Quantitative Finance and Stock Market

A Registered Investment Advisory Firm

Quantitative Finance and Stock Market Leo Chen, Ph.D. Portfolio Manger & Quantitative Strategist Cumberland Advisors 7.12.2018

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Quantitative Finance What is a quant fund?

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Quantitative Finance • Applies to all markets.

• Derivatives—Options, Warrants, Futures, Forward, Convertibles, Swaps, etc.

• Math—Log, Differential Equations, Taylor Series (derivatives), Standard Deviation, etc.

• Fixed-Income—Yield, Duration, and Convexity.

• FOREX. • Portfolio Management.

• Risk Management.

• Models—CAPM, Binomial (Hedging/No arbitrage), Black-Scholes (“Greeks”), One-Factor Interest Rate, VaR, Monte Carlo, etc.

• Arbitrage

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Quant Funds • Automation, Algo, Programs, Machine Learning, etc.

• Man Group, Renaissance, DE Shaw, Two Sigma, etc.

• Set to surpass $1 trillion this year—Doubling from 2015.

Quant Mutual Fund AUM ($B)* 1000

08% .

8 1 = CAGR 712 615 485

507

2014

2015

404 224

230

2010

2011

288

2012

2013

*Morningstar. Financial Times. **Estimated. ©

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2016

2017

2018

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Multi-Factor Model • Factors—Fundamental, statistical, macro & micro, nuance (parking lot, electricity, etc.)

• Smart-beta—Are they really “smart”?

• Momentum ©

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Arbitrage • All markets.

• Statistical arbitrage (Stat arb).

– E.g. Long-Short strategies.

– Minimize exposure to risks such as market, geographic, sector, currency, etc. (Market neutral) – Closely analyze statistical factors such as correlation, co-integration, etc.

• Similarly, fixed-income, convertible, commodity, currency arb.

– Synthetic securities.

– Spread arbitrage.

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HFT & Algo • 50-60% daily volume of U.S. equity market.

• Trading volume as a percentage spiked since 2009.

U.S. Large Cap Daily Volume $180,000,000,000 $160,000,000,000 $140,000,000,000 $120,000,000,000 $100,000,000,000 $80,000,000,000 $60,000,000,000 $40,000,000,000 $20,000,000,000 $-

06 06 06 07 07 07 08 08 08 09 09 09 10 10 10 11 11 11 12 12 12 13 13 13 14 14 14 15 15 15 16 16 16 17 17 17 18 20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 /20 / 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1/ 5/ 9/ 1/ 5/ 9/ 1/ 5/ 9/ 1/ 5/ 9/ 1/ 5/ 9/ 1/ 5/ 9/ 1/ 5/ 9/ 1/ 5/ 9/ 1/ 5/ 9/ 1/ 5/ 9/ 1/ 5/ 9/ 1/ 5/ 9/ 1/

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HFT & Algo • • • • • • •

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Speed, Speed, Speed.

1 second=1,000 milliseconds=1,000,000 microseconds.

A blink of an eye=300-400 milliseconds.

HFT reduces the duration of arbitrage opportunity down to below 10 milliseconds.

Average processing time per order—400 microseconds.

Average sharing holding period—8 months in 2000; 2 months in 2008; less than 20 nowadays.

A firm built a straight line between Chicago and NASDAQ’s server in NJ with tunnels through the Allegheny Mountains to shave off 3 milliseconds. Total cost — $300 Million.

Regular investors receive data 1,500 to 900 milliseconds later than HFT —Years in the field of HFT.

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HFT & Algo • Fun facts

– – – – ©

Sharks.

Laser beam technology—U.S. military communication.

Drones, satellites, and balloons.

Machine learning to create rules: what rules?

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Stochastics • • • •

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Forecast & Probability.

Stochastic calculus, integration, differential equations, etc.

Markov, Martingale, Ito’s Lemma, etc.

Random walk—Lognormal RW, Mean-reverting RW, Correlated RW, etc.

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Fibonacci Sequence • 0,1,1,2,3,5,8,13,21, 34,55,…

• Golden ratio 1.618 • In nature

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Quantify Market Behaviors • How do we observe and measure market sentiment?

• Is an oversold market equivalent to market fear? Vice versa?

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Cumberland Advisors • Our quantitative strategy—Market Volatility/Leveraged Market Volatility Portfolio.

• Using Bayesian updating, constantly capturing market conditions & trying to avoid human emotions.

• Designed to minimize investment risk while maximizing compounding return.

• Why should we avoid emotions?

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Thank you • Questions and comments are welcome.

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Disclosure All material presented is compiled from sources believed to be reliable. However, accuracy cannot be guaranteed. This presentation represents personal opinions only.

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