Volatility Scaling and Isolated Momentum in a Narrow Commodity-Equity Universe: What Survives Honest Inference?

We study two design choices in a risk-parity allocation engine applied to five liquid proxies for commodity exposure (CCJ, COPX, GDX, SIL, XLE; 4,091 trading days, April 2010-July 2026). First, which volatility estimator - single windows of 20 to 1,000 days, a grid of 66 blends of 20/60/252-day windows, or a static estimate - yields the lowest realised portfolio volatility, and how robust is that ranking out of sample? Second, does the engine's momentum score, isolated from the risk-parity construction, predict returns inside this narrow, positively correlated bucket? For the first question we find a monotone but economically small ordering: shorter windows deliver 12–15 basis points lower volatility than the production 20/30/50 blend, windows of 500 days or more deliver 41–73 basis points more, and all estimators exhibit the same dispersion across rolling sub-periods. Covariance-aware minimum-variance weights cut volatility by roughly three percentage points, an order of magnitude more than any window choice. For the second question, naive i.i.d. t-statistics on overlapping forward returns reach 3.4–4.8, but heteroskedasticity-and-autocorrelation-consistent (HAC) inference, block-bootstrap confidence intervals and non-overlapping samples all reduce the evidence to |t| < 1.1. Time-series predictability is absent or mildly negative, the cross-sectional spread is statistically indistinguishable from zero, a tradeable long-short implementation earns no alpha, and the production tilt changes annual return by -0.01% (95% CI [-0.81%, 0.80%]) while doubling turnover. We therefore cannot demonstrate that the tilt adds value; we also quantify what the data could have detected.