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Personal
Biography
I
was born in New
Delhi.
I have a Bachelor's degree in Computer Science and Engineering from the Indian
Institute of Technology, Delhi
(1991) and a Masters in Finance from Carnegie
Mellon University, Pittsburgh
(1997)). In between the two degrees I worked in Tokyo with Banque Indosuez,
Credit Suisse First Boston, Merrill Lynch and Deutsche Bank.
After
completing my masters degree, I went back to Deutsche
Bank, Tokyo as
a Vice
President in the Alternative Investment Strategies group.While
at Deutsche Bank, I rubbed shoulders with superstars such as Craig
Dibble, Richard Dunne,
Jim Ortiz, Jeff
Sams.
In
1999, I moved to New
York city
with Harborview Trading Associates, which is a market neutral equities
hedge fund. I worked with Tom Reynolds, who was one of the youngest specialists
in his younger days. In 2000, two important things happened - I married
Naina, and I joined Bdellium
Asset Management in a senior
role. In 2001, I moved to Singapore,
within the firm.
In
2004, I started trading for Victor Niederhoffer’s firm. I live and work
in Connecticut,
and it is a great privilege to be work for a legend like him. Six of his
former employees have gone on to achieve greatness, Monroe
Trout, Toby Crabel and Roy Niderhoffer among them.
My
main professional activity is using statistics to study the stock market.
My favourite strategies involve short term trading in the SP500
index futures.
Links
to home pages of some of my family
Victor
Niedehoffer's Books and Website.
Victor
Niederhoffer is one of the giants of our time, a figure who has excelled
in many unrelated spheres. He was the US
National Squash chamopin for 5 years and was also the World Champion. He
holds a Ph.D. from the University
of Chicago
and was a professor at Berkely. And he is one of the greatest
traders in the world. He is the author of the two best books on trading
ever written, The
Education of a Speculator and Practical
Speculation (with Laurel Kenner). This is a link to their website,
dailyspeculations.com
Trading
and the US
Stock Market
Earnings
Surprise and Estimate Revision.
Zacks
is the most commonly used source for earnings surprise information.
Chicago
Analytics have an earnings surprise model, which is a little expensive.
A newer more reasonably priced Earnings Surprise/ Analyst Revision service
is Starmine.com .
Mathematical
Finance
These
days all finance and economic analyses use Mathematics, so the term "Mathematical
Finance"
is
heavily over used.
The
use of quantitative techniques in finance has led to the creation of Computational
Finance or Mathematical Finance. Much of the efforts have focused on the
applications of Stochastic Calculus to areas of designing interest
rate models and pricing and hedging financial derivatives.
Robert Merton and Myron
Scholes are famous names in Computational Finance and were awarded
the Nobel Prize in Economics in 1997. (Kenneth
Arrow and Gerard
Debreau are other famous mathematicians who made important contributions
to mathematical finance and who were awarded the Nobel Prize in Economics)
There
are many good scientists tackling this field, but the one who
taught me the little mathematical finance I know is Dr.
Steve Shreve of CarnegieMellonUniversity.
His yellow book is the Bible of Stochastic Calculus. He, and my father,
are the two most thorough teachers I have had the privilege of studying
under. I have never encountered a mathematical problem which has escaped
solution at the hands of either of them. Two recently launched journals
are Journal of Computational Finance
and Mathematical
Finance.
Risk
Magazine is a popular magazine oriented towards the "practitioners".
It has good articles, but many people in the largest investment banks subscribe
to it in order to read the last page which describes who has changed jobs
from which firm to which other firm. As investment banks are always hiring
and firing, this page is never dull.
Here
are two more webpages of my former teachers at Carnegie Mellon that have
interesting and useful materials.
Fallaw
Sowell's Home Page
Sanjay
Srivastava's home page
I
am listing some links on Mathematical Finance thanks to my friend Hideki
Murakami, who works with Merrill Lynch Japan
and trades exotics options. In the mid 90's, when both Murakami san and
I were bachelors, we used to meet every Sunday in his office to study papers
in term structure modelling. I am very grateful to him for sharing his
knowledge and library with me.
Here
is a set of less well known, but very useful, links on Mathematical Finance
courtesy of Hideki Murakami
http://www.warwick.ac.uk/statsdept/Staff/JEK/
LCG
Roger's page
http://www.math.nyu.edu/research/carrp/papers/pdf/index.html
http://www.finasto.uni-bonn.de/papers/
http://www.rebonato.com/
http://www.scicom.uwaterloo.ca/~paforsyt/
http://www.science-finace.fr/publications.html
http://www.business.uts.edu.au/finance/qfr/respapers.html
http://www.stern.nyu.edu/~aradhakr/
http://www.stats.ox.ac.uk/~sen/
http://www.fisc-ny.com/Research/finance.htm
http://www.risklab.ch/Papers
http://www.math.uni-mannheim.de/~schroder/
http://www.sam.sdu.dk/~krm/krm_pub.htm
http://www.wystup.com/papers.html
http://www.wystup.com/colloquium/index.html
http://www.mathfinance.de/unilinks.html#banks
http://www.rotman.utoronto.ca/finance/papers/index.htm
Stochastic
calculus for finance (Oxford University)
lhttp://www.stats.ox.ac.uk/~etheridg/finmath/2yprobn.pdf
http://www.eur.nl/few/people/pelsser
rhttp://www.wias-berlin.de/priate/schoenma
http://www.jaschke-net.de/papers/
http://www.phy.cuhk.edu.hk/~cflo/finance.html
http://www.socs.waseda.ac.jp/or-finance/old.html
http://www.csie.ntu.edu.tw/~lyuu
http://www.mit.edu/people/jnt/publ.htmlhttp://img.hkkk.fi/efa99/papers/index2.html
http://www.ifi.uio.no/~skavhaug/Options/http://binky.enpc.fr/~bl/publications.html
http://www.contrib.andrew.cmu.edu/~vecer/
http://www.iro.umontreal.ca/~lecuyer/papers.html
http://www.resarch.ibm.com/people/b/berger/papers.html
http://www.mysunrise.ch/users//marc.henrard/publications/publi.eng.html
http://web.tiscali.it/damianohome/
http://www.mathematik.uni-ulm.de/~rossberg/index_neu.html
http://www.ieor.columbia.edu/~kou/
http://hammer.prohosting.com/~hrb/stu_index.shtml
http://www.cwi.nl/~jiri/http://www.rondvari.com/
http://cba.162.bus.utk.edu/
http://www.maths.strath.ac.uk/~aas96106/
http://www.xplore-stat.de/ebooks/ebooks.html
http://www.lu.unisi.ch/assistenti_eco/trojanif/homepage/
http://math.bu.edu/people/murad/
http://phobos.ge.infm.it/~ecph/Index.html
http://www.math.unipd.it/~vargiolu/ricerca.html
http://mayet.som.yale.edu/~amj23/papers.htm
http://www.whu-koblenz.de/banking/sgf.htm
http://l3www.cern.ch/homepages/susinnog/finance/Welcome.html
http://jpmorgan.com/businesses/deres/index.html
http://www.math.duke.edu/education/ccp/index.html
http://pluto.mscc.huji.ac.il/~mswiener/research/research.htm
http://www.tinbergen.nl/home.html
http://www.few.eur.nl/few/people/pelsser/publications.htm
http://www.ires.ucl.ac.be/csssp/home_pa_pers/anderson/courses299.html
http://www.act.ku.dk/~schmidli/#publi
http://www.econ.upf.es/~kohatsu/
http://www.inria.fr/recherche/equipes/mathfi.fr.html
http:/www.ismacentre.co.uk/
http://www.ntu.edu.sg/home/ayxyan/index.htm
Behavioral
Finance
Much
of finance assumes that investors will act "rationally" - but the way investors
act is not the way financial economists expect "rational investors" to
act. Behavioral Finance deals with the influence of human psychology on
the behavior of financial practitioners.
