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.