Overview

Background/Notation

• Strategies
  • Cointegration \(\color{#D7A84B}{f_\text{co}}_{R,R'}(z_0)\)
  • Mean reversion Time based \(\color{#D7A84B} {f_\text{mv}}_{R }(z_0)\)
  • Mean reversion Cross sectional \(\color{#D7A84B} {f_\text{cmv}}(z_0)\)
  • Momentum trending Time based \(\color{#D7A84B}{f_\text{mt}}_{R }(z_0)\)
  • Momentum trending Cross sectional \(\color{#D7A84B}\color{#D7A84B} {f_\text{cmt}}(z_0)\)
  • See Mathematical Framework for further information.
• Filters
  • Neutrality (beta, dollar, pc, general factors)
  • Regime based strategy execution
• Assets
  • 460 elements and related time series at daily frequency.
  • From the SP.
• Metrics
  • Sharpe over time period
  • Alpha over time period
  • Total return over time period
  • Max drawdown over time period
• Method
  • Training period
  • Validating period
  • Held-Out period
  • Roll forward and repeat

Methodology

• 2515 data points. 5 runs. 1 epoch per run.
• 1 run:
  • Training data: 500 points
  • Validating data: 200 points
  • Held out data: 260 points
• Roll forward of 260 points.
• Success means average Sharpe > 2, average annualized alpha > 2, max drawdown < 15% across all runs.
• Assets were selected for the held out period for all strategies through a two-stage training/validation process for each strategy and each rolling run.
  1. For every candidate strategy parameter set, all assets were tested individually, treated as singleton portfolios, on the 500-day training period.
  2. Individual results included the one-bar lag and trading costs.
  3. Assets were eligible only if they had:
     • Positive training return
     • Positive finite training Sharpe
     • At least 20 position changes
  4. Eligible assets were ranked by training Sharpe, then return.
  5. Only the top 10 training-ranked assets for each parameter set entered validation.
  6. Validation tested every basket size from 4 through 10 and every combination of the top 10 assets.
  7. Each basket was evaluated with total allocation on the 260-day validation period, including lag, turnover, fees, and slippage.
  8. Candidates were ranked first by whether return and Sharpe were positive, then validation Sharpe, then validation return.
  9. The winning parameter-and-asset-basket combination was frozen before held-out testing.

Results

• Training period 500 points, validation period 260 points.
• All values are average held-out results on held out period of 260 points, ranked primarily by Sharpe within each section. Roll forward of 200 points was used and there were 5 total testing runs.
• Reported metrics are arithmetic averages over the 5 runs. Alpha is annualized.
• Strategies implemented are cross sectional mean reversion, momentum trending, and cross sectional momentum. \(\color{#D7A84B}\) \(\color{#D7A84B} {f_\text{cmv}}(z_0)\) ,\(\color{#D7A84B}\color{#D7A84B} {f_\text{cmt}}(z_0)\) ,\(\color{#D7A84B}{f_\text{mt}}_{R }(z_0)\)
• Parameters were optimized during validation
• Regime filter based strategy implementation
• There is 0 return on cash and risk free rate is 0

Main CMV + MT + CMT experiments

Notes

• Time based mean reversion did not contribute positively in any type of strategy related setting.
  • This seems expected as historical results indicate time based mean reversion has no consistent edge in daily frequency time scales.
  • It was implemented in this project for modeling purposes primarily.
• Cointegration is not profitable in its current implementation in any type of strategy related setting either. Negative return and sharpe values were found when implemented alone or with a regime filter.
  • This is not historically consistent and must be examined.
• ML seems to overly optimize parameters in testing and validation when applied to the regime classifier. The preset regime filter performed the best, but learning methods had higher percent return, along with larger max drawdown. This lowered the strategy's Sharpe
• Regimes were classified in terms of autocorrelation, dispersion, volatility, correlation, and liquidity. AC seems to be most descriptive, but further analysis must be done.

Future Improvements

• Validation of both strategies and regime filters on the same period may lead to overfitting on the period. Solutions include splitting the validation period into two parts to implement each separately. Another is to use cross validation on the combined training and validation period.