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A Physicist on Wall Street. John Krane Third Millennium Trading Downtown Chicago. I don’t actually work on Wall Street, but “A Physicist on Van Buren Street” doesn’t have the same ring to it…. 8 September, 2005. Personal Bkgnd. University of South Dakota

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a physicist on wall street

A Physicist on Wall Street

John Krane

Third Millennium Trading

Downtown Chicago

I don’t actually work on Wall Street,but “A Physicist on Van Buren Street”doesn’t have the same ring to it…

8 September, 2005

personal bkgnd
Personal Bkgnd

University of South Dakota

  • B.S. Bus. Admin. – Management…plus Math, Philosophy, Chemistry, Music, Economics…found 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!

John Krane – Third Millennium Trading

kalman filter vs particle filter

By the way…

Kalman Filter vs. Particle Filter
  • 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 fit…too bad it’s impossible!

Kalman assumes

Position probability is really

cf: “The Unscented Particle Filter”, van der Merwe, Doucet, Freitas, Wan

John Krane – Third Millennium Trading

what is a quant
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

John Krane – Third Millennium Trading

third millennium trading

TMT: 3 Big Bosses 5-15 Floor Traders 5 Prop. Trad. Desk+ me, Dennis, Mark

Third Millennium Trading
  • 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.

John Krane – Third Millennium Trading

stocks equities
Stocks (Equities)
  • Derive value from
    • Old school: the size and likelihood of dividend payment
    • New school: from a company’s (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

John Krane – Third Millennium Trading

models for stock prices
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

John Krane – Third Millennium Trading

some details

Costs: commission, bid/ask spread, usu. 2.5¢/share

Some details
  • A trading company is allowed to provide less money than the stock value (2:1 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 don’t trade stocks for profit!

John Krane – Third Millennium Trading

futures

Costs/contract: ~ $10/commis + $30 bid/ask + 20% margin

Futures
  • A standardized contract to buy or sell goods at a set priceE.g.: 40,000 lbs live hogs @ $47/100lbs in March
  • A good way to remove uncertainty for farmers
  • Speculators don’t 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

John Krane – Third Millennium Trading

stock options a kind of insurance
Stock Options…a 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”

John Krane – Third Millennium Trading

a little stochastic calculus

Random walk model again…

A little Stochastic Calculus
  • 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

John Krane – Third Millennium Trading

error bands in physics often lognormal

By the way…

Error bands in physics, often lognormal!

should be

  • If distribution can’t go negative (e.g. a cross section), mis-measurements resulting from the error usually lognormal…not 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

John Krane – Third Millennium Trading

dynamic option hedging the greeks
Dynamic Option Hedging – “the greeks”
  • Find the variation of your options position w.r.t.
  • Sell offsetting stock (D=1.0) 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 won’t 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 know“the greeks”

= D dS + Q dt + V d + G dS)2

John Krane – Third Millennium Trading

re hedging heuristic
Re-hedging heuristic

A long options position

Consider a long, hedged option positionat-the-money (S=K) at t=0:Profit<0 due to costs

If D=0, 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 don’t lose the captured profit…now that’s 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)

John Krane – Third Millennium Trading

re hedging
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 position:here, you hope the pricenever moves

Profit

Stock price

John Krane – Third Millennium Trading

what do i do with my time
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 trading…investigated 3 times!What is a good predictor and what is noise?
  • International index funds, foreign currency exchange
  • Not yet: bonds, exotic options, VIX

John Krane – Third Millennium Trading

can you beat goldman sachs
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 don’t
  • Have training they don’t
  • I’m better (and more full of myself) than they are

Pride, arrogance, andhubris…Oh my!

John Krane – Third Millennium Trading

a typical day for me

8:30am market open

3:00pm market close

A typical day for me
  • Up at 5:30, train at 6:30, office at 7:50“work trader’s hours”
  • 9:00 collect stock price data, update trees, predict volatility, find options mispricings, check plots, email results to Mark, IM a summary
  • 9:30 – 2:30 research of my choice
  • 2:30 collect comodities price data, find energy/metals mispricings, paper trade, email summary to Mark
  • 3:05 re-collect closing stock price data
  • 3:20-4:45 leave for train, home 5-6pm
  • We use(d):
  • ROOT
  • Matlab
  • MySQL
  • Excel/Access
  • Minuit
  • Private libs

John Krane – Third Millennium Trading

careers in finance
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

John Krane – Third Millennium Trading

prediction company

The Predictors, Thomas A. Bass

Prediction Company
  • Doyne Farmer, Norman Packard leave Los Alamos and a U. of IL to found company in Sante Fe (1991)
  • Chaos theory just doesn’t 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 don’t tell meabout it….

www.predict.com

John Krane – Third Millennium Trading

how to prepare
How to prepare
  • Books:
    • “Options, Futures, and Other Derivatives,” John C. Hull ($150)Like Jackson’s Electrodynamics…good and bad
    • “Market Models,” Carol Alexander ($90)Advanced, interesting, useful
    • “Quantitative Finance and Risk Management: A Physicist’s 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…

John Krane – Third Millennium Trading

more how to prepare
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!

John Krane – Third Millennium Trading

reasons to love it
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 schedule…work 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

John Krane – Third Millennium Trading

closing
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 don’t expect a red carpet
  • Finance is not a mundane job you will hateI feel challenged, I don’t do the same things every day, I have my academic freedom, I like my bosses

in my experience

John Krane – Third Millennium Trading

contact info
Contact Info
  • Dr. John Kranehttp://home.comcast.net/~jkrane/312 260 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 I’m happy to look at your resume and make suggestions, etc.

John Krane – Third Millennium Trading