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=================================================================
Volume 1, No. 15, July 15, 1996
Contents
The Efficient Market Hypothesis, Part IV: Is there any Structure
in the Sea of Noise?
Delta Hedging
The TFME Toy Portfolio: Week 2, July 8 to July 12, 1996
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The Efficient Market Hypothesis, Part IV: Is there any Structure
in the Sea of Noise?
Introduction and Review
Last week I discussed the work of two highly regarded
statisticians who on the basis of empirical studies concluded
that financial markets appear to be fair games, a conjecture that
was made in 1900 by Bachelier that was based on theoretical
reasoning. The conclusions of Working, Kendall and many others
who have followed them in doing empirical work on the EMH has
been most damming to individuals who claim that all one needs to
know is the history of past prices. Bernstein, among others,
refers to these individuals as "chartists" or "technicians." In
quoting a prominent technician, Bernstein says that "[t]here
credo is ... that stock prices, which record the history of where
transactions have actually taken place, are therefore 'sufficient
in themselves' to reveal everything the profit-seeking investors
needs to know [p. 99]."
Chartists or technicians were not the only individuals that were
upset with the nihilistic conclusions of the statisticians.
Many economists, predictably, refused to accept the possibility
that the "science" of economics was mere rhetoric. Kendall
anticipated this response from the economists. The following
quotation from Kendall indicates this; furthermore it summarizes
what he wrote, and in the passage that I have emphasized is an
important point that will we discussed in some detail in the
future.
The series looks like a "wandering" one, almost as if once a
week the Demon of Chance drew a random number from a
symmetrical population of fixed dispersion and added it to the
current price to determine the next week's price. And this, we
may recall, is not the behavior in some small backwater market.
The data derive from the Chicago wheat market over a period of
fifty years DURING WHICH AT LEAST TWO ATTEMPTS WERE MADE TO
CORNER WHEAT, AND ONE MIGHT HAVE EXPECTED THE WILDEST
IRREGULARITIES IN THE FIGURES. To the statistician there is
some pleasure in the thought that the symmetrical distribution
reared its graceful head undisturbed amid the uproar of the
Chicago wheat-pit. The economist, I suspect, or at any
rate the trade cyclist, will look for statistical snags before
he is convinced of the absence of systematic movements. And he
will be very right to do so [p. 87 in Cootner].
One particular individual who took a more optimistic view was
Harry Roberts of the University of Chicago. He thought "[i]t more
likely that economic analysis could give predictive insight into
stock-market behavior than that physical analysis could help with
a real roulette." (Roberts made this claim in 1959 when
economists were more highly regarded, and hence more confident in
their abilities than is now the case).
What is interesting is that Roberts clearly recognized that what
appears completely random might appear that way because of our
limited knowledge, rather than being an intrinsic property of the
exchange process.
This is fascinating given the fairly recent interest shown in
nonlinear mathematics, specifically what is known popularly as
"chaos theory." The interest in chaos theory is an example of how
a development in technology, in this case, cheap computer power,
can lead to further development in theoretical disciplines such
as mathematics. This has also resulted in many researchers in
fields not so pure as mathematics to apply chaos theory to their
own particular fields. The way this have stimulated researchers
can be illustrated by programming a computer (or hand calculator)
to grind out a sequence of numbers generated by various simple
nonlinear equations that exhibit chaotic behavior. For example
the so-called "Tent Map," is defined as
/ a[1 - P(t)] for P(t) >= .5
P(t+1) =
\ ap(t) for P(t) < .5
for certain values of a > 0 and 0 < P(0) < 1. This simple
equation will generate a sequence of numbers that looks very much
like a random walk. In fact many standard statistical tests for
randomness conclude that a sequence of numbers generated by the
tent map, and some other simple nonlinear equations, is random,
yet each number is determined exactly by the number preceding it
by the above formula. Furthermore if the exact initial value of
P(t), P(0) is known precisely, and if our calculation of
succeeding numbers is exact, (no computer round offs), then given
the initial P, the entire history of the P's can be determined.
Understandably this have lead economists, physicists, biologists,
and all sorts of other researchers to question whether the
phenomenon of particular interest to them that appears to be
random is instead a deterministic process that follows, if they
are lucky, a path described by a simple mathematical
relationship.
I mentioned last week how Doyne Farmer and the Eudaemonians, of
Thomas Bass's book, Eudaemonic Pie, claimed to have found
structure in the game of roulette, the outcomes of which to me
anyhow appears to be purely random. This "success" has led
Farmer, a physicist, and many economists to apply chaos theory in
an attempt to unravel the behavior of the financial markets.