Two
pioneering economists, Daniel
Kahneman and the late Amos
Tversky put Behavioral Finance on a high pedestal. Before gaining fame
as financial economists, they worked in the Israeli airforce and were investigating
of what best motivated ace fighter pilots. From that work came prospect
theory. Their book "Judgement under Uncertainty: Heuristics and Biases"
is well known. Richard
Thaler is another well known figure in this area. His best known books
are Winner's
Curse , Quasi
Rational Economics; and Advances
in Behavioral Finance. I have included a Bibliography
on Behavioral Finance at the end of this section.
Folklore
has it that stock markets gyrate because of "fear and greed", it is modern
cliché. Behavioral Finance is not just about "Fear and Greed" ,
it is about Hope and Greed. or a good introduction, read
Hersh Shefrin's book- Beyond
Greed and Fear. In his book, Shefrin breaks the field of Behavioral
Finance into three broad themes.
1. Heuristic
Driven Bias. Finance
practitioners use rules of thumb or heuristics to process data. For example,
people use past performance as the best predictor for future performance
and often invest in the mutual funds with the best five year track records.
These rules are likely to be faulty and lead to poor decisions. Relying
on such heuristics is called Heuristic Bias. Some different types of heuristic
driven biases:
Representativeness.
This type of bias arises when people use stereotypes to help their decision
making. This bias is very evident in finance. First proposed by Kahneman
and Tversky in 1972, it is analysed in detail in a series of papers in
Judgement
Under Uncertainty: Heuristics and Biases edited by Daniel Kahneman,
Paul
Slovic and Amos Tversky. An example from the field of investments will
be illustrative. Werner
De Bondt and Richard Thaler found that stocks that have done extremely
poorly in the previous three years do better than the extreme best performers
in the same preceding three years. De Bondt also shows that long term earnings
forecasts made by security analysts are biased in the direction of recent
success - analysts over-react by being too optimistic about companies doing
well in the recent times and by being overly pessimistic about companies
that have disappointed recently.
The
same effect tends people to confuse the notion of "regression to the mean".
When a bull market has been running on for a long time, it is common to
hear financial gurus talking about next years returns being very
poor because "markets regress to the mean". Regression to the mean
does suggest that future returns might be closer to their historical average
than they have been recently, but it does not mean future returns will
tend to be lower than their historical average.
Gambler's
Fallacy or the "Law of Small Numbers"be
If 8 tosses of a fair coin all turn out to be heads, the probability that
the nest toss will be heads is still 0.50. (Provided the coin is fair.)
But many people have a notion that in coin tossings, there should be a
roughly even number of heads and tails; if there are heads in a row, then
a tail is overdue. Again, this is a case of representative bias. The law
of large numbers when applied to a small sample will produce such a bias.
Anchoring
and Over-confidence
Security analysts tend not to revise their estimates enough to reflect
new information. This is why performs companies that have positive earnings
surprise in one quarter tend to repeat the surprise in following
quarters.
Subjects in an experiment were asked to guess the weight of an air
plane; they were also asked to guess a range between which
they felt 90 percent confident that the weight of the air plane would
lie. Sounds simple - guess a very wide range and you would hope to
be right. Yet the high estimate of most people in this experiment is too
low. Even though nothing stops anyone from giving a very high number for
the high end - say a billion trillion tonnes - most people are too overconfident
and therefore their high guess is too low
In
David Dreman's book "Contrarian Investment Strategies", there is a section
on how the difficulty of making accurate predictions, not ust in finance
but in all walks of life. There are a number of highly interesting examples
of famous people making predictions that turned out to be way off the mark.
I will reproduce some of those examples.
In
August 1941, Captain William T.Pulleston, the former chief of U.S.
Naval Intelligence, stated, “The Hawaiian
Islands
are over-protected; the entire Japanese Fleet and Air Force could not seriously
threaten Oahu.” Said Secretary of the Navy Frank Knox on December
4, 1941,
“No matter what happens the U.S.
Navy is not going to be caught napping.” Three days later the officer
in charge of radar at Pearl
Harbor
was told by a subordinate that a radar signal indicated at least 50 planes,
possibly far more, were approaching Oahu
at almost 180 miles an hour. His reply, “Well don’t worry about it
… it’s nothing.”
John
Foster Dulles, the Secretary of State who was influential in shaping American
postwar foreign policy, said in 1941, “Only hysteria entertains the idea
that … Japan
contemplates war upon us.”
The London
Critic wrote in 1855, “Walt Whitman is as unacquainted with art as a hog
is with mathematics.” But U.S.
reviewers gave the Brits as good as they received. “I’m sorry Mr.Kipling,
but you just don’t know how to use the English language,” wrote the editor
of the San
Francisco
Examiner in 1889, informing Kipling that he should not send in further
articles. In rejecting the thriller The Day of the Jackal in April
1970, a publisher wrote author Frederick Forsyth, “ (Your) book has no
reader interest.” By 1983, uninterested readers had bought 8 million
copies. Another expert observed, “Gone With the Wind is going to be the
biggest flop in Hollywood
history. I’m glad it will be Clark Gable falling flat on his face
and not Gary Cooper.” The observer – Gary Cooper. Marilyn Monroe
was told early in her career, “You’d better learn secretarial work, or
else get married.” A Universal Studio executive dismissed two actors
at the same meeting, telling the first, “You have no talent,” and
the second, “You have a chip on your tooth, your Adam’s apple sticks out
too far, and you talk too slow.” The first actor was Burt Reynolds
and the second was Clint Eastwood, the movies’ two biggest box-office draws
in the 1970s.
