Survivorship Bias and Indexes

Suppose we are looking at a long term data series for a published index like the S&P 500 or the Russell 2000. Do these indexes suffer from survivorship bias, and if so, conceptually how would we adjust for it?

Maybe? Usually, most benchmarks have minimum liquidity requirements and/or minimum price requirements, so stocks that aren’t trading (or have declared bankruptcy) are removed - so I guess there’s an upward bias if you’re comparing to a buy-and-hold strategy when you buy something and hold it all the way to zero.

I think for the Russell 2000 it would be a wash in the end because there’s also sort of a downward bias because it’s a small cap index. Any high-flying stocks would get moved up into the Russell 1000. As a stock moves up in the Russell 2000, its weight correspondingly increases and the contribution to the index performance increases as well, so if it’s doing well and adding a lot of incremental return and then gets moved into the Russell 1000 you’re going to see a downward bias once it leaves.

However, most benchmarks are rules-based so it should be pretty easy to tell when something’s going to be dropped.

The other thing to consider here is that the inclusion rules are likely pretty consistent with a lot of institutional portfolios (i.e., $5.00 minimum price, etc.) so as an institutional investor you’d probably have to sell out of a position around the same time as the benchmark…

I’m not really sure how to adjust for it other than including all securities that have always been a part of the benchmark…

If the indexes are investible, I don’t think there is survivorship bias, even if companies are dropped from the index when they die. This is simply because the changes in the index are announced and therefore the index is replicable.

The issue with survivor bias has to do with uninvestible indexes. If index performs at such and such a rate, but in fact it would be impossible to have an investment that tracks that index because you would not have known what is included in the index or not at the time of investment, then you have survivor bias or selection bias or backfill bias or one of them.

With very long term series, the very early sequence might have it. I think Shiller has S&P data that goes back to 1881 or something, and I don’t think the S&P 500 index really existed then. If they’re clever, maybe they can replicate the index with available information, but the early years might have some survivor bias in them.