However, given the complexity and "openness" of the exchange
process, the question is not whether the seeming randomness is
deterministic, but whether any of the variability is determined,
i.e., is the movement of prices subject to both purely random
forces, for example, the input of randomly arriving market
relevant news, and also to systematic elements, for example,
perhaps under certain conditions the market might overreact to
the randomly arriving information.
Micro and Macro Technical Analysis
I have recently concluded that many individuals who classify
themselves as technicians are concerned with many other variables
than price. Most are concerned with not only price but with
volume and open interest; and others are concerned with the
structure of the market in regard to large speculators,
commercial hedgers, and small speculators, or various other
subgroups of the markets participants.
With regard to these other variables it is useful to distinguish
whether they are macro or micro variables. A macro variable with
respect to the exchange process is one that is at the level of
the market. The significant ones of these are price, volume and
open interest. Therefore individuals who use either one or all of
these variables in their analysis can be considered to be
employing macro-technical analysis. (This, of course, includes
the traditional chartists referred to above).
I have on several occasions in TFME mentioned the reason for the
adoption of methodological individualism is that it is at the
level of the individual where decisions are made, fear is felt,
and greed in manifest. Therefore if there are any regularities
they are more likely to be observed at the level of the
individual. In fact the results of Working and Kendall cast doubt
on the existence of regularities at the level of the market --
it's all just random noise. On the other hand there could be
regularities at the level of the individual that under certain
conditions can have a predictable effects on market prices.
By incorporating micro variables into the analysis, where a micro
variable is one that is either at the level of the individual
trader, or a grouping of individuals based on their individual
characteristics, we can appeal to the "forces" that operate on
individuals, such as fear and greed. For example we might be
concerned with the group of individuals who are vulnerable to
news that is perceived to be inflationary. These would be
individuals with long positions in the bond futures market and at
the same time are using considerable leverage relative to their
capitalization. The analyst who attempts to analyze the market by
forming subgroups based on common underlying individual
characteristics, while not practicing pure micro analysis, can
for practical reasons be considered to be employing micro-
technical analysis. I will come back to this point below.
Also from the practical point of view, I consider individuals
engaged in marketing research to be engaged in what can be
considered micro technical analysis in that any businesses
operating in a voluntary exchange environment must constantly
seek out where the buyers and sellers are likely to be, and this
is what individuals in the futures markets are attempting to do
when they try to find support and resistance levels.
However, with few exceptions that I am aware of, most technical
analysis, at least formally, is done with market level data, such
as prices, volume and open interest. An outstanding example of
this are the simple rules that combine price action with changes
in volume. Specifically these analysts claim that if a price rise
in accompanied by an increase in volume then the price will
continue to rise, or that conversely if a price decline is
accompanied by a increase in volume then the price will continue
to decline (trend extension).
That this is not always the case is vividly illustrated by the
action on Wall Street on Black Tuesday of October, 1987. On that
day, as I recall, the Dow-Jones Industrial average decline by
over 500 points, the largest one day decline on record. At the
same time volume was over 600 million shares, possibly still a
record. Any individual who had decided on the basis of the
conjunction of a price decline and volume of such magnitude to go
short, unless they were quick to get out, would have been greatly
disappointed, as the market after initially going down on the
next day stabilized and pretty much went up after that. Of course
market technicians only claim the rules are based on the odds
being favorable, i.e., if it is based on science, it is not a
nomological law, only a probability law. However, when the price
change and volume increase was so dramatic (a best case scenario)
and it failed one has to question whether the odds were really
favorable.
The problem is that market level data can not distinguish between
buyers and sellers because of the simple fact that for every
buyer there is a seller. This means that market level analysis
can not determine why individuals are buying (selling), and this
makes a difference.
To illustrate why this is so consider once again the situation
where the long interest in bond futures is relatively vulnerable
with respect to the short interest. Then suppose that an
unexpected report on inflation is received by participants in the
market. Let this report indicate an inflation rate of 3.4% rather
than the expected inflation rate of 3.2%. Holders of bonds will
then want a additional .2% yield to compensate them for holding
bonds. This corresponds to a price reduction in the bond futures
price. For illustration purposes assume this corresponds to a
decline of 49/32 from the before news price of the bond futures.
In a world where individuals were not risk averse the price of
bond futures would efficiently move to a level of 49/32 below
what the before news price was, say 105-17, to 104 even. However,
if individuals are risk averse, and if a significant number of
the risk averse individuals have relatively large exposure to
risk in bond futures, i.e., our longs, then they could sell down
to a point considerably below 104, perhaps as low as 103-12.
