# Solving the Puzzle of S&P 500 Equal Weighted Index Outperformance

Posted on: January 9, 2014

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 cap-weighted fund and RSP is an equally-weighted 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 Fama-French 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.

x = RSP

 Coefficients Standard Error T-Stat 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 T-Stat 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 t-stats 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"

Can you show the risk adjusted return for RSP vs SPY? (For those of us who are somewhat math-challenged.)

Jerry, for risk adjusted return, you look at alpha. I was somewhat surprised to see the RSP has no alpha and SPY has a negative alpha but not statistically significant. In other words, adjusted for Fama French factor risks, the return is essentially zero.

Put in other way, all returns are accounted for by Fama French risk factors.. Eugene Fama didnt get his Nobel Prize for nothing.

Michael, I saw the alpha values. As I understand it, alpha compares your return to your index on a risk-adjusted 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 risk-adjusted 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

Specifically, SPY’s beta1 is 0.998. This show the S&P 500 has 99.8% of the total market risk, so the old practice of using it as a proxy for market is quite valid.

On the other hand, if you regress RSP over SPY，you will likely not be able to account for all the outperformance of RSP since the other two risk factors are not considered, you will end up with a huge alpha.

You may end up concluding the passively managed RSP has skill. Or that rebalancing accounts for most of the outperformance. (Note that RSP requires rebalancing and SPY does not.)

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?

Chris,

The turnover of RSP is about 20% which is higher than SPY, but still not too bad compared to many active funds. The transaction impact of higher turnover is already in the data, but the capital gain impact is not. I suppose that will whip out whatever alpha you have. The bottom line is that you probably won’t get much (after tax) alpha from RSP, but you do get more risk premiums since RSP is exposed to more risks than SPY.

### Author

Michael Zhuang is principal of MZ Capital, a fee-only independent advisory firm based in Washington, DC.