Jan

25

Here is the data for the cases when prior 20 week returns were greater than +10%:

Date          stdev   hi chg   hi nxt
11/22/82   0.037   0.239   0.177
08/04/80   0.019   0.208   0.105
02/09/87   0.015   0.204   0.093
03/23/98   0.024   0.181   -0.030
04/11/83   0.016   0.177   0.039
04/29/91   0.021   0.165   0.019
12/28/98   0.032   0.157   0.082
01/27/97   0.016   0.155   0.143
08/11/03   0.016   0.147   0.119
05/30/89   0.015   0.147   0.066
06/16/97   0.023   0.143   0.032
07/17/95   0.011   0.140   0.115
07/10/00   0.039   0.132   -0.129
05/05/86   0.023   0.128   -0.024
12/29/03   0.015   0.119   -0.013
12/04/95   0.009   0.115   0.058
04/04/88   0.033   0.113   -0.036
12/22/80   0.026   0.105   -0.032
12/16/85   0.014   0.102   0.128

Note that currently we are at the end of a 20 week gain of 10.9%, which had a weekly standard deviation of 0.009 (tied for low in 1995).

Alex Castaldo comments:

Overlapping returns are correlated, and therefore the normal statistical procedures that we use with independent variables are not applicable, and will give misleading results. Either we switch to non-overlapping periods or we have to make adjustments for overlap (which is tricky).

The example that Prof. Andrew Lo likes to give is the computation of 20-year returns from monthly CRSP data.

Here is an example of a flawed study: First we calculate the stock market return from January-1926 to December-1945 (20 years). It is a very nice positive number, about 8% I believe. Then we calculate February-1926 to January-1946, and so forth until January-1987 to December-2006. A total of 62 twenty year (overlapping) periods are examined. If only two of these periods have negative returns (hypothetically), then we conclude: the probability of losing money when you invest for 20 years is 2/62.

This result is completely bogus due to overlap. We have not really tested 62 independent periods, so the use of 62 in the denominator is not valid. The periods used are highly overlapping; for example January-1926 to December-1945 and February-1926 to January-1946 are almost the same. They differ only by the dropping of January-1926 and the addition of January-1946. The returns differ by a few percentage points at most. In some sense, the second period is not telling us much that we don't already know from the first; the reason we like independent variables is that each brings us the same amount of new information.

A more correct approach is to note that the period from January-1926 to the present contains only about 4.05 nonoverlapping twenty year periods. We could then look at how many of these are positive or negative. (Of course the strength of any conclusions drawn from four observations will not be very high).

Scott Brooks adds: 

This conversation reminds me of tracking deer when bowhunting. When I arrow a deer, it will usually expire in less than thirty seconds, almost always within five to ten seconds. However, in that ten seconds, it can run a long way and disappear into the brush.

Sometimes the blood trail is obvious, other times it's not.

When I'm on the trail of a non-obvious blood trail, I have to employ different methods of looking for the deer. To make a long story short, I slowly walk down what I think is the trail, taking one step and stopping. I then look around 360 degrees … searching very slowly, breaking my surroundings up into mental grids, and scanning those grids carefully.

Then, before I take another step, I squat down so that my line of sight is about three feet off the ground, and then I repeat the 360 degree scan, mental grids and all.

After that, I get down on my hands and knees and carefully scan the area as close the ground as I can, especially looking ahead in the area where I'm about to step (when I move forward on the trail) to make sure there isn't the slightest bit of sign that could lead me to the deer (that I would have otherwise destroyed with my boot if I took my next step forward).

I then step forward and repeat the process.

The point I'm trying to make is this: Isn't what Kim Zussman did just one way of looking at the "landscape" of the market? His calculations of non-overlapping time frames were the equivalent of looking at one grid of the "market landscape," and looking from an upright point of view.

The professor then suggested non-overlapping periods. In my mind's eye, I see that as squatting down and looking at the same market landscape, but from a different view … and from that view, we see the same landscape but in a whole different way.

Both methodologies would seem to have value. Just as in tracking a deer, I may see "what I'm missing" or the "key piece of data." For instance:

a slight hoof indention in the ground - extra volume,

a drop of blood - over selling on fear of some nebulous announcement or rumor (see George Zachar's post, Deception of Taxonomy Notation)

a bent branch - a large money manager is trying to build/unload a position in stealth mode … without alerting the market

a pool of blood where the deer laid down (meaning that you didn't get as good a shot as you thought and you pushed the deer out of it's bed by tracking it too soon … mark that spot, backtrack carefully out of the woods and don't come back for at least three hours) - A bad announcement caused a stock to be driven down. The bloodied stock found support, but then continued to move down (maybe it's time to wait for this buy … no bottom feeding today … come back tomorrow and take a look).

a bunch of crows and buzzards in the area - time to go in and see if you can at least salvage the antlers … and then let the scavengers pick the bones clean. Even though I didn't get the meat, the trophy antlers will look good on the wall - Too late for a profit, unless your a scavenger … however, maybe you can find some talent within that company (every company has some talent). Watch where they go and see if there is a VC or an IPO opportunity!

That's why looking at the market from different angles in a meticulous, orderly and objective manner is so important. What works for deer hunting also works for investing/trading/advising!


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