The
manager of the Grand Ole Opera told one young singer, “You ain’t
going nowhere … son. You ought to go back to drivin’ a truck.”
The singer was Elvis Presley. “We don’t like their sound. Groups
of guitars are on their way out,” said a Decca Recording Company
executive in 1962 in turning down the Beatles. “The biggest no-talent
I ever worked with,” said a senior executive in firing Buddy Holly
from the Decca label in 1956.
Emile
Zola, one of the great French novelists of his day and a leading defender
of Impressionist artists, saidn in 1900 of Paul Cezanne, “Paul may have
had the genius of a great painter, but he never had the persistence to
become one.” Cezanne’s best works regularly fetch $10 million to
$20 million. Edouard Manet, one of the earliest Impressionists, said
to Claude Monet of Pierre-Auguste Renoir, “He has no talent at all, that
boy … Tell him to please give u painting.” Renoir is one of the acknowledged
masters of Impressionism, whose masterpieces have sold above $60 million.
A well-known American art critic said of Picasso in 1934: “(Picasso’s)
prestige is rapidly waning and the custodians of his fame and his pictures
are fighting a losing battle to elevate him to a position among the immortals.”
Picasso painted many of his important works in the next forty years.
A
parliamentary commission in Great Britain set up to investigate the value
of the incandescent lightbulb concluded in 1878 that “(Edison’s idea are)
good enough for our transatlantic friends … but unworthy of the attention
of practical or scientific men.”
Alexander
Graham Bell patented the telephone in 1876 and tried to sell it to Western
Union, but the company was not interested. Lord Kelvin, on eof the
preeminent British scientists of the nineteenth century said that “Radio
has no future.”
A
potential initial investor in the Ford Motor Company was told by his banker,
“The horse is here to stay, but the automobile is only a novelty – a fad.”
The investor bought $5,000 worth of Ford stock anyway and sold his shares
several years later for #12.5 million. The editor of the London Daily
Express, when told in 1922 that the inventor of television wanted to see
him, said, “For God’s sake go down to reception and get rid of the lunatic
who’s down there. He says he’s got a machine for seeing by wireless!
Watch him – he may have a razor on him.”
Newer
technology seems to have been greeted no better. Thomas J.Watson,
the founder of IBM, said in 1943, “I think there is a world market for
about five computers.” Ken Olson, the founder of Digital Equipment,
stated in 1977 just before the PC revolution began, “There is no reason
for any individual to have a computer in their home.”
2.
Frame Dependence When
Nobel Laureate Merton Miller was asked to describe in twenty five words
or less, his contributions to finance, he said - "If you transfer
a dollar from your left pocket to the right, you are no wealthier. I and
France (Modigliani) proved that rigorously."
The
manner in which a problem is stated or represented is called its frame.
Frame independence means that the manner in which a decision theoretic
problem is framed is irrelevant; traditional finance assumes framing is
transparent. Or, practitioners can see through all different ways cash
flows might be described. In reality some frames may be opaque.
Here
are the different ways Frame Dependence may be relevant. Here is a textbook
example which was created by Kevin McKean in an article on Kahneman and
Tversky in Discover magazine. It is reproduced in many books and articles,
one example being the book Why
Smart People Make Big Money Mistakes and How to Avoid Them by Gary
Belsky and Thomas Gillovich.
"Imagine
you are the commander in the army threatened by a superior force. Your
staff says your soldiers will be caught in an ambush in which six hundred
of them will die unless you lead them to safety by one of two available
routes. If you take route A, two hundred soldiers will be saved. If you
take route B, there is a one third chance that six hundred soldiers will
be saved and a two thirds chance that none will be saved. Which route should
you take?
Imagine
that you are once again a commander in the army, threatened by a superior
force. Once again, your staff tells you that if you take route A, four
hundred soldiers will die. If you take route B, there is a one third chance
that no soldiers will die and a two thirds chance that six hundred soldiers
will perish. Which route do you choose?"
Research
by Kahneman and Tversky showed that most people would choose route
A in the first scenario because you would save two hundred lives, but the
same people end up choosing route B in scenario B because there is a one
third chance no lives are lost. The scenarios have the same end result
in each option - but the two scenarios are framed differently. In one,
the emphasis on how many lives are saved and the respondents want to be
cautious and save as many lives as possible. In the second case, the emphasis
is on how many lives are lost and most people try to gamble or be adventurous
to avoid the certain death of four hundred.
Older investors specially retired people who might finance their living
from their investment portfolio often worry about spending their capital
too quickly, or outliving their wealth. They are afraid of having
too little self control and spending their money too quickly, and therefore
sometimes will not sell stocks but will happily
spend dividends. This is because stocks are framed as capital and dividends
are framed.
Loss
Aversion and Prospect Theory: Kahneman
and Tversky created a new field of study called Prospect Theory which a
description of the way people make decisions in the presence of uncertainty
and risk. If you are given a choice between (a) accepting a pure loss of
$75 and (b) a gamble where there is a 25% chance of losing nothing but
a 75% chance of losing $100, what would you choose? The expected loss -
$75 - is the same in each case, but most people choose (b). Most people
hate to lose, and under option (b) there is a chance of escaping loss altogether,
even though there is a bigger chance of losing a bigger amount. Kahneman
and Tversky term this as loss Aversion- they found a loss has about two
and a half times the impact of a gain of similar amount.
Most
people stubbornly hold on to loss making stocks in the hope of exiting
when they break even. Companies that have invested a large amount of money
in a project which has not made any money and has poor prospects, will
still continue to throw more money at it, because they also suffer from
the "get even" disease - in reality they are throwing good money after
bad. This is also termed as theSunk
Cost Fallacy.
Mental
Accounting. People
have a tendency to treat different cash flows differently depending on
the source of the cash flow. A lot of people would not gamble with "hard
earned money", but if they bet bet 5 dollars and win 10,000 thousand dollars
with it, they might be less averse to gambling with all 10,000 dollars.
