Solving the Puzzle of S&P 500 Equal Weighted Index Outperformance
Posted January 9, 2014
on:Since its inception on March 9, 2003, RSP has returned 193%. At the same time, SPY has only returned 97%. This is extremely puzzling as both RSP and SPY hold the same S&P 500 stocks.The only difference is that SPY is a capweighted fund and RSP is an equallyweighted one. This begs the question, is RSP’s outperformance normal; and more importantly, is it likely to continue?
To answer the question I asked my intern Nahae Kim to run a regression based on the Nobel Prize winning FamaFrench Three Factor Model.
R(x) – rf = alpha + beta1*(Rmkt – rf) + beta2*SML + beta3*HML
Where R(x) is the return of the selected fund, x being either RSP or SPY, alpha is the “skill” of the fund, beta1 is the market risk loading, beta2 is the small cap risk loading and beta3 is the value risk loading.
Here is what I got from the two regressions.
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x = RSP
Coefficients 
Standard Error 
TStat 

alpha 
0.00020216 
0.079515306 
0.00254 
beta1 
1.09513796 
0.021611333 
50.6742 
beta2 
0.14405660 
0.039147475 
3.67984 
beta3 
0.12852667 
0.035946467 
3.57550 
x = SPY
Coefficients 
Standard Error 
TStat 

alpha 
0.03390073 
0.022912377 
1.479581 
beta1 
0.99858269 
0.006227317 
160.3552 
beta2 
0.14290451 
0.011280365 
12.66842 
beta3 
0.01678824 
0.010357993 
1.620800 
Let’s analyze the data!

RSP’s beta1 is 1.095, that is higher than SPY’s 0.999. This means RSP is taking about 9.6% more market risk.

RSP’s beta2 is 0.144. This is much higher than SPY’s 0.14. This means RSP is taking small cap risk while SPY is avoiding any small cap risk.

RSP’s beta3 is 0.129. This is also much higher than SPY’s 0.0167. The tstats especially show a large difference of 3.57 vs 1.62. This means RSP has statistically significant value risk, while SPY has statistically insignificant value risk.

While RSP’s alpha is positive and SPY’s alpha is negative, they are both statistically insignificant.
In summary, the outperformance of RSP is due to it taking more risks. Now there is absolutely no puzzle to it! Going forward RSP will likely continue to outperform SPY simply because more risk means more reward. This is a simple truism of the capital market.
7 Responses to "Solving the Puzzle of S&P 500 Equal Weighted Index Outperformance"
Michael, I saw the alpha values. As I understand it, alpha compares your return to your index on a riskadjusted basis. However, I didn’t know what is the benchmark for RSP. If it is the S&P500, then I guess your reply makes sense.
What I meant to ask, however, is if there is a normalization that can be done to the % annual returns to account for the increased risk of RSP to directly compared it to SPY. (Is this the Sharpe ratio or the Modigliani riskadjusted performance [a.k.a. RAP a.k.a. M2]? Sorry, I am in over my head just framing the question.)
Jerry,
Not only that, you also get me confused because Fama French’s model is the most up to date normalization of comparing returns on risk adjusted basis.
In the past people used CAPM model that has only one regressor that is typically the S&P 500 itself.
Here there are three regressors corresponding to the three risk factors:
Rmkt – rt is the totaly market return above and over risk free rate
SML is the return of small cap above and over large cap stocks
HML is the return of high book value over low book value stocks
This was a fantastic article. I have recently come into some money and am considering investing it in either RSP or SPY. Can you answer one question for me? Based on the expense ratio and the fact that RSP I believe I saw has a higher turnover, what is the return after expenses of rsp vs. spy?
1  Jerry A.
January 9, 2014 at 10:11 pm
Can you show the risk adjusted return for RSP vs SPY? (For those of us who are somewhat mathchallenged.)