Noesis
The Journal of the Mega Society
 
Issue #178        September 2005
 

Contents

About the Mega Society

The Mega Society was founded by Dr. Ronald K. Hoeflin in 1982. The 606 Society (6 in 106), founded by Christopher Harding, was incorporated into the new society and those with IQ scores on the Langdon Adult Intelligence Test (LAIT) of 173 or more were also invited to join. (The LAIT qualifying score was subsequently raised to 175; official scoring of the LAIT terminated at the end of 1993, after the test was compromised). A number of different tests were accepted by 606 and during the first few years of Mega’s existence. Later, the LAIT and Dr. Hoeflin’s Mega Test became the sole official entrance tests, by vote of the membership. Later, Dr. Hoeflin's Titan Test was added. (The Mega was also compromised, so scores after 1994 are currently not accepted; the Mega and Titan cutoff is now 43—but either the LAIT cutoff or the cutoff on Dr. Hoeflin’s tests will need to be changed, as they are not equivalent.)

Mega publishes this irregularly-timed journal. The society also has a (low-traffic) members-only e-mail list. Mega members, please contact the Editor to be added to the list.

For more background on Mega, please refer to Darryl Miyaguchi’s “A Short (and Bloody) History of the High-IQ Societies,”

http://www.eskimo.com/~miyaguch/history.html

and the official Mega Society page,

http://www.megasociety.org/

 

 

 

 

 

 

Noesis, the journal of the Mega Society, #178, September 2005.

Noesis is the journal of the Mega Society, an organization whose members are selected by means of high-range intelligence tests. Jeff Ward, 13155 Wimberly Square #284, San Diego, CA 92128, is Administrator of the Mega Society. Inquiries regarding membership should be directed to him at the address above or:

ward-jeff@san.rr.com

 Opinions expressed in these pages are those of individuals, not of Noesis or the Mega Society.

Copyright © 2005 by the Mega Society. All rights reserved. Copyright for each individual contribution is retained by the author unless otherwise indicated.

Editorial

Kevin Langdon

 

 

Once again we have an interesting selection of material in this issue, but it’s always a bit of a struggle to pull it together and the need for submissions is ongoing. Please submit something for Noesis.

 

Our Constitutional Amendment has been ratified unanimously by those who bothered to vote (see page 13). Noesis is now officially an electronic-only publication and the Mega Society no longer charges dues. However, some of you have paid dues in advance and we’ll need to do something about these unfulfilled obligations of the society. Perhaps some of you have ideas about the best way to do this.

 

Ron Hoeflin has carried out his threat to resign from the Mega Society if we changed to online-only publication of Noesis. I regret this development and I hope that Ron will rejoin us.

 

The Mega Society Constitution calls for yearly election of officers, with a call for statements of candidacy in the September issue of Noesis. Ratification of the Constitutional amendment mentioned above has abolished the position of Publisher, leaving us with three officers: Administrator, Editor, and Internet Officer. If you are interested in running for one of these offices please send me your statement of candidacy.

 

Congratulations to member and former Editor Ron Yannone, who was recently inducted into the Association of Old Crows (AOC) Electronic Warfare (EW) Technology Hall of Fame.

 

Information on the background of the award can be found at the AOC website:

 

http://www.crows.org/EVENTS/2005/102305_CONV/05CONV_Preview.htm

 

The deadline for Noesis #179 is November 15.

 

 

 

 

 

 

Cover: Roman iron amulet, c. 3rd century A.D., believed to be Mithra/Mithras (photo Copyright © 2005 by Patrick Breen; all rights reserved).

 

Back Cover: An image generated with “Crossings,” a routine in Hallucinations™, by Kevin Langdon.

Option Theory: What I Knew and When I Knew It – Part 2

 

Edward O. Thorp

 

Member Ron Lee has obtained the author’s permission for us to reprint several of his columns from Wilmott magazine
under the title “A Mathematician on Wall  Street.” This is the second of those columns.

 

 

In November 1969 l and a partner, Jay Regan, launched what I believe was the world’s first market neutral hedge fund.  We called it Convertible Hedge Associates (CHA), and later changed its name to Princeton-Newport Partners (PNP).  It used warrants, OTC options and convertible bonds and preferreds, along with the underlying common stock, to construct delta neutral dynamically adjusted hedges.  (Listed options and publication of the Black-Scholes formula were still almost four years in the future).

            Since “the formula” was, to me, highly plausible but not proven, we used in addition a variety of techniques and screens, all of which the proposed mispriced security had to pass:

[1]             the formula (available for options and warrants, suitably modified for when and to what extent the economic value of short sale proceeds are actually available; generally not until expiration; in those days the brokers pocketed it.)

[2]             scatter diagrams of prices:  derivative versus stock or derivative versus derivative, over time (e.g. Figure 2.2 of Beat the Market).