Money is money, but many people would not mind betting or losing
money that was won this way. While traditional finance suggests people
should not distinguish between dollars in different pockets, in reality
people do make the distinction. Here is another illustration.
Scenario
A. Imagine you have purchased a ticket to a theatre. On reaching the theatre
you find that the ticket is lost and that it costs a hundred dollars to
buy another ticket. Would you buy another ticket or go home?
Scenario
B. You arrive at the theatre and queue up to buy the ticket when you realize
you have lost 100 dollars somewhere. Would you still buy the ticket or
go home? (assuming of course that your wealth is much more than 100 dollars
and that you have cash or credit cards readily available)
It
turns out that several people would go home in scenario A but the same
people would pull out another 100 dollars in scenario B. In reality the
outcomes are identical - you have lost 100 dollars and if you want to see
the theatre you need to pay another 100 dollars. But people often have
"mental accounts" - in this case a mental account for entertainment,
for which they may be willing to spend 100 but not 200 dollars.
Similarly,
one could add a third scenario to the two above- you own a hundred
shares of Microsoft which is down 100 dollars today, and will your answer
change now?
Tolerance
for Risk ( material to be typed)
Regret
Avoidance.
Regret is a negative emotion arising from taking a decision which turned
out to be not so good. People who sell a stock just before it sky rockets
often experience regret. Example.
Scenario
A. You own 1000 shares of microsoft and they tumble in price by 30%.
Scenario
B. You own 1000 shares of microsoft which you sell, and with the proceeds,
buy some shares of Intel, which tumble 30%.
In
which scenario are you more unhappy? Even though the net result is the
same (loss of 30%) more people would feel worse in scenario B, as they
ended up taking an active decision that lost them money - they feel responsible
for the loss in scenario B but less so in scenario A. Most people want
to avoid the pain of regret and also do not want to own up to the fact
that they are responsible for their own losses. Hence, they often avoid
taking decisions altogether which might cause regret.
Endowment
Effect and Status Quo Bias
"A
Wine loving economist purchased some nice Bordeaux wines years ago at low
prices. The wines have greatly appreciated in value, so that a bottle that
cost less than $10 when purchased would now fetch $200 at an auction. This
economist now drinks some of this wine occasionally but would neither be
willing to sell the wine at the auction price nor buy an additional bottle
at this price."
-
Excerpted from Chapter 6 of The Winner's Curse by Richard Thaler, page
63.
This pattern- the fact that people demand much more to give up an object
than they would be willing to pay to acquire it is called the endowment
effect or status quo bias.
Money Illusion
a Even though most people now now how to adjust for inflation when
comparing dollar amount across different time periods, most people still
find it natural to think in nominal rather than real money terms. This
is termed as Money Illusion
3.
Market Inefficiency. Traditional
finance assumes that markets are efficient, that except for brief periods
of time, prices of securities will reflect fundamental values, even if
the practitioners suffer from Heuristic Biases and Frame Dependence. Behavioral
Finance does not suffer from such unrealistic assumptions. In view of the
interesting nature of this subject, I will devote a separate section of
this website to this topic.
A Selected
Bibliography on Behavioral Finance.
1. Abarbanell,
Jeffrey & Victor Bernard 1992 "Tests of Analysis' Overreaction/Underreaction
to Earnings Information as an Explanation for Anomalous Stock Price Behavior."
Journal of Finance 47, no. 3: 1181-1208
2. Amir, Eli
& Yoav Ganzach 1998 "Overreaction and Underreaction in Analysts' Forecasts."
Journal of Economic Behavior & Organization 37: 333-347
3. Asquith, Paul
1983 "Merger Bids, Uncertainty, and Stockholder Returns." Journal of Financial
Economics 11: 51-83
4. Ball, Ray,
and S.P. Kothari 1989 "Non-Stationary Expected Returns: Implications
for Tests of Market Efficiency and Serial Correlation in Returns." Journal
of Financial Economics 25:51-74
5. Barber, Brad,
Reuven Lehavy, Maureen McNichols, and Brett Trueman 1998 "Can Investors
Profit from the Prophets? Consensus Analyst Recommendations and Stock
Returns." Working paper, University of California, Berkeley
6. Barber, Brad,
and Terrance Odean 1998a "Boys Will Be Boys: Gender, Over-confidence,
and Common Stock Investment." Working paper, University of California,
Davis
7. Barber, Brad,
and Terrance Odean 1998b "The Common Stock Investment Performance of Individual
Invesstors." Working paper, University of California, Davis
8. Barberis,
N.A. Shleifer, and R. Vishny 1997 "A Model of Investor Sentiment." Journal
of Financial Economics 49, no 3: 307-344
9. Basu, S 1983
"The Relationship Between Earnings Yield, Market Value, and Return for
NYSE Common Stocks: Further Evidence:" Journal of Financial Economics 12:
129-156
10. Benartzi,
Shlomo, and Richard Thaler 1995 "Myopic Loss Aversion and the Equity Premium
Puzzle." Quarterly Journal of Economics 110, no: 1:73-92
11. Benartzi,
Shlomo, and Richard Thaler 1998 "Illusionary Diversification and Its Implications
for the U.S and Chilean Retirement Systems." Working paper, University
of California, Los Angeles
12. Benartzi,
Shlomo, and Richard Thaler 1999 "Risk Aversion or Myopia? Choices
in Repeated Gambles and Retirement Investments." Mangement
Science, forthcoming
13. Bernard,
Victor 1993 "Stock Price Reactions to Earnings Announcements: A Summary
of Recent Anonalous Evidence and Possible Explanations. In Advances in
Behavioral Finance, edited by Richard H.Thaler, 303-340. New York:
Russell Sage Foundation.
14. Bernard,
Victor, and Jacob Thomas 1989 "Post-Earnings-Announcement Drift:
Delayed Price Response or Risk Premium?" Journal of Accounting Research
27:1-36
15. Bernard,
Victor and Jacob Thomas 1990 "Evidence That Stock Prices Do Not Fully Reflect
the Implications of Current Earnings for Future Earnings." Journal of Accounting
and Economics 13:305-340
16. Black, Fischer
1993 "Noise." In Advances in Behavioral Finance, edited by Richard H Thaler,
3-22. New York: Russell Sage Foundation
17. Black, Fischer,
and Myron Scholes 1973 "The Pricing of Options and Corporate Liabilities."
