Math and the Markets
Presentation to OLLI
4-26-13
Irvine
Tom Gladd
Consulting Quantitative Analyst
Morgan Stanley
New York
Review of Part 1
● Introduction to Math and the Markets
● Introduction to derivatives
● Models for roulette, stocks and options
● Great recession
● What happened and continues to happen
● Role of derivatives supported by math models
● Be wary of models for markets
Mini Flash Crash on Tuesday
Part 2
● Hour1 - More math and derivatives
● What is a model?
● How are derivatives used?
– Risk management
– Leveraged bets
● Hour 2 – What is happening now?
● Regulation and institutional risk management changes are occurring
● The London Whale
● On the horizon – Central Banks Bubble?
● Wrapping up
This is a train
This is a model of a train
This is another model of a train
What is a mathematical model?
The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work. -John Von Neumann
This is a financial market
This is a financial market
This is a financial market
A SUBSTANTIAL part of all stock trading in the United States takes place in a warehouse in a nondescript business park just off the New Jersey Turnpike. Article in New York Times, Jan 2, 2011.
https://www.youtube.com/watch?v=2Vdjin734gE
Brownian Motion
https://www.youtube.com/watch?v=xlKWdd_DhW0
Stock and volatility movement
Math models of a financial market
dS𝑡
𝑆𝑡= 𝑟 − 𝑞 dt + 𝜎 dz𝑡
This is the first model of stock prices (Bachelier in 1900!!!!)
This is a better model of stock prices (Black-Scholes 1973)
dS𝑡
𝑆𝑡= 𝑟 − 𝑞 dt + 𝑉𝑡 dz𝑆.𝑡
dV𝑡 = 𝜆 𝑉∞ − 𝑉𝑡 dt + 𝜂 𝑉𝑡 dz𝑉.𝑡
< dS𝑡 dV𝑡 >= 𝜌 dt
𝑑𝑆𝑡 = 𝜎 𝑑𝑧𝑡
This is a popular model of stock prices (Heston, 1993)
Mathematical models in finance should be judged on the basis of how
useful they are for their intended purpose
Models that can be used to make money are useful
Models that prevent the loss of money are useful
How are derivatives used?
● To manage risk
● To make leveraged bets
● To tell the future
Managing Risk
● Suppose, last September, you inherited
3000 shares of AAPL stock at $700/share.
● Worth $2,100,000, but probate etc. meant
you could not legally sell it until next week
(about 7 months).
Expected behavior of AAPL
400 600 800 1000 1200 1400S
Expected price distribution of AAPL at 7 months
3 chance S down 30 , you lose $630000
12 chance S down 20 , you lose $420000
29 chance S down 10 , you lose $210000
AAPL stock down 43% in 7 last months! Less than 0.1% probability!!
If you just waited, you lost $900,000!!!
Let’s take away that downside risk
400 600 800 1000 1200 1400S
price distribution of AAPL at 7 months
with downside risk removed
Cost $159723 or 7.6
Don’t have any spare cash?
400 600 800 1000 1200 1400S
price distribution of APPL at 7 months
with costless collar
Cost free almost
Managing risk is about shaping the distribution of profits and losses
● Derivatives allow you to change profit and
loss distributions at relatively low cost.
● The Black Scholes model (and many
others) are useful for the purpose of
allowing such transactions to be priced.
Stock trading is about taking views on the direction of stock prices
● Derivatives allow you to leverage your
capital to benefit from correct views
● Derivatives also allow you to manage the
risk associated with your trades.
● Stock selection models and derivative
models are useful for making bets.
Derivatives tell us about the future (sort of)
● Last week I told you the historical volatility
of IBM was about 20%
● However, the market for IBM options was
setting the volatility at 60%
Why implied volatility is important
How can I learn about investing and derivatives?
My advice is - don’t trade derivatives. • Invest in things you know something about. • Seek professional advice but watch out for sales pitches and
arrange to have access to second opinions. • Don’t be trusting. Be skeptical of every word you hear.
• I have spent fifteen years studying derivatives and have
experience in watching how derivatives are traded by professionals. I don’t trade derivatives except in very conservative ways.
• Frankly, I just don’t think that I have any “edge” over the market.
What to read
• Read the Wall Street Journal. Watch Bloomberg on TV. Investing • The Intelligent Investor, Benjamin Graham (1973) • Common Stocks and Uncommon Profits, Philip Fisher (1996) • A Random Walk Down Wall Street, Burton Malkiel (1973) • The Essays of Warren Buffett, Warren Buffett (2nd Ed. 2008)
Trading • Reminiscences of a Stock Operator, Edwin Lefevre (1923) • Market Wizards: Interviews with Top Traders, I and II, Jack Schwager (1980s??) • Extraordinary Popular Delusions and the Madness of Crowds, Charles MacKay
(1841) • Fooled by Randomness, The Black Swan, Nassim Taleb (2000s)
End of Hour 1
What is happening now?
