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The Chairman
Victor Niederhoffer

3/28/2005
Victor Niederhoffer on Foraging

Optimal foraging theory studies the efforts and strategies of species to gain food relative to the costs of obtaining it. The key variables are the energy gained by the activity versus the chances of survival and subsequent ability to reproduce, the size of the animal, the activities of other animals, and the danger of being killed.

The key principles used to analyze are the laws of diminishing returns from using a resource, the related decreasing returns to additional search, and the equating of the marginal value of additional time spent.

The field is applied to all sorts of predator behavior ranging from the time spent hunting by the lion, to the selection of trees by the beaver, the time spent copulating by the dungfly. But so far, never to investments, a gap which must be filled.

One notes the startling fact that over the last 10 days, the cumulative move from the close the previous day to the open in the S&P futures has been 10 points , but the cumulative move from the current open to the current close has been - 50 points. Apparently the bears are hunting much more actively from open to close than overnight -- an ideal application for optimal search theory.

Some good books I have used to study this field are:

Jim Sogi comments:

Brings to mind nocturnal and day time creatures and their cycles. Pigs, rats and cockroaches only come out at night; Birds and mongoose only during the day. Who are the night traders/holders and the daytime traders? Who is more bullish? Is it time zones, or holding/folding, or something else that causes the phenomenon noted by the Chair?

Bruno comments:

Things have changed to some extent, because of online trading and VWAP-type programs. In the past, the little fish showed up at the open. That's when the sharks ate them. The close was when the whales hunting plankton scattered the sharks.

An Interesting Foraging Pattern

 

3/30/2005
Foraging Time

Trader X writes: "you still breakin out your cane you clueless one idea moron?"

Like day follows night, whenever the hate mail becomes extraordinarily virulent, the prediction is that the carnivores will not enjoy waiting at the water hole at the usual time in the imminent future.

A wag comments: "Is that Trader X, or X Trader?"

3/30/2005
Ask the Chair

Q: I enjoyed your comparison to what is happening in the markets to foraging. I am wondering, how we can use that analogy to help us predict what will happen in the markets?

The Chair's Response: I am trying to figure out the same thing. Eventually the prey doesn't go to the same waterhole at the same time. They use game theory in modern social foraging theory.

3/31/2005
Foraging Related to Time of Day, by Victor Niederhoffer

"Night is of paramount importance -- i.e., the animal needs to build up energy reserves and therefore it pays to choose a higher rate of foraging even if this results in a slightly higher probability of starvation whilst foraging." "Behavioral Ecology: An Evolutionary Approach," by J. Krebs and N. Davies, Chapter 4.

There have been several remarkable series of major declines in the S&P during the afternoon this year, most recently starting with the move from 1192 to 1170 after the Fed announcement on March 22, and continuing through the four subsequent trading days, covering a continuous decline of some 45 points. From Jan. 19 to Jan. 25, a series of five consecutive declines covering 28 points transpired. For eight consecutive days from Dec. 30 to Jan. 10, the S&P futures fell from 1 p.m. to close for a total decline of 33 points. These moves seem unusual, non-random and of practical importance. How do we explain them?

The classic model involves the foraging behavior of starlings as they search for worms in a patch environment. How far should they travel? Not only are there diminishing returns because they find the good spots quickly, but as they load up with worms their efficiency decreases because the worms weigh them down. At the beginning of their search the starlings are likely to find big worms, so they strike and capture often. They donít search widely; rather, they sit and wait. But near the end of their search they are finding worse pickings, and they reduce the frequency of their captures and are much more likely to move to another patch and search widely.

This is an example of applying the equal marginal value of energy gained theorem to predict behavior. Modern methods rely upon stochastic dynamic programming and stochastic game theory but as far as I can tell, they do not yield better predictions or explanations than the classical models. where the two key strategies that a predator can follow are #1 (sit and wait ) or #2 (search widely).

"This dichotomy has substantial value. Among snakes, for example racers and cobras forage widely when compared to boas, pythons and vipers. Among hawks, Cooper's hawks and goshawks often hunt by ambush using a sit and wait strategy whereas most falcons more widely forage. Web building spiders and sessile filter feeders such as barnacles typically forage by sitting and waiting, exerting considerable time building their webs rather than moving in search of prey." (from "Evolutionary Behavior " by Eric Pianka)

The dynamics of predator hunting by bears apparently makes a sit-and-wait strategy more profitable. There are abundant bulls who must get out at the end of the day, including day traders and over margined hopeful longs. A little bit of predatory behavior against them can lead to big returns during the last hour. Also, the danger of having an enemy predator attack you is least near the end of day as it takes them time to find you out and gather their resources. Such activity by the enemies apparently has been coming in the overnight session in Europe.

Furthermore, the chance of reproductive success for the funds is greatly increased if they can show good marks on their positions as of the end of a quarter. Thus, near the end of the day, the bear predators can gain the maximum amount of energy, their prey is the fattest, weakest, and most numerous and the reproductive value is maximized. These are the ideal correlates for a sit and wait strategy in real life. Furthermore , we can add that during the end of the quarter, and especially when these predators are having a bad period, where their ability to reproduce, i.e. gain additional funds might be close to zero unless a heroic move occurs, the tendency to this behavior might be expected to be at a maximum. This would also explain a day like March 30 where the move in the last hour was way up as a consequence of the stronger energy and thus greater difficulty of capture of the bull adversaries.

The one caveat to this comes from the field of game theory. Prey learn not to be eaten by staying in the same patch too conspicuously.

Steve Ellison comments:

In dry conditions, predators can succeed by hiding near locations with water. The fact that these locations are likely to contain taller vegetation than drier locations helps conceal the sit-and-wait predators. However clever the target animals may be in varying their movements, sooner or later they have to get water.

Kim Zussman responds:

Having collected and kept snakes, it is interesting to observe how different species are specialized as to hunting and the related suitability as pets. Arboreal boas of central America sit quietly in trees, awaiting the errant bird or rodent fooled by random camouflage. Subsequently boas have slow metabolism, eat rarely, and are slow and docile thus making good pets (i.e, rarely bite). California Red Racer coachwhip snakes are true hunters. Nervous, fast, aggressive, they travel quickly and don't even bother to constrict (they are not constrictors) or envenomate (they are non-poisonous) their prey. They simply strike and swallow. Racers make horrible pets -- they bite and flail when held and more often than not are quickly released to the joy of both parties.

Each species is well adapted to its niche, with millennia invested in the best fit. When ecology shifts, however, the most specialized become the most vulnerable.

Southern California's unusually heavy rain this year has noticeably changed the flora of local hills. One notes many plant species now flourishing which in prior years grew poorly. Toad tadpoles wiggling in numerous ponds and puddles. The deer evidently satisfied with ample wild grass and currently boycotting our roses. The "trickle-down" of heavy rain undoubtedly has changed the energy struggle between species.

Evolution should drive species to flourish best in durable climate regimes. However specialization to narrow niches entails greater risk of inadaptablitiy to atypical (but possible) climates. Specialization maximizes probability of great success assuming climatic continuity but generalization trades the chance of large success against minimizing probability of extinction.

 

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