Behavioral Forecasting MSE 444 Final Presentation Rachit Prasad

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

Motivation Division of Investor Classes n n Fundamentalists: Trade on belief in intrinsic value of asset Chartists: Trade on current market trend, and use knowledge of previous movement of prices Assumptions n n 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 2

Agent Prediction Model n Fundamentalists: Ef( t, t+1 S) = - (St – St*) St: Asset price at time t : Mean-reversion coefficient St*: Fundamental price at time t n Chartists: Ec( t, t+1 S) = a 0 + b 0 t + Σ 2 i=1 aisin(bit + ci) ai, bi, ci: constants found by fitting across a window of past asset prices Behavioral Forecasting 3

Fundamentalist Prediction Behavioral Forecasting 4

Chartist Prediction Behavioral Forecasting 5

Agents’ Predictions Behavioral Forecasting 6

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+1 S) = wf Ef( t, t+1 S) + wc. Ec( t, t+1 S) Behavioral Forecasting 7

Model Prediction Fitting Window Behavioral Forecasting 8

Dynamic Weight Adjustment Fundamentalists Dominate Chartists Dominate Behavioral Forecasting 9

Dependence on Learning Rate Behavioral Forecasting 10

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

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

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

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

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

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

Constant Parameters: USDJPY Behavioral Forecasting 17

Conclusions n Hit-Rate of about 53% is observed across asset classes. n Profits generated are sufficient to overcome transaction costs. n In addition to the base model, various strategies were attempted. The binary model showed good promise. Behavioral Forecasting 18

Thank You ! Behavioral Forecasting 19