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 Physics University 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 analysis or give me death!


Kalman Filter vs. Particle Filter: 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) By the way… Kalman assumes Position probability is really cf: “The Unscented Particle Filter”, van der Merwe, Doucet, Freitas, Wan True path Best fit…too bad it’s impossible!


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


Third Millennium Trading: Third Millennium Trading Market Maker You 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 Trading Trades to make money from owning or shorting the instruments. Can acquire position in the course of MM-ing. TMT: 3 Big Bosses 5-15 Floor Traders 5 Prop. Trad. Desk + me, Dennis, Mark


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


Models for Stock Prices: Models for Stock Prices 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) Histo: actual 30-sec price for a 3-stock basket Yellow blocks: actual 20-min average price Dots: A mass-and-spring model The more aggressive the model, the bigger the mistakes at market reversals! Random walk does better than this model Example of autoregression: Fibonacci numbers anyone? or any other time series…


Some details: 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 Costs: commission, bid/ask spread, usu. 2.5¢/share Thus we don’t trade stocks for profit!


Futures: Futures A standardized contract to buy or sell goods at a set price E.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 Costs/contract: ~ $10/commis + $30 bid/ask + 20% margin


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” The contract finished “in the money” The contract finished “out of the money” American options allow early exercise


A little Stochastic Calculus: 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 Random walk model again…


Error bands in physics, often lognormal!: Error bands in physics, often lognormal! 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 By the way… Does a fractional error make sense? If so, deviations due to the error are lognormal. Thanks Iain Bertram should be


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 Time Volatility 2nd w.r.t. price = D dS + Q dt + V d + G dS)2 Traders often know little PDE, but they know “the greeks”


Re-hedging heuristic: Re-hedging heuristic If D=0, slope = 0 Stock price Profit Stock price Profit Stock price Profit Unrealized gain Profits captured! 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… The valley gets more shallow away-from-the-money (i.e. G→0) A long options position Consider a long, hedged option position at-the-money (S=K) at t=0: Profit<0 due to costs Profits increase “on paper” when the price moves from hedged price


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 Stock price Profit A short options position: here, you hope the price never moves


What do I do with my time?: What do I do with my time? Options model, running for 1+ years, modified Predicting 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


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, and hubris…Oh my!


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 8:30am market open 3:00pm market close A typical day for me We use(d): ROOT Matlab MySQL Excel/Access Minuit Private libs


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 Jobs Recoding existing work, analysis miracles, anything in between Where are the jobs for Ph.Ds? London New York City Eastern US Conn, NJ, Bahamas Chicago Elsewhere


Prediction Company : 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.) The Predictors, Thomas A. Bass www.predict.com So don’t tell me about it….


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 Dennis keeps taking it home… My personal favorite


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!


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


Closing: Closing Directions of stock price movements are very hard to predict Price volatility, price relationships much easier to predict Pairs/baskets insulate you from market tides, but costs multiply Applies 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 hate I feel challenged, I don’t do the same things every day, I have my academic freedom, I like my bosses in my experience


Contact Info: Contact Info Dr. John Krane http://home.comcast.net/~jkrane/ 312 260 5220 (10am-1pm is best) jkrane_at_netzero_dot_com just 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.