BACKGROUND & PERFORMANCE
Vanguard Small Cap ETF (Ticker: VB) is a market cap weighted fund that seeks to track the performance of the CRSP U.S. small cap index. Morningstar rates this fund with five stars; the highest the rating can go. It has a distribution yield of 1.38%. For the following analysis I will be using data from a specific time frame; March 2009 to September 2019. Below I summarize basic statistics of VB and the designated market fund SPY. VB’s return is slightly higher but has a moderately larger standard deviation. Both funds have similar Sharpe ratios but SPY’s remains slightly higher for this time period.
CAPM
After running a regression on the market minus the risk-free rate against VB’s performance we get the stats listed below. These statistics indicate a statistically significant relationship between the two variables due to a p-value less than 0.05 and a t-stat substantially greater than 0, however the alpha value is negative meaning the market itself would have offered a higher return for the specific level of risk. Economically speaking, it would make sense that that the market would perform better in the recent expansion better than a fund comprised of small stocks. Especially with the recent tax cuts that help larger corporations more than small companies with lower taxable income. This may be the reason for the negative alpha.
One-Factor CAPM:
Alpha - (0.3115)
P-Value - 0.04281
T-Stat - 32.67707
FAMA AND FRENCH
Expanding the regression to include the small stock effect and the value stock effect we get the result listed below. While we cannot say there is a statistically significant relationship between the three factors and VB due to a p-value greater than 0.05. However, we can say there is a suggestive but inconclusive chance that the relationship between the variables and VB is not due to chance. The mostly high positive t-stats do indicate the relationship in question is certainly a positive one. Most importantly however is that the alpha level is still below one which further discredits VB as a potential investment. In this regression you might expect the relationship between these three variables to be more significant. I believe we have not gotten that result for three reasons:
1. The returns of a fund that holds small stocks likely isn’t influenced greatly by what happens to value stock return fluctuations.
2. Adding an additional two variables reduces our degrees of freedom, essentially making our data subset smaller, which gives the power an outlier has on the results stronger.
3. A decades worth of monthly returns may seem like a lot but the regression would be more accurate by using the largest amount of data possible. For example, using daily return values for all factors and using the maximum time periods that overlap all of the used factors.
Three-Factor Model:
Alpha - (0.11503)
P-Value - 0.148594
T-Stat:
Mkt-RF: 50.37
SMB: 18.17
HML: 2.97
RECOMMENDATION
It is my recommendation to avoid investing in VB due to its alpha being negative in both the one-factor model and the three-factor model. While the p-value in the one-factor model does suggest its returns are explained well by the market, its negative alpha suggests just investing in the market itself would actually be a better investment than buying VB.