Behavioral Forecasting

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

2. 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 Forecasting

3. Agent Prediction Model • Fundamentalists: Ef(t,t+1S) = - (St – St*) St: Asset price at time t : Mean-reversion coefficient St*: Fundamental price at time t • Chartists: Ec(t,t+1S) = a0 + b0t + Σ2i=1aisin(bit + ci) ai, bi, ci: constants found by fitting across a window of past asset prices Behavioral Forecasting

4. Fundamentalist Prediction Behavioral Forecasting

5. Chartist Prediction Behavioral Forecasting

6. Agents’ Predictions Behavioral Forecasting

7. Market Prediction Model wf = #fundamentalists / #investors wc = #chartists / #investors wf = exp(Pf)/ [exp(Pf) + exp(Pc)] Pf: Risk-adjusted profitability (over training period) : Learning rate parameter Pf = ∑Pf - µσf [ µ: Risk aversion parameter σf: Volatility of profits E(t,t+1S) = wf Ef(t,t+1S) + wcEc(t,t+1S) Behavioral Forecasting

8. Model Prediction Fitting Window Behavioral Forecasting

9. Dynamic Weight Adjustment Fundamentalists Dominate Chartists Dominate Behavioral Forecasting

10. Dependence on Learning Rate Behavioral Forecasting

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

12. USDJPY Exchange Rate • Window Length: 15 • Transaction Cost: 0 01/02/1975 – 09/26/1979 Behavioral Forecasting

13. Daily Returns: USDJPY 01/02/1975 – 11/15/1985 Behavioral Forecasting

14. Cumulative Profit: USDJPY 01/02/1975 – 09/26/1979 Behavioral Forecasting

15. Microsoft Stock 04/28/1986 – 09/28/1989 Behavioral Forecasting

16. Binary Model: USDJPY 09/05/2000 – 06/20/2002 Behavioral Forecasting

17. Constant Parameters: USDJPY Behavioral Forecasting

18. 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 Forecasting

19. Thank You ! Behavioral Forecasting