How Can Quantitative Behavioral Finance Uncover Trader Motivations?

How Can Quantitative Behavioral Finance Uncover Trader Motivations? Gunduz Caginalp University of Pittsburgh April 5, 2013 unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 1 / 36

REFERENCES. "Are flash crashes caused by instabilities arising from rapid trading?" Wilmott (2011) (with Mark DeSantis and David Swigon). Multi-group asset flow equations, (with Mark DeSantis) Discrete and Continuous Dynamical Systems, Series B 16, 109-150 (2011). "Quantifying Non-Classical Motivations and the Behavioral Impact of News Announcements on Stock Prices," (with Mark DeSantis) Corporate Finance Review,16, 21-31 (2011). Nonlinear dynamics and stability in a multi-group asset flow model, (with D. Swigon and M. DeSantis) SIAM J. Applied Dynamical Systems 11, 1114-1148 (2012). The Price Dynamics of Large Market Capitalization Equity ETFs (with Mark DeSantis and Akin Sayrak) Preprint (18 pages). Stock Price Dynamics: Nonlinear Trend, Volume, Volatility, Resistance and Money Supply (with Mark DeSantis) Quantitative Finance 11, 849 861 (2011). Nonlinearity in the Dynamics of Financial Markets, (with Mark DeSantis) Nonlinear Analysis 12, 1140-1151 (2011). The Dynamics of Trader Motivations in Asset Bubbles, (with V. Ilieva), Journal of Economic Behavior and Organization 66, 641 656 (2008) Overreaction Diamonds: Precursors and Aftershocks for Significant Price Changes, (with A. Duran) Quantitative Finance 7, 321-342 (2007).

Parameter Optimization for Differential Equations in Asset Price Forecasting (with A. Duran) Optimization Methods and Software, 23, 551-574 (2008).

Introduction Classical Finance, E cient Market Hypothesis (EMH) based on game theory; each participant is seeking to maximize while cognizant that others are doing the same. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 2 / 36

Introduction Classical Finance, E cient Market Hypothesis (EMH) based on game theory; each participant is seeking to maximize while cognizant that others are doing the same. While some market participants may make cognitive errors, or be subject to behavioral bias, the large amount of money managed by savvy investors quickly capitalizes on these errors and restores e ciency. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 2 / 36

Introduction Classical Finance, E cient Market Hypothesis (EMH) based on game theory; each participant is seeking to maximize while cognizant that others are doing the same. While some market participants may make cognitive errors, or be subject to behavioral bias, the large amount of money managed by savvy investors quickly capitalizes on these errors and restores e ciency. Hence, the actions of the "uninformed" investors contribute only small uctuations. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 2 / 36

Introduction Classical Finance, E cient Market Hypothesis (EMH) based on game theory; each participant is seeking to maximize while cognizant that others are doing the same. While some market participants may make cognitive errors, or be subject to behavioral bias, the large amount of money managed by savvy investors quickly capitalizes on these errors and restores e ciency. Hence, the actions of the "uninformed" investors contribute only small uctuations. Any info available to public (e.g., graphs) is immediately incorporated into the asset price. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 2 / 36

Behavioral Finance: Investors have biases e.g., unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 3 / 36

Behavioral Finance: Investors have biases e.g., anchoring, whereby a price (unrelated to value) is xed in investors minds; unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 3 / 36

Behavioral Finance: Investors have biases e.g., anchoring, whereby a price (unrelated to value) is xed in investors minds; framing (e.g. as loss or gain), disposition e ect; unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 3 / 36

Behavioral Finance: Investors have biases e.g., anchoring, whereby a price (unrelated to value) is xed in investors minds; framing (e.g. as loss or gain), disposition e ect; over-reaction unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 3 / 36

Behavioral Finance: Investors have biases e.g., anchoring, whereby a price (unrelated to value) is xed in investors minds; framing (e.g. as loss or gain), disposition e ect; over-reaction under-reaction unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 3 / 36

Traditional evidence for behavioral nance Events of recent years: large price changes w/o valuation change on various time scales (bubbles, ash crashes, etc.) unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 4 / 36

Traditional evidence for behavioral nance Events of recent years: large price changes w/o valuation change on various time scales (bubbles, ash crashes, etc.) Kahneman psychological experiments indicating that subjects are in uenced by "framing" and "anchoring." unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 4 / 36

Traditional evidence for behavioral nance Events of recent years: large price changes w/o valuation change on various time scales (bubbles, ash crashes, etc.) Kahneman psychological experiments indicating that subjects are in uenced by "framing" and "anchoring." Vernon Smith et. al. asset market experiments indicating that bubbles arise endogenously. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 4 / 36

