partial lunar eclipse in earth's penumbraThe penumbra is a partial shadow around an opaque body like the moon or market where only faint sight is possible. It was applied in a classic article by Taussig to the region around the intersection of supply and demand curves within which stocks fluctuate in a seemingly haphazard fashion. As anything Taussig wrote 100 years ago is infinitely superior to what passes for economic analysis of markets today, it is worth quoting in full on the concept of a penumbra. First described in stocks by Taussig in 1910 ish. For reference:

IS MARKET PRICE DETERMINATE? By Frank William Taussig. The Quarterly Journal of Economics 1921, vol XXXV

[ … ]

This does not mean that there are unlimited or quite unpredictable fluctuations. The underlying conditions of supply and demand are known for all the staples well enough to make possible a rough prognostication of the season's course of prices. It may be quite clear that potatoes will be higher than last year. But there will be a penumbra of uncertainty. Within this there will be ups and downs, many and perhaps wide fluctuations.

[ … ]

Now it is with regard to the fluctuations within the penumbra, the familiar ups and downs of the market, that we need to be cautious in stating any theory of market price. The daily or weekly or monthly "equilibrium" of supply and demand is a very ticklish matter. To return to the egg market, mentioned at the outset by way of illustration: demand and supply and price are not necessarily connected, for short periods, in the way commonly assumed. Suppose a well-known dealer cuts the price and puts eggs on the market at a lower figure; others follow his lead; the price will fall further; the lower price will quite possibly stimulate still others, not to make purchases, as is usually assumed, but on the contrary to make sales — until the edge of the penumbra is approached. Then indeed there will be a reaction, or at least a check. Eggs will not go down indefinitely. But within the penumbra there is no certainty about the effect of lowered price on supply or demand or on the further course of prices. Conceivably the course of events may be just the opposite of that just described. The well-known dealer who cuts his price may be confronted by another dealer equally well-known, who snaps his offers up and bids for more at the same figure. Then still others will follow his lead, country dealers will hold back, not force their supplies on the market, and eggs will go up until the other edge of the penumbra is approached. And so it is, I take it, in the wheat pit or at the cotton post. There is no telling what immediate response there will be to an offer of larger supply or to a decline in the day's or week's quotation. A heavy sale by a big operator and a lower price accepted by him may easily mean, not that more will be bought by others, but that buyers will be scared off and that price will fall still further. This is precisely what the big bear operator expects to bring about. Or the bear's maneuver may not succeed. Price may not fall further; it may rebound and rise.

To put the matter in more technical terms: the demand curve over "short periods" — which may be a matter of weeks or even months — is not necessarily inclined throughout in the same direction. It may be inclined positively.1 And similarly the supply curve, indicating what quantities are offered for sale at different prices, does not necessarily have that constant positive inclination which is usually assumed. In the course of the higgling of the market this in its turn may have a negative inclination.

The combats of bulls and bears, familiar phenomena of the market, are incomprehensible under the orthodox theory of market price. They can be understood only if we admit that within the penumbra there is no determined or determinable market price. A good observer has said that the successful speculator is not necessarily a man of wide statistical information or of much experience in the trade. But he must be a shrewd judge of human nature. As regards the fluctuations within the penumbra, there is much truth in the statement. The market may react in all sorts of ways to changes in offers and bids and going prices. The outcome depends on men's hopes and fears and guesses and momentary states of mind. The nervy man may make money by coolly watching his more sensitive fellows and playing on their frailties.

[ … ]

From a reference that I cited with approval in my 1964 thesis, and that Professor Zeckhauser has been looking for for 30 years, and kindly provided by Alston Mabry. The area beyond the penumbra is one that Taussig felt might have continued moves indicative of shifts in the demand curve and new equilibria.

I thought to test this starting with the pencil and paper at an elementary level. I considered the 10 best Nasdaq and 10 worst performing Nasdaq 100 stocks in the first quarter of a year. Next I looked at the subsequent performance of these two groups of 10 stocks in the subsequent 9 months. I repeated this process for each of the last four years. The results are interesting.

Year Best10 Worst10 Medn10 Comment

2006    11      6        3   sd = 40% non signif (ILMN = 50%)

2007    93     46       22   sd 200% FSLR up 500% 1 rnk both periods

2008   -28    -29      -38

2009    90    130       63   reversal of fortune


Year - Calendar Year

Best10 - Performance of best 10 stocks in next 9 months

Worst 10 - Performance of worst 10 stocks in next 9 months

Medn10 - Median performance of all stocks

The results indicate that in the bad year, the worst stocks did the best in the last three quarter, but in the good years, the best stocks in the first quarter continued to excel. The 10 best performing stocks this year are Baidu, Liberty, Wynn, Sears, Garmin, Illumina, Hologic, Ross Stores, NII Holdings, Mylan. The 10 worst performing stocks this year are nvidia, Linear Tech, Foster Wheeler , Google, Qualcomm, Expedia, Warner Chilcott, First Solar, FLIR , KLA Tencor . One would be interested in other first efforts to explore the penumbra concept of Professor Taussig.

Phil McDonnell performed his own study:

In 1921 Taussig argued that there exists a penumbra around the current price in a market. He based this on the argument that at any given time the supply in a market is relatively inelastic. There is only so much wheat and more cannot be grown until next year. There are only so many shares of stock and it would take a while for the company to issue more.

This suggests a simple strategy. One could keep an average of recent highs and lows and use that as a predicted high or low for the day. One would buy at the predicted low and exit at the close. One would sell at the high and exit at the close. The following study was done using SPY daily data. For this study the average was a 10.72 day with lag removed.


       Sell Hi     Buy Lo

avg   0.022%    0.040%

std    0.994%    1.255%

count 1290        1273 %

up     48.84%     51.61%

t-stat 0.79           1.13

Results are not significant.

Dr. McDonnell is the author of Optimal Portfolio Modeling, Wiley, 2008

Alston Mabry shares another Taussig work:

The Silver Situation in the United States F. W. Taussig 3rd ed, 1900

A discussion of the silver situation in the United States divides itself naturally into two parts. On the one hand, we have the purely economic aspects of the problem — the working of the silver legislation, its history, the results that have flowed from it in the past or may be expected in the future. On the other hand, we have the intricate and difficult questions of policy involved — the right and wrong of the legislation, the evils or benefits that have ensued and may be expected, the best course to be followed in view of all the emergencies of the situation; the treatment of the problem not only from the economic, but from the wider social and political point of view.


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