It might appear that these distressed sellers are being
irrational in selling at a price below 104, but the 20/32 they
are willing to give up in order to reduce their risk exposure can
be considered a risk premium.
On the other hand if there were not a significant number of
vulnerable longs, it is unlikely that the price would decline
much below the 104 level. Furthermore, the case where the fleeing
longs reduced the price to 103-12 will likely result in the
market turning around and going back up to the 104 level. Of
course as time goes by new unexpected will affect the behavior of
the market participants and hence the overall market. Some of
this new news could also be bearish for the bond market and so
the individual who tried to profit from buying at the 103-12
level in expectation of a rise to the 104 level might be
disappointed, but, on the other hand, it could be bullish news.
The work of Bachelier, Working, and Kendall suggests the
probability of good or bad news is equally likely. This would
imply that buying in the vicinity of 103-12 would be not where
the odds are favorable, but where in dollar terms the game is
more than fair. I will have more to say about this in the future.
The above analysis was done in terms of groups rather than with
individuals. This is because, unfortunately, there are formidable
problems in doing market research at the individual level. This
is because the required data on individual characteristics is
just not available. Consequently we must find a middle ground
between analysis based on market level data and individual level
data. Looking at various groups of market participants is the
obvious compromise solution to the low information content of
market level data.
These groupings, however, cannot be arbitrary. They must be based
on common characteristics. It is important to attempt to do this
as only when a group has common individual characteristics, e.g.,
all short and highly leveraged, can appeal be made to the
"lawlike" response that the individuals will make in the event of
bad news, and then to reason that the groups common behavior will
have an effect on the market.
Since myself and other writers on futures markets consider the
characteristic of being relatively vulnerable a useful category,
the question arises as to who fits into this category? Small
speculators, hedgers, etc., or are these traditional categories
ambiguous because at times speculators hedge (spread), and
hedgers speculate, let alone the differences among all
participants in the futures markets with respect to their risk
exposure management skills. This suggests that all members who
participate in the futures markets, irregardless what they are
called for tax or textbook reasons, can at times be relatively
vulnerable and at other time relatively safe. This makes forming
groups based on individual characteristics far easier said than
done. The two groups -- vulnerable and less vulnerable, for
example, are likely to contain mixes of significantly different
individuals from day to day, if not from hour to hour. Therefore
without privileged information that could possibly reveal such
things as the distribution of risk exposure in the market, one
must make do with making "informed" inferences, perhaps guided by
a combination of theoretical understanding and market experience.
Understanding the role of fear and greed in the markets is an
example of how theoretical understanding might be useful. In the
TFME I have several time suggested that fear and greed are
constants of human nature and that fear and greed always have and
always will have a major role in financial markets.
Risk aversion and profit maximization are the economists
formalization of these notions of fear and greed. Profit
maximization is discussed in undergraduate economics, but risk
aversion must wait until uncertainty is introduced into the study
of economics. This is often not done until the student takes
advanced classes in economics; however, the example of Bernoulli
and the St. Petersburg game indicated a long history of interest
by individuals in studying the implications of uncertainty on
economic behavior.
The ideas of risk preference and risk premiums, however, can be
understood without advanced training in economics. It is not even
necessary to use the St. Petersburg game to illustrate the idea.
A simple coin flip game does just as well. Specifically go to
your favorite bar and find out how many individuals will take a
bet where you require them to pay $500 to play and where they
have a 50% chance of winning either 0 or $1000. The mathematical
expectation of this game is $500. If an individual is willing to
forego $500 for the chance of winning, with equal probability,
either 0 or $1000, they are risk neutral. On the other hand if an
individual refused to play unless their entry fee was reduced to
something significantly less than $500, say $350, then they are
risk averse.
Except perhaps except for the very drunk most individuals offered
the bet would refuse it unless given an entry fee less than the
mathematical expectation of the game. The difference between the
mathematical expectation and the amount they are willing to pay
is the risk premium. In the above example this would be $500, the
expected gain, minus the $350 they pay to play the game, to give
a risk premium of $150. I will have must more to say about risk
premiums in the future, but for now let me just say that one of
the reasons that wealth tends to flow from the vulnerable to the
less vulnerable is because the more vulnerable, in general, pay
higher risk premiums, and they pay them to the less vulnerable.
Finally to conclude this weeks discussion of material relevant to
the EMH the introduction of risk aversion and risk premiums can
under certain conditions result in the exchange not being a fair
game in the mathematical expectation sense.