Traditional evidence for behavioral nance Events of recent years: large price changes w/o valuation change on various time scales (bubbles, ash crashes, etc.) Kahneman psychological experiments indicating that subjects are in uenced by "framing" and "anchoring." Vernon Smith et. al. asset market experiments indicating that bubbles arise endogenously. EMH theorists are not convinced by either approach. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 4 / 36

Evidence for Classical Finance: Raw data seems to be noise... 0.15 0.1 0.05 0 0.05 0.1 0.15 0.2 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 5 / 36

Mean (%) But data also yields... 15 10 The Deviation Model: Mean vs Threshold Positive 2.5 < thr <= 5 Negative 5 <= thr < 2.5 Positive 5 < thr <= 9 Negative 9 <= thr < 5 Positive 9 < thr <= 50 Negative 50 <= thr < 9 5 0 5 10 15 20 5 4 3 2 1 0 1 2 3 4 5 Day Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 6 / 36

And also... 15 D 10 15 0.5 100.25 5 000 5 0.25 0.5 R 5 5 10 10 15 15 T Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 7 / 36

R 0.002 5 2.5 0 0 2.5 T 5 0.002 0.004 0.006 Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 8 / 36

How can we decide which is a suitable model? Basic issue is what fraction of assets are controlled by "knowledgeable" and bias-free investors. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 9 / 36

How can we decide which is a suitable model? Basic issue is what fraction of assets are controlled by "knowledgeable" and bias-free investors. Even then, who makes the decision in a mutual fund? Manager or "uninformed investor" who can redeem shares. Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 9 / 36

How can we decide which is a suitable model? Basic issue is what fraction of assets are controlled by "knowledgeable" and bias-free investors. Even then, who makes the decision in a mutual fund? Manager or "uninformed investor" who can redeem shares. Stochastic changes in valuation make testing of hypotheses di cult. Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 9 / 36

Classical or Behavioral? The issue is quantitative. What fraction of the assets are controlled by trend-based traders? unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 10 / 36

Classical or Behavioral? The issue is quantitative. What fraction of the assets are controlled by trend-based traders? By rapid algorithms? By value-based managers? unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 10 / 36

Classical or Behavioral? The issue is quantitative. What fraction of the assets are controlled by trend-based traders? By rapid algorithms? By value-based managers? How do we deduce the motivations of traders/investors from data with so much noise? Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 10 / 36

Our Approach Quantitative study of over 100,000 data points (daily closing prices) for 119 closed-end funds (1998-2008). unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 11 / 36

Our Approach Quantitative study of over 100,000 data points (daily closing prices) for 119 closed-end funds (1998-2008). Why closed-end funds? unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 11 / 36

Our Approach Quantitative study of over 100,000 data points (daily closing prices) for 119 closed-end funds (1998-2008). Why closed-end funds? Clear valuation (NAV); trade like any other stock. Similar study with ETFs; work in progress on Dow Jones stocks. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 11 / 36

Our Approach Quantitative study of over 100,000 data points (daily closing prices) for 119 closed-end funds (1998-2008). Why closed-end funds? Clear valuation (NAV); trade like any other stock. Similar study with ETFs; work in progress on Dow Jones stocks. Why daily data? Few changes in corporate structure on this time scale. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 11 / 36

Mixed E ects Regression (with DeSantis) BASIC IDEAS: By adjusting for changes in valuation, we can remove much of the "noise." unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 12 / 36

Mixed E ects Regression (with DeSantis) BASIC IDEAS: By adjusting for changes in valuation, we can remove much of the "noise." Need to understand valuation and make that an indep variable, together with price trend, volatility, money supply and other variables. Program adjusts for the fact that each stock has its own characteristics. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 12 / 36

Mixed E ects Regression (with DeSantis) BASIC IDEAS: By adjusting for changes in valuation, we can remove much of the "noise." Need to understand valuation and make that an indep variable, together with price trend, volatility, money supply and other variables. Program adjusts for the fact that each stock has its own characteristics. Variables can be standardized, so it is possible to compare the impact of trend versus valuation, etc. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 12 / 36

Regression variables R (t) = P (t) P (t 1) P (t 1) V (t) = NAV (t) P (t) NAV (t) (weighted avg ten days) T (t) = weighted trend variable (10 days) R (t + 1) = β 0 + β 1 T (t) + β 2 T 2 (t) + β 3 T 3 (t) + β 4 V (t) +... Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 13 / 36