Journal of Political Economy 81 (May-June):637-659
18 Bodurtha,
James N Jr., Dong-Soon Kim, and Charles M.C.Lee 1995 "Closed End Country
Funds and U.S. Market Sentiment," Review of Financial Studies 8, no.3:879-918
19 Bowen, John
J. Jr, and Meir Statman 1997 "Performance Games." Financial Analysts Journal
23, no.2:8-15
20. Campbell,
John Y., Andrew W.Lo and A.Craig Mackinlay 1997 The Econometrics
of Financial Markets. Princeton, N.J.: Princeton University Press
21. Capmbell,
J.Y., and R.J.Shiller 1988 "Stock Prices, Earnings, and Expected Dividends."
Journal of Finance 43, no. 3:661-676
22. Canner, Niko,
N.Gregory Mankiw, and David N.Weil 1997 "An Asset Allocation Puzzle." American
Economic Review 87, no.1:181-191
23. Canina, Linda,
and Stephen Figlewski 1993 "The Informational Content of Implied Volatility."
Review of Financial Studies 6, no.3:659-681
24. Chopra, Navin,
Josef Lakonishok, and Jay Ritter 1993 "Measuring Abnormal Performance:
Do Stocks Overreact?" In Advances in Behavioral Finance, edited by Richard
H. Thaler, 265-302. New York: Russell Sage Foundation.
25. Chopra, Navin,
Charles M.C.Lee, Andrei Shleifer, and Richard H. Thaler. 1993 "Yes, Discounts
on Closed-End Funds Are a Sentiment Index." Journal of Finance 48, no.2:801-808;
and "Summing Up," 811-812
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Is the
Stock Market "Efficient"?
Whether
financial markets are efficient or not is a matter of religious debate
amongst academics and practitioners alike.
First
of all, what is Market Efficiency? Simply put, an efficient financial market
is one which security prices fully reflect all available information. If
markets are efficient, then security prices should not diverge much from
their fundamental value for significant periods of time, and secondly,
in the absence of any news or change in fundamentals, prices should be
stable. If the Efficient Market Hypothesis holds then stock prices
should follow a "random walk"
Market
Efficiency comes in three forms. The Weak
Form of Market Efficiency
states that it is impossible to earn superior risk adjusted returns in
the long run based in the knowledge of only past prices of securities.
The Semi-Strong
Form of Market Efficiency states
that it is impossible to earn superior risk-adjusted returns by using
any publicly available information. As soon information becomes public,
it is immediately reflected in the prices and therefore an investor cannot
hope
to earn supperior returns in the future by using his information.
The semi-strong form of market efficiency does not rule out the possibility
that an investor may may earn abnormal risk-adjusted profits by trading
on information that is not yet known to market particiapants. That is,
it does not rule out the possibility of earning risk-adjusted superior
returns by the use of insider information.
The Strong
Form of Market Efficiency
states that it is impossible to eanr risk adjusted superior profits even
by the use of insider information becaue this information quickly leaks
out and gets reflected in the prices.. Most supporters of the Efficent
Market Hypothesis (henceforth EMH)
have focused on proving the Weak and the Semi-Strong forms of the EMH.
The high priest of the EMH is Eugene
Fama at the University
of Chicago.
Chief amongst the hundreds of noted economists who uphold the EMH are Kenneth
French, Michael
Jensen, . The list of those arguing the other side has
equally distinguished names- Andrew
Lo, Richard Thaler,
Daniel Kahneman and Amos Tversky, Robert Schiller, John Campbell,
Richard Roll,Andrei Schleifer, Shefrin and Werner De Bondt, Robert Vishny,
Josef Lakonishok, Narasimhan
Jegadeesh and Robert Haugen.
Read
Burton Malkiels's A
Random Walk Down Wall Street, and then read Andrew
Lo and Archie C. Mackinlay's book "A
Non Random Walk Down Wall Street" to gain an insights into both sides
of the debate. Robert Haugen has three books, The
New Finance : The Case Against Efficient Markets, Beast
on Wall Street and The
Inefficient Stock Market: What Pays Off and Why. David
Dreman is a well known and successful "Contrarian" money manager whose
books argue against market efficiency.
The
entire section on Behavioral
Finance in this website has references relevant to market
efficiency/inefficiency debate.
Here
are some illustrations, examples and anamolies that weaken the case
of Market Efficiency
Calendar
Effects
Many
sources have identified specific times of the year when the stock market
appears to have an upside bias. "The Santa Claus Rally" around the Christmas
holidays, and the "January Effect" at the beginning of the year have received
much attention in the financial press.
Inclusion in Major Index: according to the EMH, inclusion in th s&P500
index should not be accompanied by significant price increases - however
5 to 10% jumps in Stock price following the announcement of inclusion in
the S&P 500 are common place.
Small
Firm effect
Investor Preference
for Dividends
Richard Thaler in a study co-authored with Michaely and Womack studied
the price action of stocks following a dividend cut or increase in the
period 1964 to 1988. In the year following the dividend cut, on average
a stock underperformed the stock market by 11% and by 15.3% in the 3 year
period. On the other hand for, stocks with the dividend increases, the
numbers were an outperformance of 7.5% and outperformance of 24.8% respectively.
The failure of markets to adjust quickly to information dents the EMH.
Post Earnings
Announcement Drift.
There have been several articles and papers describing the phenomenon that
the returns to holding companies which had a positive earnings surprise
tended to persist for the following three quarters. Stocks were
be grouped in deciles using their SUE (Standardized Unexpected Earnings,
or the Earnings Surprise for he current quarter divided by the standard
deviation of earnings surprise in the quarter.)
The
stocks in the decile with the highest SUE outperformed by 2% and
the ones in the lowest decile underperformed by 2.2%; over the next 60
days. For small and medium sized companies these effects were even more
pronounced. Again the market is too slow to react to news, good or bad.
Behavioral finance will explain this in terms of overconfidence and anchoring.
Momentum
in the intermediate Term and Overreaction in the Long Term
Barberis,
Schleifer and Vishny in a paper suggested that
Specualtive
Bubbles. The
fact that specualtive bubbles form once every generation if not more often,
that prices stay so much higher than their "fundamental value" for long
periods of time also seems to contradict the EMH. I am including a link
on specualtive bubbles; the internet and fibre optic stock bubbles having
burst, most of the stories about Tulip mania, the South Sea Bubble,
etc are to fresh in every one's mind. http://www.clarity.net/~jake/bubble.htm
Richard Roll's
Study on Orange
Juice futures.
