Why does an unweighted synthetic index have better returns than the S&P 500?
As part of a statistical study of stock returns I noticed that using unweighted windowed gains has a much larger return than the S&P 500. The data are all from Yahoo and standard data massaging techniques are used to remove bad data from the Yahoo data. As required, the results are essentially the same independent of the window length (from 1 to 400 trading days) except for the expected reduced volatility. The unweighted data is selected using the criteria that once a stock closes below $5 it is dropped going forward, and a 20 day exponential trailing moving average of dollar volume is above some discriminator (in this case $1e6 and $1e8). All of these data are computed using the Adjusted Close and the result for each point is the mean of all returns (e.g. on Day 1 you bought $1 of every stock and on Day 2 you sold every stock).
Depending on the discriminator and the date range there are between 20 and 3000 stocks in each window (here just the 1 day window is shown). The gain is then cumsum(log(a[2:length(a)]/a[1:(length(a)-1])) for a window of length 1 (as shown).
Obviously an index constructed this way is artificial but it in some ways represents are more accurate representation of the overall stock market as a holder of individual stocks approaches the market. I suspect many people who hold individual stocks (as I always have) keep their portfolios roughly balanced by dollar holdings not market cap.
I noticed some time back that over 30+ years in the market I appeared to have better returns than the S&P 500. Of course not nearly what these data show since 1970 (S&P 500 total return ca. 25x (7.1%/yr), index return 400x (13.6%/yr), both nominal not real).
Anyway what most impressed me with the unweighted index approach is how linear it is in log space. This does support an efficient market hypothesis view, the gains from rebalancing every (window length) days appear substantially more log linear than the S&P 500.
The questions are 1.) Is there an inherent bias in taking the windowed gains? 2.) If the result is mostly valid what does it say about market cap weighting?
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