Before I get into the details, GCAP=S&P 500 index (blue) and RUT=Russell 2000 index (small cap index, red). Also, the chart above is in log-scale so that the changes over time can be seen more easily.
Now, with that out of the way, we can start with the trivial (yet important) observations. The first thing is that the two generally follow each other in direction and, at least roughly, in magnitude. This makes sense because a crash is usually associated with an economic downturn, but both large and small companies recover eventually and in roughly similar time frames.*
The conventional wisdom is that small cap stocks generally generate greater returns at the cost of higher volatility, so one might expect that they fall further and recover faster, and you’d be at least partially correct. In order to get a sense of the recovery in the year or two after a crash, I calculated the rolling 1 and 2 year log returns and plotted the results.
Those two charts contain the answer you’re looking for. You can see that the rate of recovery is roughly the same after the 2008 crash and the dot-com crash.
I suppose I should also explain how to read the log return charts correctly. It is similar to the rolling percentage returns, but unlike percentage returns, log returns can be added together. So if the log return over period 1 is 0.5 and in period 2 it is -0.25 than the overall log return through both periods would be 0.5−0.25=0.25.
The formula for the n-day log return is 𝐿𝑛(𝑡)=ln(𝑆𝑡𝑆𝑡−𝑛) where 𝑆𝑡 denotes the price on day t. There are 251 trading days in a year.
When the log return crosses the black line at 0 after a crash it means that its value is equal to its value n-trading days ago. Keep in mind that these charts show rolling returns, not overall return.
All the technical details out of the way, I can’t say there’s much to see. The rates of recovery very similar. So the answer is that neither one recovers faster.
I also have two other charts for the curious, the daily log returns and the 5-year log returns. I’ll go ahead and post them just for context.
* Keeping in mind that there is selection bias in either index, but more so in RUT because small companies are more likely to fail and be replaced in the index more often. Hence, the companies in RUT after a crash are likely to be at least somewhat different than those in the index before. It shouldn’t matter too much for this discussion.