, and each quintile s returns were calculated by market cap-weighting each stock that was present in that quintile. The end result was a stream of monthly historical returns for the five different quintiles with Quintile 1 being the basket of securities with the highest value exposure and Quintile 5 being the one with the highest growth exposure. Exhibit 6 below shows the growth of wealth of the five quintiles as well as of the Russell 2000 Growth index (the index from which the quintiles were created). As expected, the most value-oriented quintile, Q1, has the greatest growth of wealth and Q5, the most growthoriented portfolio, has the lowest growth of wealth. The index, which one would assume to find in the middle of the pile, slightly underperforms Q3. Exhibit 7 shows the annualized returns of the five quintiles and the Russell 2000 Growth index as well as their annualized standard deviations (as calculated from the monthly return streams). The pattern of returns is clear; there exists a substantial decrease in annualized returns as one goes from the most value-oriented quintile to the most growth-oriented quintile. However, the pattern in risk (as measured by standard deviation) is not as expected. One would expect the most value-oriented quintile to have the highest standard deviation and the most growthoriented quintile to have the lowest. Though there is a reduction in risk as we go from Q1 to Q2, it increases steadily thereafter as we move towards the growthier Exhibit 6: Growth of Wealth of $1 Monthly Data: Jan. 1, 1980-Dec. 31, 2010 70 Quintile 1 Quintile 2 60 Quintile 3 Quintile 4 Quintile 5 50 Index 40 30 20 10 0 1980 1985 1990 1995 2000 2005 2010 Source: Russell Investments, MSCI Barra, Gerstein Fisher Research Research 3
quintiles, with Q5 having the highest risk of any of the five quintiles. This goes against the predictions of the factor model, as less value means less risk, which should imply a reduction in volatility. The risk-reward relationship seems to break for the bottom three quintiles, especially Q5. A gauge commonly used to quantify this risk-return relationship is the Sharpe ratio. It is a reward-to-variability ratio that measures additional return per unit of risk. The higher the ratio, the greater is the return compensation for every unit of risk. Exhibit 7 also shows the Sharpe ratio for each of the five quintiles. Quintile 1 has the highest Sharpe ratio, implying it provides the most additional return for every unit of risk compared to the other quintiles. As we move towards the growthier quintiles, there is a steady decline in the Sharpe ratios, with Quintile 5 having the lowest Sharpe ratio. Exhibit 7: Annualized Returns, Standard Deviations, and Sharpe Ratios Monthly Data: Jan. 1, 1980-Dec. 31, 2010 Ann. Return (%) Std. Dev. (%) Sharpe Ratio Quintile 1 14.44 24.18 0.45 Quintile 2 11.40 19.63 0.39 Quintile 3 9.29 20.25 0.29 Quintile 4 6.77 22.84 0.17 Quintile 5 5.60 27.88 0.15 Index 8.30 23.47 0.23 Source: Russell Investments, MSCI Barra, Gerstein Fisher Research As with the previous example of large cap value vs. large cap growth, can the differences in risk and return be explained by the factor exposures of the different quintiles? Exhibit 8 shows the regression results for the five different quintiles. As expected, there is a clear decrease in the value (HmL) exposure as we go from Q1 to Q5 with Q1 having an HmL exposure of 0.45 and Q5 having an HmL exposure of -0.57. Another interesting trend is seen with the small cap (SmB) exposures. With the exception of going from Q1 to Q2, the size exposure increases as we move towards the growthier quintiles. According to the Fama-French three-factor model, this should imply greater returns. As was seen in Exhibit 7, however, this greater size exposure for the growthier quintiles isn t enough to compensate for the lower value exposures. The greater small cap exposure may nonetheless be the reason for the greater risk associated with the growthier quintiles, especially Q5, which has a small-cap exposure that is 25% greater than that of Quintile 4, the quintile with the next greatest small cap exposure. This trend of the growthier quintiles having