=================================================================
Delta Hedging
The main risk exposure management techniques I am employing for
the TFME Toy portfolio are adequate capitalization,
diversification, and options. Additionally stop-loss orders will
be used on a selective basis.
The portfolio at this time consists of 11 different modules
corresponding to 11 different markets. Each module consists of
various combinations of futures and option positions. At this
time I have all short options positions. Furthermore I like these
to be well in the money options. When that is the case they act
somewhat like futures positions (the more in the money they are
the more like a futures they become) with the added feature that
they offer the possibility of capturing some return from what is
called the time decay of the options premium. There is a cost to
this in that short options do not offer as much protection as do
long options, but the buying of long options, which I do not rule
out, requires the payment of time decay premium, that can be
substantial.
However, at this time I do not wish to discuss option theory.
There are zillions of books out there that do a good job of
explaining the basics of options theory that interested readers
can refer to. In this article I only what to discuss a certain
property of options, the delta, and how it relates to hedging in
the TFME Toy portfolio.
In standard option theory the formula for an option is a function
of 5 variables: (1) the price of the underlying instrument; (2)
the short-term interest rate; (3) the time to maturity; (4) the
strike price; and (5) the volatility of the underlying
instrument.
The derivative of the formula with respect to the price of the
underlying instrument is called the delta. The delta is also a
function of the same 5 variables. This means that when one of
these other variable changes, not only does the theoretical value
of the option change but the delta also changes. This can be a
problem in using options to hedge with as the change in the delta
of an option can significantly affect its hedging ability. In the
TFME portfolio this problem is compensated in part by using
diversification and adequate capitalization. Nonetheless the
delta of a option must be constantly monitored to judge the
effectiveness of the hedging ability of the option.
One can compute all kinds of first, second, and crossed partial
derivatives of the standard Black-Scholes option formula. Some of
these are important and others are mere curiosities. The second
derivative of the option or the first derivative of the delta
with respect to the price of the underlying instrument gives an
idea as to how the value of delta changes with a change in the
price of the underlying instrument. For a call option this
derivative tells us that as an option gets closer to or further
into the money its delta increases. Conversely as the price of
the underling instrument become less in the money or further away
from the money its delta decreases.
Deltas for call options are either expressed as a number between
0 and 1 or sometime by a number between 0 and 100 percent. A
short option position can be considered to have a delta equal to
the delta of the call multiplied by -1 to indicate it is a short
position. For put options just the opposite is the case, with the
delta of a put being between -1 and 0, and one in a short
position being between 0 and 1. Finally the delta of a future
position is either +1 for a long position or -1 for a short
position. Forming a simple linear combination of the deltas for
the constituents of a module gives the delta of the module.
The module delta indicates, roughly, the number of futures
positions long, when it is positive, or short when it is
negative. A module delta less than 1/3 in magnitude I consider a
mildly bullish (+) or mildly bearish (-) position for the module.
A module delta between 1/3 and 2/3 is similarly either moderately
bullish or bearish. Furthermore one between 2/3 and 1 is either
bullish or bearish. One whose magnitude is greater than 1 is
excessive and needs careful watching, possibly even taking
immediate action to reduce the exposure. However, these values
are relative to the overall size of the portfolio. If the initial
capitalization of the TFME portfolio was 1 million dollars rather
than 100,000, then the acceptable module delta would also be
increased by a factor of 10. Also, I might add the effectiveness
of the diversification is a consideration. For example since it
is usual for foreign currencies to move in parallel against the
US dollar, a negative module delta for D-Marks combined with a
positive module for Yen is treated differently than if they both
had the same sign.
===============================================================
The TFME Toy Portfolio: Week 2, July 8 to July 12, 1996
It was a crazy week. Added to the craziness was a mistake I made
with respect to an order that turned out to be very costly. I put
in an order to buy when I wanted to sell Sep Coffee. So be it,
there are all kinds of mistakes that one can make in the futures
markets, rather than just getting the direction wrong, but they
all have the same thing in common -- you must pay for them.