Results Term Value (x100) Std. Error (x100) t-value p-value (Intercept).0265656.00543 4.88 <.0001 Price Trend.1668129.00679 24.54 <.0001 Valuation.2911161.00623 46.71 <.0001 Trend 2 -.0117148.00388-3.02 0.0025 Trend 3 -.0105260.00112-9.37 <.0001 Valuation 2.0064430.00180 3.57 0.0004 Valuation 3 -.0007622.00016-4.75 <.0001 Trend * Val -.0268997.00485-5.54 <.0001 Trend 2 * Val -.0087231.00177-4.92 <.0001 Trend * Val 2 -.0008461.00098-0.87 0.3865 Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 14 / 36

Gunduz Caginalp University of Pittsburgh Nonlinear () Quantitative In uence Behavioral of Trend Finance (CEFs) April 5, 2013 15 / 36 Return Versus Trend (Normalized) Return 0.2 5 2.5 0 0 St. Deviation of Trend 2.5 5 0.2 0.4 0.6

1.5 5 1 5 Trend 2.5 2.5 0 0.5 0 2.5 0.5 1 5 2.5 5 1.5 Return as a Function of Nonlinear Trend and Valuation unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 16 / 36

0.2 Return 0.1 0 3 2 1 0 1 St. Dev. of Trend 0.1 0.2 Nonlinear E ect of Trend for Large Capitalization ETFs unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 17 / 36

What do learn about trading these assets? When the uptrend is something we see 15% of the time, the pro t taking and trend following cancel out. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 18 / 36

What do learn about trading these assets? When the uptrend is something we see 15% of the time, the pro t taking and trend following cancel out. When the downtrend is something we see 2.5% of the time, the "buyin on dips" and trend following cancel out. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 18 / 36

What do learn about trading these assets? When the uptrend is something we see 15% of the time, the pro t taking and trend following cancel out. When the downtrend is something we see 2.5% of the time, the "buyin on dips" and trend following cancel out. We have similar regressions with direct changes (instead of "standard deviations") as well. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 18 / 36

Other variables. Short term and long term volatility, long term trend; unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 19 / 36

Other variables. Short term and long term volatility, long term trend; Resistance unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 19 / 36

Other variables. Short term and long term volatility, long term trend; Resistance Money supply (M2) Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 19 / 36

How do we compare apples and spa treatments? With each variable standardized, we compare the e ects one st. dev. events. E.g., If Trend has coef 0.10, while M2 has coef 0.05, then an uptrend that is observed 15% of the time (i.e., 1 st. dev.) cancels an M2 decrease that we see 2.5% of the time (2 st. dev). Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 20 / 36

Term Value (x100) St. Err. (x100) t-value p-value (Intercept) 0.0417343 0.00479 8.72 <.0001 Price Trend 0.1184948 0.00579 20.5 <.0001 Valuation 0.2658618 0.00547 48.6 <.0001 M2 Money 0.0470137 0.00479 9.826 <.0001 Sh. Term Volatility 0.0520087 0.00556 9.366 <.0001 L. Term Volatility -0.0138966 0.00530-2.62 0.0088 L. Term Trend -0.0050647 0.00540-0.938 0.3481 Volume Trend 0.0310028 0.00482 6.438 <.0001 Resistance -0.0708118 0.0602-1.176 0.2398 unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 21 / 36

The complex role of volatility If the data were classical, then the volatility coe cient would be negative. I.e., if two assets are the same in every respect, except that one has greater volatility, then it should have lower return. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 22 / 36

The complex role of volatility If the data were classical, then the volatility coe cient would be negative. I.e., if two assets are the same in every respect, except that one has greater volatility, then it should have lower return. Our results show that this is the case for long term volatility. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 22 / 36

The complex role of volatility If the data were classical, then the volatility coe cient would be negative. I.e., if two assets are the same in every respect, except that one has greater volatility, then it should have lower return. Our results show that this is the case for long term volatility. For short term volatility the result is opposite; it increases the return. Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 22 / 36

Measuring the impact of news Two issues: True change in valuation; Over-reaction Example: Nonfarm payroll is released in US. There is some change to economic and pro t forecast. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 23 / 36

Measuring the impact of news Two issues: True change in valuation; Over-reaction Example: Nonfarm payroll is released in US. There is some change to economic and pro t forecast. How much should the S&P change? How much can we expect it to over-react? Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 23 / 36

