PARTIAL · sizing only
Hypothesis
Position size inversely proportional to forecast volatility (vol-targeting) improves risk-adjusted return versus fixed size, because realized vol is forecastable even when returns are not.
Math — GARCH(1,1) forecast
Conditional variance recursion:
$$ \sigma_t^2 = \omega + \alpha\,\varepsilon_{t-1}^2 + \beta\,\sigma_{t-1}^2 $$
Scale exposure to a target volatility $\sigma^\*$:
$$ w_t = \frac{\sigma^\*}{\hat\sigma_t}\,w_0 $$
Method
Fit GARCH(1,1) per symbol by QMLE, forecast 1-step $\hat\sigma_t$, scale a fixed momentum book to 60%/yr target vol. Compare to flat sizing.
Results
| Vol forecast $R^2$ (1-step) | 0.34 |
| Return (similar) | ~flat |
| Max drawdown | −41% → −29% |
| Sharpe | 0.5 → 0.74 |
Returns roughly unchanged, but drawdown and Sharpe improve materially — because volatility is forecastable ($\alpha+\beta\approx0.95$, strong persistence) even though direction is not. Adopted as a sizing layer, not an entry signal.
You cannot forecast returns, but you can forecast variance. Almost all of the durable, defensible value in quant trading lives on the risk side, not the signal side.