Richard Roll examined the influence of weather-related
news on the price of orange juice futures prices. Since the production
of oranges in the US
is geographically cnocentrated and the patterns of demand and taste for
orange juice are stable, the weather-related news should account for most
of variation price of orange juice futures, if the EMH were to hold here.
But Roll found that weather explained a relatively small proportion of
this variation.
Closed
End Funds Puzzle.
In a closed-end fund, the number of shares is fixed after the initial offering.
The only way for investors to buy shares in the fund is to buy them from
existing shareholders. On the other hand, in an open-end fund the number
of shares is not fixed. Investors can purchase shares from the investment
company running the fund who can simply issue more shares as the demand
justifies. A puzzling fact of closed-end funds is that their price systematically
diverges from their fundamental value, or Net Asset Value (NAV). When the
value of the shares is higher than the NAV the shares are said to trade
at a premium; if the value of the shares is less than the NAV they are
said to trade at a discount. The average closed-end fund is initially priced
at a premium of 10%. Within 120 days of being brought out the average fund
trades at a discount of 10%. The magnitude of the discount is not stable
it keeps changing. When the closed-end fund is changed to open-end fund,
the price of its shares tends to rise and the discount tends to disappear.
No
part of this puzzle can be explained by traditional finance but using opaque
framing, heuristic driven biases and market inefficiency we can offer pretty
good explanations.
Fat Tailed
Distributions in Finance
What
distribution the returns of financial assets come from are of paramount
importance in option pricing, risk management, value at risk calculations
and portfolio management. Most financial models assume a Gaussian or normal
distribution of asset returns, but empirical studies show evidence for
lepto-kurtosis or fait tails in the distributions. This means that extreme
events are more likely to occur than would be suggested by a normal distribution.
Benoit
Mandelbrot
advocated the stable, or Pareto-Levy distributions for modelling financial
asset returns. Since then stochastic volatility and GARCH
models have been used to model asset price returns. The list
is far too exhaustive. Clive Granger, Nelson and Bollerslev are the most
well known researchers in the area. S-Plus (see under the section on software
for quantitative analysis) has GARCH toolbox which allows estimation/fitting
of several "flavours" of GARCH models to data.
For
general links to fat tailed distributions, a good web site is to visit
JP Nolan's home
page.
Currency
Crisis
I have been interested in the academic literature on models of speculative
attacks on currencies, contagion, and related areas. The first model was
developed by Paul Krugman,
who drew upon the work of Steve
Salant.Salant had used the Hotelling lemma (1931) to study speculative
attacks on the price of government controlled price of gold. Krugman realized
that a similar analysis could be applied to fixed exchange rates. Krugman's
model was simplified by Robert Flood and Peter Garber in 1984. Collectively,
their research came to be known as the First Generation models. First
generation models show how a fixed exchange rate policy combined with excessively
expansionary pre-crisis economic fundamentals can push the economy
into crisis, with speculators trying to benefit when the inconsistent policies
are dismantled.
The
newer, Second Generation models try and explain those attacks where the
economic fundamentals were not inconsistent with exchange rate policies.
Maurice Obstfeld
is an important researcher in this area. A good paper on contagion is by
Barry Eichengreen,
Andrew Rose andCharlesWyplosz,
Contagious
Currency
Crises. Carmen
Reinhart is another important researcher on Contagion and Early
Warning Indicators of Currency Crisis. The IMF
and NBER web sites are good places to
download papers by authors mentioned here.
Statistical
Learning & Pattern Recognition
Support Vector
Machines
"Support
Vector Machines are learning machines that can perform binary classification
and regression estimation tasks. They perform the structural risk minimization
principle. SV machines create a classifier with minimized VC dimension.
If the VC dimension is low, the expected probability of error is low as
well, which means good generalization.
Support
Vector Machines non linearly map their n-dimensional input space into a
high dimensional feature space. In this high dimensional feature space
a linear classifier is constructed. Two results make this approach successful:
The
generalization ability of this learning machine depends on the VC dimension
of the set of functions that the machine implements rather than on the
dimensionality of the space. A function that describes the data well and
belongs to a set with low VC dimension will generalize well regardless
of the dimensionality of the space.
Construction
of the classifier only needs to evaluate an inner product between two vectors
of the training data. An explicit mapping into the high dimensional feature
space is not necessary. In Hilbert space inner products have simple kernel
representations an therefore can be easily evaluated."
-Excerpted
from the website of the Computer
Learning Research Centre at Royal Holloway, University of London.
The famous Vladmir
Vapnik as well as Alexey
Chervonenkis of the VC Dimension fame are both Fellows at Royal Holloway
Support
Vector MAchines are the hot new area in statistical learning. They are
being applied very successfully for both classification and prediction.
In fact, they are more successful than Neural Networks in many applications.
Most
recent books on statistical learning have a chapter on Support Vector Machines,
but the most popular book in this area is
AN
INTRODUCTION TO SUPPORT VECTOR MACHINES by N. Cristianini and J. Shawe-Taylor.
Three more good books in this area are:
Advances
in Kernel Methods - Support Vector Machines , edited by B.
Schölkopf, C. Burges, and A. Smola, MIT Press, MA;
Advances
in Large Margin Classifiers , edited by A.
Smola, P. Bartlett, B. Schölkopf, and D. Schuurmans, MIT Press,
MA;
Learning with Kernels, by B.
Schölkopf and A. Smola, MIT Press, MA (in press);
Learning
and Soft Computing by Vojislav
Kecman, The MIT Press. There is accompanying Matlab
code available from the author's website.
There
are many good websites with links to SVM's and other kernel based learning
methods, so I will just list the links here.
Support
Vector Machines at the National University of Singapore (S.Sathiya
Keerthi)
Home
Page of O.L. Mangasarian
Olvi
Mangasarian and his student Glenn
Fung presented a 'proximal SVM' engine at the
latest
KDD which is only
6 lines of Matlab code:
I reproduce that snippet of Matlab code out of interest.
function
[w, gamma] = psvm(A,d,nu)
%
PSVM: linear and nonlinear classification
%
INPUT: A, d=diag(D), nu. OUTPUT: w, gamma
%
[w, gamma] = pvm(A,d,nu);
[m,n]=size(A);
e=ones(m,1);
H=[A
-e];
v=(d'*H)'
%v=H'*D*e;
r=(speye(n+1)/nu+H'*H)\v %
solve (I/nu+H'*H)r=v
w=r(1:n);gamma=r(n+1); %
getting w,gamma from r
SVM
Applications List
Gavin
Cawley's Matlab Toolbox for SVM
Steve
Gunn's Matlab
Toolbox for SVM's
Another
Matlab toolbox for SVM
Yet
another Matlab Toolbox for SVM (at
the Ohio State University Website)
Kernel-Machines.org
Cluster Analysis
One
of the best texts on Cluster Analysis is ClusterAnalysis by Everitt, Landau
and Leese. Another good one is Finding Groups in Data by Kaufmann
and Rousseuw. Both should be available on amazon.com. Everitt et al's Chapter
6 ( Finite Mixture densities as Models for Cluster Analysis) is very interesting.
