Monte Carlo · Return processes
Filtered Historical Simulation (regime layer, unconditional-variance fallback)
fhs_gjr_regime_uv_fallback
Identical to the variance-regime process in every respect but one: what happens to a single holding whose volatility fit is rejected. If every holding fits, the two produce the same run.
The one difference
Every FHS process runs admission checks on each holding's fitted volatility model, and a holding whose fit fails them needs something to fall back to. Elsewhere that fallback is EWMA. Here it is the holding's unconditional variance over the estimation window, which is the same GARCH recursion with the dynamics removed:
The window's sample variance is both the one-step forecast and the long-run level. It reverts in a single step and has no memory.
Why that is not obviously worse
EWMA looks like the richer fallback, and for a single forecast it is. But its variance recursion has a unit root: the weights sum to one exactly, so a shock never fully decays and the process has no unconditional variance to revert to.
That is tolerable in a one-step risk estimate and awkward inside a multi-year simulation, where a holding on the EWMA path can carry a shock forward indefinitely while every other holding mean-reverts through its own fitted dynamics. This fallback trades that holding's conditional responsiveness, which the rejected fit failed to establish anyway, for a recursion that stays stationary.
Neither answer is obviously right, which is why both exist and both were measured rather than argued about.
What the measurement says
In rolling-origin testing this arm tracked realised volatility to +3.1%, +6.3%, +5.2% and +6.6% at one day, one month, three months and one year, against +2.0%, +3.4%, +1.6% and +1.8% for the EWMA fallback variant. Both carry no rejecting gates; the EWMA fallback is the better calibrated of the two on this panel.
Read that as a result about this panel rather than a general verdict on the two fallbacks. It depends on how often fits are rejected and on which holdings, and a portfolio whose composition differs from the study's could land the other way. That is the reason to keep both selectable rather than to pick one on these numbers.
Neither is validated out of sample. Both are insufficient_evidence, not accepted, and every probability stays conditional on the selected model, the frozen optimizer-time inputs, the effective configuration, the engine version and the seed.