At the beginning of the week to portfolio was as follows:
Prior to the markets opening the TFME portfolio was as follows,
where the indicates the settlement prices from the previous
Friday:
106.13 Short 2 Sep US Bonds
1.6 Short 4 Sep Bonds 110 puts
delta=-.81
module delta=1.24
6571 Long 2 Sep D-Mark
136 Short 2 Aug D-Mark 6450 Calls
delta=.8
module delta=.4
9124 Short 2 Sep Yen
290 Short 2 Aug Yen 9400 Puts
delta=-.87
module delta=0.26
727 Short 2 (10000 bu) Nov Beans
68 Short 4 (20000 bu) Nov Beans 775 Puts
delta=.65
module delta=.6
6890 Long 2 Oct Cattle
380 Short 4 Oct Cattle 6600 Calls
delta=.71
module delta=-0.84
8780 Short 3 Sep Copper
1115 Short 4 Sep Copper 9400 Puts
delta=.58
module delta=-0.68
385.1 Long 4 Oct Gold
15.5 Short 4 Oct Gold 370 Calls
delta=.89
module delta= 0.44
2038 Long 2 Sep Crude Oil
200 Short 2 Sep Crude Oil 1850 Calls
delta= .86
module delta= 0.28
2794 Long 2 Sep Natural Gas
344 Short 2 Sep Nat Gas 2500 call
delta=.79
module delta=0.42
116.50 Long 2 Sep Coffee
6.95 Short 4 Sep Coffee 115 Calls
delta=.56
module delta=-.24
7284 Long 3 Dec Cotton
378 Short 4 Dec Cotton 7200 Calls
Delta=.55
module delta=.8
The bond module looked a bit overexposed. Some of the other
positions I decided to modify. The following trades were made:
Monday
Sold 1 Sep Natural Gas at 2.8265 close out trade 1 comm
Sold 1 Dec Cotton at 7335 close out trade 1 comm
Sold 1 Sep US Bond at 106-20 opening trade
Gross change in equity +2405
Tuesday
Bought 1 Sep Natural Gas at 2.790 opening trade
Bought 1 Sep Coffee at 116 opening trade
Gross change in equity +1076.25
Wednesday
Sold 1 Oct Gold at 386.50 close out trade 1 comm
Sold 1 Sep Crude Oil at 2080 close out trade 1 comm
Sold 1 Sep US Bond at 107-14 opening trade
Gross change in equity +1681.25
Thursday
Sold 1 Sep D-Mark at 6590 close out trade 1 comm
Sold 1 (5000 bu) Nov Beans at 770 opening trade
Bought 1 Sep Copper at 8870 close out trade 1 comm
Bought 1 Sep Coffee at 115.90 opening trade. Mistake, I
wanted to sell.
Gross change in equity -2125
Friday No trades. i tried to sell 2 Sep Coffee at 116.2, but was
unable.
Gross change in equity -4857.50
P/L
Equity Balance at end of week 1 Gross +10422.50 +422.50
3 rt commissions at 75 each Net +10197.50 +197.50
Equity Balance at end of week 2 Gross + 98602 -1397.50
6 rt commissions at 75 each (9 total) Net + 97927 -2073.00
The week started well but ended poorly. My mistake in order
placement as of now cost 1481.25 plus commission.
---------
The beginning of week 3 has the portfolio looking as follows:
108.11 Short 4 Sep US Bonds
2.28 Short 4 Sep Bonds 110 puts
delta=-.66
module delta=-1.36
6589 Long 1 Sep D-Mark
147 Short 2 Aug D-Mark 6450 Calls
delta=.86
module delta=-0.72
9105 Short 2 Sep Yen
306 Short 2 Aug Yen 9400 Puts
delta=-.88
module delta= -.24
809 Short 3 Nov Beans
32 Short 4 Nov Beans 775 Puts
delta=.65
module delta=-1.6
6962.5 Long 2 Oct Cattle
422.5 Short 4 Oct Cattle 6600 Calls
delta=.77
module delta=-1.08
8840 Short 2 Sep Copper
870 Short 4 Sep Copper 9400 Puts
delta=.63
module delta=.52
387 Long 3 Oct Gold
17.3 Short 4 Oct Gold 370 Calls
delta=.91
module delta=-0.64
2120 Long 1 Sep Crude Oil
276 Short 2 Sep Crude Oil 1850 Calls
delta= .92
module delta=-0.84
2.773 Long 2 Sep Natural Gas
3.19 Short 2 Sep Nat Gas 2500 call
delta=.79
module delta=.42
111.95 Long 4 Sep Coffee
3.66 Short 4 Sep Coffee 115 Calls
delta= .43
module delta=2.28
7418 Long 2 Dec Cotton
460 Short 4 Dec Cotton 7200 Calls
delta=.61
module delta=-0.44
The serious problem is with the coffee. This is way to much
exposure. I will sell 1 on the open and another one at around
112. The beans are also a problem. Much depends on the weekend
weather. The bonds require watching, but I doubt they will reach
110, the point where the puts are at the money.
=================================================================
Logon, learn, enjoy. Knowledge is too important to be left to the
professors, or any other special interest group.