A Physicist on Wall Street

1
A Physicist on Wall Street

• John Krane
• Third Millennium Trading
• Downtown Chicago

I dont actually work on Wall Street,but A
Physicist on Van Buren Streetdoesnt have the
same ring to it
8 September, 2005
2
Personal Bkgnd

• University of South Dakota
• B.S. Bus. Admin. Managementplus Math,
  Philosophy, Chemistry, Music,
  Economicsfound Physics
• B.S PhysicsUniversity of Nebraska -- Lincoln
• M.S. Physics, minor Mathematics
• Ph.D. Physics, The Ratio of Inclusive Jet Cross
  Sections at sqrt(s) 630 and 1800 GeV, plus W
  cross section at 630 GeV
• GSA 1996-97
• Iowa State University
• Pit fighting
• Global Tracking code (kalman/root/C)
• QCD Group Convenor
• jet algorithm work (Matthais Toennesmann)
• Neutrino Mag. Moment (Fritz DeJongh)
• YPP 2000-01
• 8 years total at FNAL

Give me analysisor give me death!
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Kalman Filter vs. Particle Filter
By the way

• Standard Kalman filter Gaussian errors, linear
  problem
• Extended Kalman Filter Gaussian errors,
  non-linear problem (Taylor)
• Unscented Kalman Filter Gaussian errors,
  non-linear problem (coordinate transformation)
• Particle Filter non-Gaussian errors! (a Monte
  Carlo technique)

True path
Best fittoo bad its impossible!
Kalman assumes
Position probability is really
cf The Unscented Particle Filter, van der
Merwe, Doucet, Freitas, Wan
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What is a Quant?

• Fundamental Financial Analyst Price/Earnings
  ratios, global economy, demand for products
• MSNBC
• Financial reports company by company
• Quantitative Financial Analyst large data sets
  of historical prices, etc, and statistical models
• Data mining, pattern recognition, analysis
• Technical Analyst moving average trend
  lines,Elliot wave theory, visual patterns in
  pricing (cup and bowl, evening star)
• Generally not well-founded in statistics

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Third Millennium Trading
TMT 3 Big Bosses 5-15 Floor Traders 5 Prop.
Trad. Desk me, Dennis, Mark

• Market MakerYou want to sell 1000 options
  contracts, we buy them at the bid price. They
  want to buy 1000 contracts, we sell them at the
  ask price.
• On average, a market maker collects the bid/ask
  spread and has no market risk. They are paid to
  provide liquidity (like eBay does for garage
  sales)
• Proprietary TradingTrades to make money from
  owning or shorting the instruments. Can acquire
  position in the course of MM-ing.

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Stocks (Equities)

• Derive value from
• Old school the size and likelihood of dividend
  payment
• New school from a companys (perceived) worth
• Can buy them (go long) or sell them (go
  short)Can sell stock without actually owning
  it, but you must provide collateral in an
  account
• Pairs trading go long and short in two
  closely-related stocks
• If the entire market unexpectedly loses value,
  both stocks move similarly and you are protected
• Essentially, you are making a bet on
  mean-reversion
• Basket trading generalization of pairs trading
• per/stock costs can hurt profits

all these stock concepts apply to other
instruments
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Models for Stock Prices
Example of autoregression
or any other time series

• Prices are a time series (fractional daily s
  1) modeled with autoregression, nearest
  neighbor, min/max, voodoo
• hard to beat the Random Walk Model (future
  price current price e)

Fibonacci numbers anyone?
Histo actual 30-sec price for a 3-stock
basketYellow blocks actual 20-min average
price Dots A mass-and-spring modelThe more
aggressive the model, the bigger themistakes at
market reversals! Random walk does better than
this model
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Some details
Costs commission, bid/ask spread, usu.
2.5/share

• A trading company is allowed to provide less
  money than the stock value (21
  leverage)required whether short or long
• Trading rules for robots Buy/Sell signal,
  stop-loss, profit-take signal, chicken-out,
  time-limit
• Have to beat 40 / year ROI most of my
  attempts with stocks could not overcome costs!
  ? hard to predict direction of short-term price
  moves

