Professor Kenneth French

Last month I did a study to understand why equally weighted the S&P 500 index RSP has outperformed value weighted S&P 500 index SPY by almost 3% a year since its inception. My conclusion is that it’s mostly due to Fama French risk factor loading.

However, my research also found after removing the effect of risk factors, RSP has a slight alpha advantage over SPY. I conjecture this alpha advantage is due to the fact that RSP requires annual rebalancing and SPY does not. In other word, this could be the so-called “rebalance bonus.”

To test its robustness, I extended my study to six pair of Fama French “indices.”

Let me first explain how these indices are constructed. Fama and French split the universe of stocks into six equal parts. They first split all stocks in half by market capitalization, so we have large cap and small cap. They then split all stocks into 3 equal shares by book-to-mark ratio, so we have value, neutral and growth. They then let these two splits intersect to form six styles with equal number of stocks.

For each style, they then form two time series, one value weighted and one equally weighted. The value weighted “indices” do not need rebalance, while the equally weighted one do. These are the source data I use to test the value of rebalance.

Of course, to test the value of rebalancing, I must strip out return differentials caused by risk factor loading. The following are the alpha differentials (equally weighted alpha minus value weighted alpha.)

Table: Alpha differentials of Equal minus Value Weighted Index

The result is very interesting: equally weighted indices do not always have alpha advantages – in fact, for the two growth styles, the value weighted indices have advantages.

Could it be because growth stocks exhibit more momentum while value stocks exhibit more mean reversion? I don’t know, but evidences so far do not show periodic rebalancing reliably add value.

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