List of news announcements About 60 announcements each (during 2005-2010) : Business Inventories Capacity Utilization Consumer Sentiment Consumer Spending Durable Goods Housing Starts New Home Sales Non Farm Payrolls Personal Income Philadelphia Federal Survey Retail Sales Unemployment Rate Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 24 / 36

x = E a E f ; E = average fe a g je j so x is the fractional deviation from expected value y = x m ; m = mean of fxg s so y is the measure (in st. dev.) from the norm. Use indicator functions for day k after the announcement. Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 25 / 36

Daily Coefficients for Business Inventories, Phil. Fed. Survey, Retail Sales, Durable Goods, New Home Sales 0.0015 0.0010 Variable Average Coefficient Null Hypothesis 0.0005 Data 0.0000-0.0005-0.0010-0.0015 1 2 3 Day 4 5

Potential of Methodology Any possible e ect that can be quanti ed can be tested with data. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 27 / 36

Potential of Methodology Any possible e ect that can be quanti ed can be tested with data. Methods can be used to test an idea using a set of stocks. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 27 / 36

Potential of Methodology Any possible e ect that can be quanti ed can be tested with data. Methods can be used to test an idea using a set of stocks. Coe cients can be calibrated for a single stock for trading. Ongoing research suggests that one can use a simple valuation model in place of NAV. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 27 / 36

Potential of Methodology Any possible e ect that can be quanti ed can be tested with data. Methods can be used to test an idea using a set of stocks. Coe cients can be calibrated for a single stock for trading. Ongoing research suggests that one can use a simple valuation model in place of NAV. Similar methods for going long on one stock while hedging with SPY. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 27 / 36

Mean (%) Dynamics of over-reaction 15 10 The Deviation Model: Mean vs Threshold Positive 2.5 < thr <= 5 Negative 5 <= thr < 2.5 Positive 5 < thr <= 9 Negative 9 <= thr < 5 Positive 9 < thr <= 50 Negative 50 <= thr < 9 5 0 5 10 15 20 5 4 3 2 1 0 1 2 3 4 5 Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Day Finance April 5, 2013 28 / 36

On a longer time scale, similar issue Large part of population underinvested (e.g., 1982, now). Stocks suppressed, values compelling, public disenchanted. Catalyst starts an uptrend (e.g., dissatisfaction with interest rates). Uptrend fuels more buying. Excess cash moves into the market pushing the market much higher. Eventually, connection between stock price and value disappears. Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 29 / 36

Available Cash is Important Issue In 1982 interest rates were high while stocks had been underperforming for 15 years Now fear is high enough that people are willing to lend to governments at near zero rates. In both cases there is ample cash on sidelines. Improving economics leads to uptrend which leads to greater con dence. Further feedback as con dence leads to improving economics. Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 30 / 36

Key ingredients of a behavioral model Quantitative way to incorporate an open collection of motivations, e.g., trend, resistance, etc. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 31 / 36

Key ingredients of a behavioral model Quantitative way to incorporate an open collection of motivations, e.g., trend, resistance, etc. Distinct groups with di ering motivations and assessments of value. unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 31 / 36

Key ingredients of a behavioral model Quantitative way to incorporate an open collection of motivations, e.g., trend, resistance, etc. Distinct groups with di ering motivations and assessments of value. Di erent time scales for di erent groups (e.g., high frequency trading). unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 31 / 36

Key ingredients of a behavioral model Quantitative way to incorporate an open collection of motivations, e.g., trend, resistance, etc. Distinct groups with di ering motivations and assessments of value. Di erent time scales for di erent groups (e.g., high frequency trading). Finite cash; absence of in nite arbitrage Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 31 / 36

Asset ow: di erential equations and computing Ingredients above can be incorporated into a DE model unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 32 / 36

Asset ow: di erential equations and computing Ingredients above can be incorporated into a DE model Computing can show us the price evolution, wealth of each group unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 32 / 36

Asset ow: di erential equations and computing Ingredients above can be incorporated into a DE model Computing can show us the price evolution, wealth of each group Parameters can be altered easily to see how situation changes unduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 32 / 36

Asset ow: di erential equations and computing Ingredients above can be incorporated into a DE model Computing can show us the price evolution, wealth of each group Parameters can be altered easily to see how situation changes Most di cult part: estimating the cash position of each group Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 32 / 36

P E ect of shorter time scales in trend investing 50 40 30 P = 9.939 4B 20 10 4E P = 9.834 0 P = 9.6 100 Gunduz Caginalp University of 90 Pittsburgh 80() 70 Quantitative Behavioral Finance April 5, 2013 33 / 36

Papers at ssrn.com Thank you! Gunduz Caginalp University of Pittsburgh () Quantitative Behavioral Finance April 5, 2013 34 / 36