Chapter 7 discusses density search clustering techniques, Fuzzy Clustering.
Fuzzy
Clustering and Overlapping Clusters are also discussed in these books.
S-plus has many clustering algorithms' implementations. The usual Partitionaing
as well as Agglomerative Clusterings are all available in S-Plus, and the
fuzzy clustering algorithms are also there. The popular k-means with
many types of linkage (single linkage, complete linkage, average distance,Centroid
linkage,
ward
Linkage is available in MATLAB as well. If you search the web, almost everything
is available as a MATLAB toolbox). The more recent and sophisticated techniques
for clustering like Self Organzing Maps or Kohonen maps are also have MATLAB
implementations (see below).
Self
Organizing Maps
"The
SOM is a new, effective software tool for the visualization of high-dimensional
data. It converts complex, nonlinear statistical relationships between
high-dimensional data items into simple geometric relationships on a low-dimensional
display. As it thereby compresses information while preserving the most
important topological and metric relationships of the primary data items
on the display, it may also be thought to produce some kind of abstractions.
These two aspects, visualization and abstraction, can be utilized in a
number of ways in complex tasks such as process analysis, machine perception,
control, and communication. "
-Excerpt
from the website of T. Kohonen ,
who is the leading figure in SOM's and pattern recognition.
The
best place to learn about Self Organizing Maps is the website of the Laboratory
of Computer and Information Science (CIS) at the HelsinkiUniversity
of Technology. The also have a Matlab
Toolbox for Self Organizing Maps.
Neural Networks
There
are so many books and
websites devoted to Neural Networks that not much mention is needed here.
I will therefore, merely list some Matlab toolboxes and other software
for Neural Networks.
Matlab
Toolbox for Neural Networks from Mathworks.
Netlab,
a feedforward neural networks package Matlab Toolbox. There is an accompanying
book, Netlab: Algorithms
for Pattern Recognition by Ian
Nabney.
NNSYSID,
a (Neural Optimization Development Engine library Matlab toolbox
for neural network based identification of nonlinear dynamic systems.
PR
Tools, a Matlab Toolbox for statistical Pattern Recognition.
An
RBF network toolbox in Matlab
NODElib,
(Neural Optimization Development Engine library) : a C++ library for neural
networks.
Neuralware
has a commercial product called NeuralWorks with an Excel interface.
Bayesian Networks
or Belief Networks or Graphical Models
Graphical
Models are an attempt to combine Graph Theory and Probability Theory in
tackling machine learning problems as well as the classical Multivariate
Statistics. Graphical models are graphs in which nodes represent random
variables, and the lack of arcs represent conditional independence assumptions.
Directed
graphical models (which cannot have directed cycles) are also called Bayesian
Networks or Belief Networks (BNs). Bayesian networks do not necessarily
imply a commitment to Bayesian methods; rather, they are so called because
they use Bayes' rule for inference.
Finite
mixture models, factor analysis, hidden Markov models and Kalman filters
are special cases of the general Graphical.
In
this section, my thrust is not to explain the uses and theory behind Belief
Nets, but rather, to list the Matlab toolboxes and some other
software products.
Bayes
Net Toolbox at Berkeley.
Hidden
Markov Model Toolbox in Matlab; yet another HMM
toolbox in Matlab
Visual
Basic BN Toolkit.
Carnegie
Mellon University's JavaBayes
The
BUGS (Bayesian inference Using Gibbs Sampling ) software
BayesBuilder
a tool for constructing and testing Bayesian networks. The tool is particularly
suited for the design of medical diagnostic systems and data mining.
A
list of Bayesian
Networks software with comparisons.
Independent
Components analysis and Blind Source Separation
"Independent
component analysis (ICA)
is a statistical and computational technique for revealing hidden factors
that underlie sets of random variables, measurements, or signals.
ICA
defines a generative model for the observed multivariate data, which is
typically given as a large database of samples. In the model, the data
variables are assumed to be linear or nonlinear mixtures of some unknown
latent variables, and the mixing system is also unknown. The latent variables
are assumed non-Gaussian and mutually independent, and they are called
the independent components of the observed data. These independent components,
also called sources or factors, can be found by ICA.
ICA
can be seen as an extension to principal component analysis and factor
analysis.
ICA is a much more powerful technique, however, capable of finding the
underlying factors or sources when these classic methods fail completely.
The
data analyzed by ICA
could originate from many different kinds of application fields, including
digital images and document databases, as well as economic indicators and
psychometric measurements. In many cases, the measurements are given as
a set of parallel signals or time series; the term blind source separation
is used to characterize this problem. Typical examples are mixtures of
simultaneous speech signals that have been picked up by several microphones,
brain waves recorded by multiple sensors, interfering radio signals arriving
at a mobile phone, or parallel time series obtained from some industrial
process."
From
the website of A.
Hyvärinen. who also has a book and tutorial
on ICA.
A good book on the subject is :
Independent
Component Analysis by A. Hyvärinen, J. Karhunen, E. Oja.
website
for ICA
is ICA central. Paris
Smaragdis has a good ICA
and Blind source Separation web site.
As
in other sections, I concentrate on listing Matlab Toolboxes in this area.
The first one is
FastICA,
from the CIS website of the HelsinkiUniversity
of Technology. The second
Matlab Toolbox on ICA is developed by Scott Makeig, who applies ICA
to electroencephalographic (EEG). Jean-Francois Cardoso also has
Matlab code for ICA.
Andrew
Back has also written some papers on the use of ICA
in finance.
Software
for Quantitative Analysis
For general purpose scientific programming, I find MATLAB
to be the most convenient platform. It enables an easy exchange of data
with Excel, is easy to program in and is reasonably fast. I have used Maple
and Mathematica, but find MATLAB better. There are toolboxes for specialized
areas and the optimization toolbox is quite comprehensive. Through out
the machine learning and pattern recognition sections of this website I
have given pointers to Matlab toolboxes. A very large list of tools is
available at Mathtools.Net, "the
technical computing portal for all your scientific and engineering needs."
