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 4.5.2018

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Quantitative Finance What society thinks I do

What David thinks I do

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What I actually do

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Quantitative Finance

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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.

• Portfolio Management.

• Risk Management.

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

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The Random Behavior Dow 30,000

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The Random Behavior • Random Walk— Often refers to a stochastic process in a two-dimensional space.

• Wiener Process— Continuous-time stochastic process.

• Brownian Motion— Particle diffusion process.

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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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Stochastics • • • •

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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Goodhart’s Law • “When a measure becomes a target, it ceases to be a good measure.”— Charles Goodhart • Quantitative finance makes it even more difficult for investors to consistently generate abnormal returns over time using popular measures that are publicly available than the past.

• Caution—This does not negate the significance of any indicator; rather, investors should not rely on any single factor known by the general public to be “powerful”.

• The CBOE Volatility Index (VIX) is among many of the Goodhart’s Law victims.

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Volatility Implied Volatility vs. Realized Volatility 90

60

80 50 70

60

40

50 30 40

30

20

20 10 10

0

0

Implied Volatility ŠCopyright 2018 Cumberland AdvisorsŽ. Further distribution prohibited without prior permission.

Realized Volatility

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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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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 2010.

Quant Mutual Fund AUM ($B)* 1000**

712 615 485

507

2014

2015

404 288 224

230

2010

2011

2012

2013

2016

2017

2018

*Morningstar. Financial Times. **Estimated.

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HFT • 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

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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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