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
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50 30 40
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20 10 10
0
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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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