[3]             cross-sectional scatter plots on standardized coordinate diagrams (at a fixed time, such as that day’s closing prices) to compare derivatives within a class (e.g. Figure 10.2 of Beat the Market).

 

1969-1972

            The first market neutral hedge fund, which consisted of a collection of derivatives hedges, each of which was (dynamically) approximately delta neutral, prospered.  See track records in (Thorp, 71, 75, 00).

 

Early 1973

            The CBOE announced it would soon begin trading exchange-listed options.  We at Convertible Hedge Associates were electrified (figuratively and literally) by the news.  This could facilitate a major expansion of our business.  I had an HP 9830A desktop computer which was easy to program in BASIC, was math user friendly, and drove a pen plotter with which we drew magnificent color coded graphs.

            I had the “integral formula” programmed and drawing option and warrant curves when, out of the blue I got a letter and an article from someone called Fisher Black.  He said “I am an admirer of your work” and explained that his approach was like Beat the Market but he and Scholes took another step:  they explored the (analytic) consequences of the no arbitrage principle as applied to our (dynamically adjusted) delta neutral hedge, noting that such a hedge should then return the (appropriate time period) riskless rate on net equity invested. 

            I sat down, programmed in his formula and drew option curves.  Shock!  The graphs disagreed with my graphs.  It couldn’t be.  But then I realized I was graphing the “short warrants or options, long stock” version of my formula.  This version assumed that the interest from the proceeds from the short sale of the warrant or option was captured by the broker, not the investor, as was the practice then for the warrants and over the counter options which I had been trading.  But the proceeds from shorting listed options (only calls on a limited number of large companies were initially available when the C.B.O.E. opened in 1973) would be credited to the investor on settlement date for the trade.  Thus one needed to pre-multiply by  to discount the expected terminal value of the warrant to expected present value.  Now the graphs were identical!

 

1973

            What I already had, in fact, was not just the Black-Scholes formula but a more general pair of formulas, with the Black-Scholes formula as the limiting case.  One of them incorporated a parameter to account for the loss to the broker of some or all, as the case might be, of the interest earned by the short sale proceeds (SSP interest) on the warrant (or option) short versus stock long hedge.  This family of curves started with the Black-Scholes curve (all SSP interest available) and moved continuously higher as the fraction of available SSP interest dropped, with the highest curve being my old warrant curve, corresponding to no SSP interest available.

            The other formula covered the warrant (or option) long versus stock short hedge.  This one parameter family started with the Black-Scholes curve and had successively lower curves as the economic value of the stock SSP interest available to the investor was reduced.

            The equations for highest and lowest curves are presented in Thorp (1973).  That was written a few weeks after I got the Black-Scholes paper and was immediate because I already knew these formulas.  In the original version of Thorp (1973) I had a section showing how I had found the Black-Scholes formula by setting and equal to in the formula for the expected value of the warrant or option (as discussed in the previous column).  But I had to delete this to fit my abstract into the spaced allowed.

The two formulae create a “band” around the Black-Scholes value, within which the delta neutral hedger cannot expect to achieve the riskless rate.  This band widens further when one adjusts the required pair of stock and option (or warrant) prices to cover (expected) transactions costs, present and future.

            As years passed, industry practice changed with competitive pressures and investors tended to gain some of the interest from their short sale proceeds, splitting this economic benefit with their broker-dealer.  Currently, in the U.S. some hedge funds and other institutional investors get an interest credit equal to Fed Funds (a proxy for the “riskless rate”) minus seventy five basis points (0.75% annualized) or better.  So the pair of one parameter families has remained relevant.  Yet, even today they have not, as far as I know, been discussed in the literature.  This is curious, given their practical value for so many users of the Black-Scholes formula.

            Planning ahead for the opening of the CBOE, I had prepared a catalog of standardized call option diagrams (see Beat the Market, chapter 6 for standardized variables), of (option price)/(exercise price) versus (stock price)/(exercise price).  For stocks which paid no dividends during the life of the call option, for each of a range of and (volatility) pairs there was one set of curves for various times until expiration.  These “universal” Black-Scholes curves covered all cases where our hedge was short CBOE listed calls (full cash credit at once for SSP) versus the underlying common stock long.  We knew how to use numerical methods to calculate correct values for the option price in cases where the stock paid dividends during the life of the option, but is was usually sufficient to use easy approximations which covered most cases and could be incorporated as a quick correction directly on the graphical plot. 

Remember, this was 1973 when computing power was comparatively limited, scarce and expensive.  With market prices continually changing and the number of options expanding rapidly, plus the need to monitor a substantial list of warrants and convertibles, graphical short cut methods were valuable in this era.  We simply plotted the latest recent (stock, option) price pairs on the appropriate  diagram and looked to see whether it was far enough above or below the appropriate curve to offer a profitable hedge.  Delta, the hedge ratio, corresponded to the slope of the tangent and could be immediately read off the picture.  We expanded the  catalog of diagrams as needed.