Thus we dont trade stocks for profit!
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Futures
Costs/contract 10/commis 30 bid/ask 20
margin

• A standardized contract to buy or sell goods at a
  set priceE.g. 40,000 lbs live hogs _at_
  47/100lbs in March
• A good way to remove uncertainty for farmers
• Speculators dont actually have to buy the goods,
  instead just sell before expiry anybody want
  40,000 lbs butter?
• Can also go short agree to sell them in the
  future without owning them now
• Oil, gasoline, heating oil, gold, platinum,
  silver, copper, wheat, cheese, milk, urea

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Stock Optionsa kind of insurance

• For 5, you get a contract allowing purchase of
  100 shares of X at K/share in Z months (can
  also go short of course)
• After Z months, if the price S is higher than
  K, you exercise the option and pocket
  (S-K)100 cash settlement
• If the price S is less than K, let the option
  expire and you only waste 5

K is the strike price
American options allow early exercise
The contract finished in the money
The contract finished out of the money
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A little Stochastic Calculus
Random walk model again

• Assume stock prices follow geometric Brownian
  motion
• The expectation of the stock price distribution
  is lognormal(i.e., Ln(S) is Gaussian)
• 1973 Fischer Black, Myron Scholes, Robert Merton
  publish (will win Nobel prize for Economics
  with) the above and their option pricing formula.
  

Frac. Price change drift random motion
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Error bands in physics, often lognormal!
By the way
should be

• If distribution cant go negative (e.g. a cross
  section), mis-measurements resulting from the
  error usually lognormalnot Gaussian.
• In Run I, DÆ QCD had an elegant way to represent
  lognormal error effects in (D-T)/T

Does a fractional error make sense? If so,
deviations due to the error are lognormal.
Thanks Iain Bertram
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Dynamic Option Hedging the greeks

• Find the variation of your options position
  w.r.t.
• Sell offsetting stock (D1.0) to suppress price
  sensitivity.
• If your option was originally mispriced, you make
  money if the market moves up or down!
• Mispricings usu. result from misprediction of
  price volatility (s)
• Short options selling insurance that the price
  wont change
• Long options buying such insurance
• You can add D for your portfolio to see if you
  are net long or net short

Stock price
2nd w.r.t. price
Time
Volatility
Traders often know littlePDE, but they knowthe
greeks
D dS Q dt V d? G ?dS)2
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Re-hedging heuristic
A long options position
Consider a long, hedged option positionat-the-mon
ey (SK) at t0ProfitIf D0, slope 0
Profit
Stock price
Unrealized gain
Profits increase on paper when the price moves
from hedged price
Profit
Stock price
Even if price returns to original,we dont lose
the captured profitnow thats worth a Nobel
Prize
Re-hedge at new price
Profits captured!
Profit
Stock price
The valley gets more shallow away-from-the-money
(i.e. G?0)
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Re-hedging

• For a delta-neutral and vega-neutral
  portfolio
• Clearing house always demands approximate
  delta-neutrality (or a really good
  risk-dispersion model)
• Second term is jump risk. If a stock price
  changes by 30, a short position could tank even
  if you were delta-neutral

A short options positionhere, you hope the
pricenever moves
Profit
Stock price
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What do I do with my time?

• Options model, running for 1 years,
  modifiedPredicting volatility is key, watch out
  for jumps!
• Commodities model (energy/metals)paper trading
  it now, shows promise, need courage
• Stock tradinginvestigated 3 times!What is a
  good predictor and what is noise?
• International index funds, foreign currency
  exchange
• Not yet bonds, exotic options, VIX

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Can you beat Goldman Sachs?