greater small cap exposure seems unintuitive at first; one would expect the growthier stocks to have a higher price and hence a higher market capitalization. However, it is important to remember that a growth stock s price is high relative to its book value, not relative to the price of other stocks in the market. Exhibit 8: Fama-French Factor Exposures Monthly Data: Jan. 1, 1980-Dec. 31, 2010 Mkt SmB HmL Alpha Quintile 1 1.23 0.76 0.45-0.04 Quintile 2 1.06 0.63 0.32-0.18 Quintile 3 1.05 0.66 0.11-0.26 Quintile 4 1.07 0.79-0.22-0.32 Quintile 5 1.14 1.01-0.57-0.26 Russell 2000 Index 1.11 0.87-0.21-0.23 ken.french/data_library.html#histbenchmarks), Russell Investments, MSCI Barra, Center for Research in Security Exhibit 8 also shows the alphas associated with each of the quintiles as well as the index. In general, there is a decrease in the value of alpha as we move towards the growthier quintiles. This result is surprising considering that the method used for the construction of the Fama-French factors results in a negative alpha estimation for value indices and a positive alpha estimation for growth indices. Portfolio Implications Given these results, a possible alternative to using a plain vanilla small cap growth index would be to build a portfolio that removes the growthiest small cap stocks from such an index. To implement this while still maintaining stock diversification, the bottom quintile of stocks can be removed from the index and the remaining stocks can be market cap-weighted to create a modified small cap growth index. Exhibit 9 shows the annualized return, annualized standard deviation, and Sharpe ratio of this enhanced small cap growth index and the Russell 2000 Growth index, the index from which the enhanced index was created. 4 Gerstein Fisher
Exhibit 9: Annualized Returns, Standard Deviations, and Sharpe RatiosMonthly Data: Jan. 1, 1980-Dec. 31, 2010 Ann. Return (%) Std. Dev. (%) Sharpe Ratio Modified Index 10.00 20.53 0.32 Russell 2000 8.30 23.48 0.23 Growth Index Source: Russell Investments, MSCI Barra, Gerstein Fisher Research As can be seen in Exhibit 9, the enhanced index has a much higher annualized return as well as a lower standard deviation than the index. Additionally, the enhanced index also has a greater Sharpe Ratio, implying that it provides more return per unit of risk than the index. This is a direct consequence of removing stocks from Quintile 5 that have lower return and higher risk relative to the stocks from the rest of the quintiles. Conclusion There is no definitive explanation for why small cap growth stocks have underperformed other capitalization and style categories on a risk-reward basis. The higher risk of the growthiest of small cap growth stocks may be a direct consequence of their greater small cap exposure. However, the extra small cap exposure doesn t help improve the returns of these growthier quintiles.this strange, yet consistent, phenomenon offers investors the potential to enhance their risk-adjusted returns in this segment of the market. As demonstrated in this paper, this has been achieved by removing the most growth-oriented stocks from the small cap growth universe; not only has this resulted in greater returns, it has also lowered the realized risk of the custom small cap growth index. Exhibit 10: Fama-French Factor Exposures Monthly Data: Jan. 1, 1980-Dec. 31, 2010 Mkt SmB HmL Alpha Enhanced Portfolio 1.07 0.72 0.10-0.22 Russell 2000 Growth Index1.11 0.87-0.21-0.23 ken.french/data_library.html#histbenchmarks), Russell Investments, MSCI Barra, Center for Research in Security Exhibit 10 above shows the risk-adjusted returns and factor exposures for the modified index and the Russell 2000 Growth index. As expected, the modified index has a higher value exposure since it does not contain any of the growthiest stocks. The alpha values for the two are similar, as are the market exposures. The Russell 2000 Growth index has a higher small cap exposure since it contains the stocks from Quintile 5; as was seen in Exhibit 8, Quintile 5 has the greatest small cap exposure relative to the rest of the quintiles. Research 5
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