May

10

One check on whether declines are faster than advances is to compare the size of extremal moves over equal times. SPY c-c (93-p) daily returns were ranked top to bottom. The largest gain day was paired with the largest loss day, second largest to second largest, etc. Then took the difference between each ranked extremal gain and the absolute value of the correspondingly ranked loss, for the top 200 extremes. The effect is subtracting the decline tail from the gain tail:

G1-L1

G2-L2

G3-L3

…….

G200-L200

The attached chart plots these differences, beginning with the top ranked gain - loss (14.5%-9.9%).

At least for the 24hr time-frame, "which is bigger" is a complicated question. At the tip of the tails, extremal gains are much larger than losses. The difference rapidly declines, and goes in favor of losses at point 3. The advantage switches to gains at point 9, then oscillates above and below zero until point 29 - when gains again outsize losses all the way to point 81. From 81 on, losses are smaller than gains all the way to point 200 (which is 400 pair-differences; about 10% of the total series of 4350 days).

The contest may be different for shorter (and longer) time-frames, as seen in a certain 5 minutes yesterday. Having reformed from intra-day data this study will be left for others.


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