Behavioral Forecasting MS&E 444: Final Presentation Rachit Prasad, Sudeep Tandon, Puneet Chhabra, Harshit Singh Stanford University

Behavioral Forecasting2 Motivation Division of Investor Classes Fundamentalists: Trade on belief in intrinsic value of asset Chartists: Trade on current market trend, and use knowledge of previous movement of prices Assumptions Bounded Rationality: Agents cannot assimilate all the information in a market, so perfect foresight may not hold Prediction: Based on heuristic techniques Fundamentalist: Mean reversion to intrinsic value Chartist: Extrapolation of historical prices

Behavioral Forecasting3 Agent Prediction Model Fundamentalists: E f (  t,t+1 S) = -  (S t – S t *) S t : Asset price at time t  : Mean-reversion coefficient S t *: Fundamental price at time t Chartists: E c (  t,t+1 S) = a 0 + b 0 t + Σ 2 i=1 a i sin(b i t + c i ) a i, b i, c i : constants found by fitting across a window of past asset prices

Behavioral Forecasting4 Fundamentalist Prediction

Behavioral Forecasting5 Chartist Prediction

Behavioral Forecasting6 Agents’ Predictions

Behavioral Forecasting7 Market Prediction Model w f = #fundamentalists / #investors w c = #chartists / #investors w f = exp(  P f )/ [exp(  P f ) + exp(  P c )] P f : Risk-adjusted profitability (over training period)  : Learning rate parameter P f = ∑P f - µσ f [ µ: Risk aversion parameter σ f : Volatility of profits E(  t,t+1 S) = w f E f (  t,t+1 S) + w c E c (  t,t+1 S)

Behavioral Forecasting8 Model Prediction Fitting Window

Behavioral Forecasting9 Dynamic Weight Adjustment Fundamentalists Dominate Chartists Dominate

Behavioral Forecasting10 Dependence on Learning Rate

Behavioral Forecasting11 Estimation of Model Parameters Model parameters ( , , µ, S*) change with feedback (profits) The optimal parameters found by grid search and nonlinear optimization Predict: Chartist & Fundamentalist Find Prediction Errors & Profits over Training Window Input Price Data Minimize MSE Predict Next Period Price Optimal Parameters Advance by 1 day Window Length Training Period k Window Length Training Period k+1

Behavioral Forecasting12 USDJPY Exchange Rate Window Length: 15 Transaction Cost: 001/02/1975 – 09/26/1979

Behavioral Forecasting13 Daily Returns: USDJPY 01/02/1975 – 11/15/1985

Behavioral Forecasting14 Cumulative Profit: USDJPY 01/02/1975 – 09/26/1979

Behavioral Forecasting15 Microsoft Stock 04/28/1986 – 09/28/1989

Behavioral Forecasting16 Binary Model: USDJPY 09/05/2000 – 06/20/2002

Behavioral Forecasting17 Constant Parameters: USDJPY

Behavioral Forecasting18 Conclusions Hit-Rate of about 53% is observed across asset classes. Profits generated are sufficient to overcome transaction costs. In addition to the base model, various strategies were attempted. The binary model showed good promise.

Behavioral Forecasting19 Thank You !