• There are many big players (GS, Merryl Lynch,
  hedge funds galore)
• But moving big money also moves the market
• Exploit small mispricings they cannot
• Have visualization tools they dont
• Have training they dont
• Im better (and more full of myself) than they are

Pride, arrogance, andhubrisOh my!
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A typical day for me
830am market open 300pm market close

• Up at 530, train at 630, office at 750work
  traders hours
• 900 collect stock price data, update trees,
  predict volatility, find options mispricings,
  check plots, email results to Mark, IM a summary
• 930 230 research of my choice
• 230 collect comodities price data, find
  energy/metals mispricings, paper trade, email
  summary to Mark
• 305 re-collect closing stock price data
• 320-445 leave for train, home 5-6pm

• We use(d)
• ROOT
• Matlab
• MySQL
• Excel/Access
• Minuit
• Private libs

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Careers in Finance

• Coder (C, C, SQL, perl)Easy to get if you
  have the skills
• Junior Quant (join a big company)Difficult to
  get, need to test well
• Insurance Analyst, etc.Very concerned with
  non-Gaussian prob.Monte Carlo
• New Effort (small team getting started)Rare
  opportunity
• Temp JobsRecoding existing work, analysis
  miracles, anything in between

• Where are the jobs for Ph.Ds?
• London
• New York City
• Eastern USConn, NJ, Bahamas
• Chicago
• Elsewhere

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Prediction Company
The Predictors, Thomas A. Bass

• Doyne Farmer, Norman Packard leave Los Alamos and
  a U. of IL to found company in Sante Fe (1991)
• Chaos theory just doesnt work in financial
  markets
• They try other means, as discussed earlier
• Farmer returns to academia (Sante Fe Institute)
• Packard still runs Prediction Co., 25 owned by
  UBS
• See also D.E. Shaw (NY) and Citadel (Chi.)

So dont tell meabout it.
www.predict.com
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How to prepare

• Books
• Options, Futures, and Other Derivatives, John
  C. Hull (150)Like Jacksons Electrodynamicsgood
  and bad
• Market Models, Carol Alexander (90)Advanced,
  interesting, useful
• Quantitative Finance and Risk Management A
  Physicists Approach, Jan W. Dash (100)
  Written by physicist, odd notation, Reggeon
  Field Theory?
• Option Volatility and Pricing, Sheldon
  Natenberg (40)Very introductory, math in the
  appendix, helps you talk to traders
• My Life as a Quant, Emanuel Derman
  (20)Written by ex-physicist, quant apologist
  wishes he was physics theorist

My personal favorite
Dennis keeps taking it home
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More How to prepare

• Web sites
• www.numa.com ? employment offered/wanted
• Wilmott.com forums
• Monster.com, careerbuilder.com
• Grow your skill set
• Review want ads and learn skills they demand!
• Grow a thick skin
• Recruiters can be brutal
• Many Masters-level programs (e.g. U.Chicago)
  teach this stuff directly

Look here first!
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Reasons to Love It

• Positive
• Analysis (large data sets, pattern recognition,
  data mining)
• Linking sub-analyses into a result, then a
  working system
• Objective measure of goodness (fïckle
  peer-approval not so relevant)
• Be your own scientist, trusted to find most
  fruitful path (in my job anyway)
• Some probability of doing real short-term social
  good
• Physics seems fairly mature, Economics is
  certainly not
• Great parties
• Missing negatives
• No hustling for grant money
• No computing division
• No email avalanche, no culture of workaholism
• No conference schedulework is done when its
  ready
• No teaching load
• No politicization of results
• No career bottle-neck

Less
My papers are 3 pages, my grant is 10

• Negatives
• No foreign travel
• Barrier for women

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Closing

• Directions of stock price movements are very hard
  to predictPrice volatility, price relationships
  much easier to predict
• Pairs/baskets insulate you from market tides, but
  costs multiplyApplies to portfolios of
  stocks/options/whatever
• Options dynamic hedging quadratic profit/loss
  curve ? if long make money if market goes up
  or down! ? if short must hedge as frequently
  as you can afford but often the price changes
  while the market is closed
• Quant analysis/experimental physics analysis very
  similar
• Ph.D.s common in finance, not always better, not
  always respected, so dont expect a red carpet
• Finance is not a mundane job you will hateI feel
  challenged, I dont do the same things every day,
  I have my academic freedom, I like my bosses

in my experience
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Contact Info

• Dr. John Kranehttp//home.comcast.net/jkrane/31
  2 260 5220 (10am-1pm is best)
• jkrane_at_netzero_dot_comjust replace the _at_
  and the _dot_
• Contact me any time, and I mean that. My company
  is not hiring, and we have no plans to do so, but
  Im happy to look at your resume and make
  suggestions, etc.