Apr

12

"What kind of animal would you be if you were reincarnated?"

"Where would you live if you were the richest person in the world?"

"What would you do if you were the president?"

"What happens to compounded returns by excluding extrema, empirically and simulated?"

OK, that last one has a dollop of testosterone. However inspired by a friend, here is a revisit of prior study on effects of final sum compounded by simultaneously removing (as if by magic!) the paired top and bottom daily returns for SPY from 1993-present (includes dividends): "But wait; we can't get right to it. Let's first do a simulation!"

(Yes dear.)

Using SPY daily returns since 1993, calculated daily mean return and standard deviation. From this used random number engine to generate 10,000 daily returns with a normal distribution having the same mean and st dev. This series was then ranked, and compounded returns calculated after successively removing top and bottom return pairs. Here is the graph of final compounded return.

From this graph, one notes that removal of top and bottom returns initially boosts compounded result, but quickly the final value declines monotonically as the normal distribution tails are clipped. This suggests that were returns normally distributed, both tails contribute to final compounded return (since their symmetrical removal reduces final sum).

"But wait!"

This graph compares this result to the actual empirical SPY series, successively pruned of top and bottom day returns. 

"Oh that one's different!"

Here we see the same short initial boost in final cpd sum by removal of tips of tails, followed by a decline in total return as more of the tails are clipped. However unlike the simulation, further paired pruning of tails improves final compounded sum, and for many iterations this sum exceeds buy and hold. Evidently removing the non-normal/fat tails (but-yours is perfect, dear!) of the empirical distribution actually improves returns, whereas cutting tails from the normal hurts.

"So just by taking away the top and bottom returns, we would be even richer? Have you figured out how to do that?" 


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