           

 

 

References

 

[1]             Thorp, Edward O. “Portfolio Choice and the Kelly Criterion.” Proceedings of the 1971 Business and Economics Section of the American Statistical Association, 1971, 215-224.  Reprinted in Stochastic Optimization Models in Finance, edited by W.T. Ziemba, S.L. Brumelle, and R.G. Vickson, Academic Press, 1975, 599-620.

[2]             _____. “Extensions of the Black-Scholes Option Model.”  Contributed Papers 39th Session of the International Statistical Institute, Vienna, Austria, August 1973, 1029-1036.

[3]             _____. “Options in Institutional Portfolios, Theory and Practice.”  Proceedings, Seminar on the Analysis of Security Prices, Volume 20, No. 1, May 15-16, 1975, 229-252.  Center for Research in Security Prices, Graduate School of Business, University of Chicago.

[4]             _____. “Common Stock Volatilities in Option Formulas.”  Proceedings, Seminar on the Analysis of Security Prices, Vol. 21, No. 1, May 13-14, 1976, 235-276.  Center for Research in Security Prices, Graduate School of Business, University of Chicago.

[5]             _____. “The Kelly Criterion in Blackjack Sports Betting and the Stock Market.”  Finding the Edge: Mathematical Analysis of Casino Games, eds. Olaf Vancura, Judy A. Cornelius and William R. Eadington, University of Nevada, Reno Bureau of Business & Economic Res., 2000.

[6]             Thorp, Edward O. and S.T. Kassouf. Beat the Market. New York: Random House, 1967.

 

Copyright © 2001 by Edward O. Thorp. All rights reserved.

Reprinted by permission of the author and Wilmott magazine.

 


My Hip Malfunction and What I Know About It

 May 1986

 

Kevin Langdon

 

 

     I  was  born in 1943,  with a condition later  diagnosed  as

bilateral hip dysplasia.   The condition was not discovered until

I was a year old.   During my early childhood,  I had a series of

operations intended to correct this condition,  including implan-

tation  of a pair of steel pins which are still in my hip joints,

but they did not produce fully satisfactory results.

 

     I  walked  with  a limp throughout my  childhood  and  early

adulthood.   On  my thirty-third birthday,  I had a fall out of a

tree  which caused enough trauma to my hips that I had to  appeal

to  passing  hikers to carry me  home  (which,  fortunately,  was

nearby).   I recovered from this incident, but I believe it weak-

ened my hips significantly.

 

     A year or two later, I was living in a walk-up apartment and

I reached the point one day of being unable to walk.   My  ortho-

pedic  physician,  Dr.  Sanford H.  Lazar,  who practices in  San

Francisco, prescribed complete bed rest for two weeks with super-

vised  therapeutic exercises for the hip joints,  in a  hot  pool,

every week day.   At the conclusion of the two weeks,  I was back

to the point at which I'd been before this incident.  I moved out

of the walk-up.

 

     By this time,  it had become clear that there was a slow but

steady deterioration of function in my hips.   A few years later,

in approximately 1982,  I began walking with a cane.  By February

or March 1986, my condition had deteriorated to the point where I

experienced a lot of pain and stiffness in my knees as well as in

my hips and I started using a walker.

 

     My condition has been diagnosed as osteoarthritis; recent X-

rays  show that nearly all of the cartilage is gone in  my  hips,

but my knees do not show any abnormality.   Dr.  Lazar has recom-

mended replacement of both hip joints.

 

     I  do not want to undergo such a radical and expensive  pro-

cedure  until I have exhausted all other avenues of  relief  from

this condition.   I am currently taking indocin and a variety  of

nutritional supplements, trying to keep the stress on my hips and

knees to a minimum, and arranging to be able to exercise in water

every  day.   I  am also investigating several other  approaches,

though more cautiously,  including Chinese and Tibetan  medicine,

homeopathy, etc.  I am sceptical, but I don't rule out any possi-

bility.  If I knew of a good faith healer, I'd try that.

 

     I  would appreciate any further information about this  con-

dition and other possible approaches to a solution.

 

The Rest of the Story (So Far) (2005)

 

Kevin Langdon

 

 

In May of 1986, my hip joints failed complete, within an hour of one another. There are two “cutouts” in the bottom of the pelvis where the femora join it, known as the acetabula. Additionally, there are smaller “cutouts” above the asatabula, known as the “false acetabula.” In each case my femur had ridden up into the false acetabulum. I couldn’t straighten up further than about 135 degrees and I was unable to walk until my mother, with whom I was living at the time, arranged to get me a walker.

 

In addition to the loss of function, I was in excruciating pain most of the time. When it was worst I took some pain medication but I avoided it most of the time because I didn’t want to dull my awareness.

 

Severe pain is debilitating and it consumed a great deal of my energy. I needed relief but because the state of the art of hip-replacement surgery was changing rapidly and the old, cemented type, which was what was available then, tended to fail within ten years and I was in my early forties it didn’t make sense to rush into it.