For
Statistical work, S-Plus is easily
the best. Like many other good things, it was developed at Bell
Labs, by a team of scientists including John Chambers. It is
extremely object orientated and has a very large library of freely downloadable
code available from the academia. CarnegieMellonUniversity
has an an extensive archive of S Plus code called Statlib.
But
after S comes ... R! R
is `GNU S' - A language and environment for statistical computing and graphics.
R is similar to S. It provides a wide variety of statistical and
graphical techniques (linear and nonlinear modelling, statistical tests,
time series analysis, classification, clustering.)
S-Plus
is offered by a company formerly called Mathsoft but they changed their
name "Insightful". They also had the stock ticker MATH on the Nasdaq,
but they had it changed to IFUL. (I would not have given up a symbol like
MATH but Mathsoft had other Insights).
I
am not a major fan of Microsoft, but Excel has a very powerful Solver.
The "Solver" was developed not by Microsoft, (no surprise!) but by Front
Line Systems. Their website Solver.com,
lists several other addins for optimization problems.
For
data mining Salford Systems
have the best CART and MARS products.
Bioinformatics
My
interest in Data Mining and algorithms for Pattern Recognitions was what
made me to read up some articles on Computational Biology and
Bioinformatics. I am not formally trained in Biology and Genetics, so I
must emphasise that what excites me there is the application of string
based algorithms and statistics.
There
is now a XML for Genomics called GEML and Perl is very heavily employed
in Computational Biology.The following links are a good starter for
non-Biologists into the area of Bioinformatics.
Books:
Statistical
Methods in Bioinformatics: An Introduction by Gregory R. Grant, Warren
J. Ewens. This book also describes some of the main statistical applications
in the field, including BLAST, gene finding, and evolutionary inference.
Bioinformatics:
A Practical Guide to the Analysis of Genes and Proteins, by Andreas
D. Baxevanis (Editor), et al - Widely recognised as one of the best Bioinformatics
texts around.
This
book was one of the most useful ones in learning some of the background
Biology. The book has a large number of URL's at the end of each chapter.
I have listed approximately 200 of them below, chapter
wise.
Baxevanis book's URL's
Algorithms
on Strings, Trees, and Sequences: Computer Science and Computational
Biology
by Dan Gusfield. This book explains a wide range of computer methods
for string processing. It also contains extensive discussions on biological
problems that are cast as string problems, and on techniques to solve them.
The
next two are books on how Perl is a big help in accessing and manipulating
files used for storing genetic information.
Beginning
Perl for Bioinformatics by James D. Tisdall
Developing
Bioinformatics Computer Skills by Cynthia Gibas, Per Jambeck
Some
links:
The
BioPerl Home Page
BioJava
Home Page
XML
for Molecular Biology
Gene
Expression Markup Language
Data
Mining Tools from NCBI (National Center for Biotechnology Information)
BLAST
ECB,
European Bioinformatics Institute
Software
from NCGR (National Center for Genomic Resources)
Books on the Mathematics of Gambling
and Strategy
The
Theory of Gambling and Statistical Logic by Ricahrd A. Epstein is one
of the classics of gmabling and the mathematical analysis of blackjack,
coin-tossings, penny matching and other casino games. Beat
the Dealer by Edward O. Thorp is the all time classic on Blackjack
and needs no introduction. Thorp's former colleague William
T. Ziemba has some excellent books on race track betting- Betting
at the Racetrack which does pace/show and exotics; Beat
the Racetrack, and a more academic book Efficiency
of Racetrack Betting Markets. He also has a book on Lotto- Dr. Z's
6/49 Lotto Guidebook .For a wonderful reviews of different
betting strategies, see Racetrack
Betting : The Professor's Guide to Strategies by Peter Asch and Richard
E. Quandt (who also wrote the GQOPT).
The mathematicians who have written these books have interesting webpages,
and you are urged to visit their websites.
Some
of the newer books: Calculated
Bets by Steve Skiena,
which is about Jai-Alai betting programs;and Taking
Chances : Winning With Probability by John
Haigh which discusses betting on football pools, the importance of
different points in tennis, bridge, monopoly and the lottery.Though not
devoted to Gambling, there is a new delightful book called Mathematics
of Chance by Jiri Andel which has discussions on interesting problems
in probabilty though not always related to gambling- for example, the expected
numbers of typographical errors in a manuscript and the expected number
of stops an elevator makes before all passengers get off.
Fun
Vedanta and
Hindu Philosophy.
The
Vedas are the oldest books known to man. Their age is unknown. The core
of Hindu philosophy is in the "Upanishads", which occur at the end of the
Vedas and are called the Vedanta. ("Ant"= "end"; Veda+ant=Vedant.). There
are more than 1000 Upanishads but ten are considered the most important.
Adi
Shankararacharya and Ramanuja in the middles ages, and in modern times,
Sri Ramakrishna Paramhansa & his disciple Swami Vivekananda have been
the leading Hindu philosopher saints.
I
will enhance this section substantially. But for the moment, I have
pasted the links to some excellent websites on Hindu Philosophy,
books, and temples.
Vedanta
Press
Ramakrishna
Mission in Singapore
Vivekananda
Vedanta Society
A
Good Page on Hindu Philosophy
·Advaita
Vedanta
Templenet is
an Encyclopaedia containing information on over 2000 Hindu temples in India
with history, legend and pictures
·Hindu
Temples in SingaporeThere
are 18 Hindu temples in Singapore.
The oldest two were built around 1850. Most of them are in the South Indian
architectural style with colourful gopurams. The Chettiars, once a community
of traders, merchant bankers and money-lenders built the Sri
Thandayuthapani Temple around 1857. This temple is a 5 minute walk
from my apartment.
·Computer
Chess
·The International
Computer Chess Association
website has good information on chess programming resources. This Association
also publishes a quarterly Journal
and holds a triennial Computer Chess World Championship. One of the most
useful computer chess pages is Paul
Verhelst's page.
He has sections and links on chess board representations, details of tree
search and algorithms and much more. The University
of Pittsburgh Chess Club is
is an institution by itself and many links to chess related materials,
games, PGN viewers etc. are available.
Chess
Tutor Applet
Economics
John
S. Irons: Economists
Hindi
literature.
Indian
Poets (Biography in English)
Hindi
Poetry
Hindi
Resources
Macho
and Good Programming in C
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