# Presentation: 581291

## 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 analysis****or   give me death!**

## 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”?

**Fundamental Financial Analyst:**  Price/Earnings ratios, global economy, demand for products
- MSNBC
- Financial reports company by company
**Quant****itative 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

- 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.

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

## 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

- Prices are a time series (fractional daily = 1%) modeled with:  autoregression, nearest neighbor, min/max, voodoo
-  hard to beat the Random Walk Model (future price = current price + )

**Histo**: actual 30-sec price for a 3-stock basket**Yellow 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

- Example of autoregression:

- Fibonacci numbers anyone?

**or any other time series...**

## 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

- 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

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

## 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

- 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!

- If distribution can’t go negative (e.g. a cross section), mis-measurements resulting from the error usually **lognormal**...not Gaussian.
- In Run I, D**** 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”

- Find the variation of your options position w.r.t.
- Sell offsetting stock (=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 ()
- Short options = selling insurance that the price won’t change
- Long options = buying such insurance
- You can add  for your portfolio to see if you are “net long” or “net short”

**Stock price**

**Time**

**Volatility**

**2****nd**** w.r.t. price**

*********S  +  ************t  +   V************  +    ************S****)****2 ***

- Traders often know littlePDE, but they know“the greeks”

## Re-hedging heuristic

- If =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. →0)

**A long options position**

- Consider a long, hedged option positionat-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 pricenever moves

## 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

## 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!**

## 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

- 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

**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 

- 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 

- 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

- Web sites:
- _[www.](http://www.numa.com/)__[numa](http://www.numa.com/)__[.com](http://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

- 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

- 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**

## 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.