● Much stronger government regulation is occurring
● How risk management works for institutions
● Recent newsworthy risk management failure THE LONDON WHALE
● Geoeconomic/geopolitics risks on the horizon
● US is stuck, or improving very slowly
● Debt in Europe is just as bad, nerves are fraying
● Japan is massively inflating their economy
Stronger government regulation
• Dodd/Frank – Many provisions but vague about details
– Rules left up to agencies but they are acting slowly
– Having a paralyzing effect on financial institutions
• Basel 2.5 and 3
• Many European restrictions on banks and financial institutions
Types of Risk
• Market Risk
• Credit Risk
• Operational Risk
• Legal Risk
• Reputational Risk
• Regulatory Risk
• …
Risk Metrics
• “Greeks”
• Value at Risk (VaR)
• Stress tests
• Various detailed reports
• Ad hoc analyses
Greeks – Delta Δ
Value at Risk VaR
3 2 1 0 1 2 3PL $MM
Distribution of daily PL
5 VaR $MM 1.65
Business Unitnitvz
Market Risk Credit Risknitvz
Model Risk Risk Metricsnitvz
Complianceitvz
Internal Audititvz
BU Risk officersz
Chief Risk Officeritvz
Board Membernitvz
Regulators OCC, SEC, Fed,
…itvz
New Basel 2.5 Risk Metrics
• Enhancements of VaR
• Stressed value at risk SVaR
• Incremental Risk Charge (IRC)
• Comprehensive Risk Measure (CRM)
• Standardized Charge (SC)
• Extended operational risk metrics (AMA)
Some regulation is good – but Macro level problems
• Interferes with commerce – Banks hunker down, don’t give loans to marginal companies – Financial institutions decide some business areas are not worth
the effort and withdraw
• Diverts resources away from activities that are conducive to economic growth
• Corporate world is shrinking – Corporations going private – Private equity (beginning to own a lot of stuff) – Hedge funds, Dark Pools (trade away from public eye) – Corporations going multinational for tax arbitrage reasons
Financial Institutions cutting jobs
Some regulation is good – but Micro level problems
• Regulators don’t know how to regulate – Many Dodd Frank rules still unwritten – Basel banking rules took forever and are still wishy-
washy – Just what is the regulatory requirement?
“We hear criticism from bankers that our models are a 'black box' which frustrates their efforts to anticipate our supervisory findings," Bernanke said. He said that over time, the banks should better understand the standards the tests are measuring.”
Some regulation is good – but Micro level problems
• Regulators know much less than the regulatees. • Congress and policy wonks who push the
regulators know MUCH less than the regulatees. • Regulators try to formulate rigid rules for risks
that are not amenable to rigid rules. • Regulators focus on the last crisis when the next
one will be different. • Banks actually weaken their risk models to
comply with regulations because it is too difficult to argue that the regulation doesn’t make sense in some contexts.
IRC for 2008 credit risk problems
• More loan defaults/bankruptcies than expected • Money lost on ratings downgrades • Recovery from defaults was lower than normal (40%)
• You can get market quotes for recovery on default for troubled
companies – JC Penny • You cannot get a reliable quote for recovery on default for safe
companies – IBM
• Why not just focus the model on troubled companies? • Answer: Regulators wouldn’t agree. Have to be safe. No exceptions
• Result – bad risk model based on bad data.
Some regulation is good – but Micro level problems
• Compliance is the path of least resistance for banks • New class of corporate manager whose only job is to keep
regulators happy. • Follow every rule, fill out every form, dot every “i”, cross
every “t”, attend every meeting and smile. • Compliance doesn’t require experienced, expensive quants
performing analysis. • Rule based, risk management is being outsourced to
cheaper foreign locations, e.g., Mumbai and Budapest.
The London Whale
• In Feb 2012, a hedge fund guy noticed that the CDS market was being distorted by a large aggressive trader in London.
• “Everyone knows The Whale, whenever there was a big move in CDS markets, you knew it was the Whale”
• Turned out to be Bruno Iksil, a London based trader for Chief Investment Office of J P Morgan
The London Whale
Jamie Dimon Ina Drew
The London Whale
• Iksil (and his bosses) traded too big for the market
• The sharks (hedge funds) circled
• It cost JPM over $6 billion dollars to extricate themselves
The London Whale
• The Office of the Chief Investment Officer had been very successful and received special treatment with regard to risk management
• Ian Drew and her risk managers DID NOT have control of the situation
• Various risk management and regulatory rules were broken. It is possible that Iksil’s immediate bosses may be charged with crimes.
The London Whale
• Lower level JPM risk managers and quants did know of trouble and issued repeated warnings.
The London Whale
• Huge mess. Multiple congressional hearings with live TV coverage.
• Senator Carl Levin, reigning arch enemy of Wall Street, had a field day.
• Jamie Dimon embarrassed and politically weakened as critic of regulation. Actually took a pay cut for 2012.
The London Whale
• So – how did JPM do in 2012?
Risks on the horizon
• The Fed has been pumping the economy for five years – zero interest rates, TARP, QE1, QE2, Operation Twist, monetary policy now tied to unemployment rate, buying $85 billion/month in treasuries and mortgage backed securities.
• People and institutions are desperate for yield. No place to put your money except the stock market
• Some real estate is superheating – bidding wars again in San Diego.
• The stock market is distorted. New bubbles are growing.
Utilities are the new Apple?
How does this end?
Europe is still a mess
• Greece bailed out but politically unstable – must cut 15000 government workers by end of year
• Cyprus bailed out but almost required seizing funds of small depositors
• Spain has 27% unemployment
• Italy elected a bureaucrat, a philanderer and literally, a comedian. After 4 months of fighting, the philander seems to have won out.
• Unemployment rising in France. Socialists turn out to be of bunch of rich dudes. The budget minister (who made his fortune on hair transplants) had a secret foreign bank account.
Everyone hates Germany
Japan is going crazy
• Japan has been in a deflationary cycle for 15 years and the new government is deliberately trying to create 2% inflation.
• They have doubled the number of Yen in circulation
• The stock market has exploded upward – but is it growth?
• The Yen has dropped and there is talk of “currency wars.”
Wrapping up
● Mathematics and computer technology play an
increasingly important roll in contemporary financial
markets
● Despite recent events, it seems that the trend to greater
complexity of models will continue.
● We live in interesting times and 2012 should be a doozy.
● We live in interesting times and 2013 should be a doozy.
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