How it works
Gold's portfolio case rests on one statistical property: its long-run correlation with stocks hovers near zero, and combining imperfectly correlated assets lowers total volatility below any simple average — sometimes below either component alone. This calculator applies the two-asset variance formula directly: portfolio volatility equals the square root of w²σg² + (1−w)²σs² + 2w(1−w)ρσsσg, where ρ is the correlation you supply. Moving 10% of a 16%-volatility stock portfolio into 15%-volatility gold at 0.10 correlation drops blended volatility to roughly 14.6% — a 1.4-point reduction bought with about 0.2 points of expected return, assuming 7% stocks against 5% gold. The weight sweep exposes the shape of the trade-off: benefits strengthen as correlation falls toward zero or negative, and there is a mathematically optimal minimum-variance weight the schedule locates for your inputs. Three honesty notes temper everything: correlation is regime-dependent and can spike upward in panics exactly when diversification is needed most; gold produces no cash flow, so its expected return is assumption rather than yield; and lower volatility is a comfort feature, not a return feature — the calm costs basis points of growth by construction.
Formula
σp = √(w²σg² + (1−w)²σs² + 2w(1−w)·ρ·σs·σg)
Tips
- Correlation is the active ingredient — test 0.3 panic-case alongside the 0.1 average.
- Most studies put useful gold sleeves at 5–15%, past which drag outweighs calm.
- Gold's zero yield means its expected return is faith plus scarcity, not cash flow.
- Rebalance annually or the sleeve drifts away from the weight you chose here.
- Compare against low-correlation alternatives (TIPS, short bonds) doing the same job.
Frequently asked questions
- How much gold should a portfolio hold?
- Most institutional and academic analyses land at 5–15% for volatility reduction, with diminishing and eventually negative effects beyond. At 10% with realistic correlations the calculator shows roughly a point or more of volatility trimmed for modest return sacrifice. Beyond 25–30%, gold's own price swings increasingly dominate and expected return erodes without offsetting benefit.
- Does gold actually reduce portfolio volatility?
- Historically yes on average, because gold's correlation with equities has run near zero over long samples. The two-asset formula shows even modestly positive correlation produces diversification when vols differ. The caveat: in acute crises correlations sometimes rise toward positive territory, shrinking the benefit precisely when portfolios need it — hence testing panic-case assumptions here matters.
- What correlation does gold have with stocks?
- Long-run estimates cluster near zero, oscillating between mildly negative and moderately positive across regimes — roughly −0.2 to +0.4 depending on the decade and crisis. Gold's strongest diversification stretches coincide with monetary stress and inflation scares. Treat any single correlation estimate as a central scenario, and stress-test the edges with the slider.
- Is gold a good inflation hedge?
- Over very long horizons and specific inflationary regimes (the 1970s, post-2021 surge), yes meaningfully; across all decades, inconsistently. Gold's real price spent long stretches going nowhere between spikes. It functions better as a crisis-and-currency hedge than a reliable CPI tracker, and the volatility math here captures its risk side that hedging narratives omit.
- Why does adding gold lower expected return?
- Because gold generates no earnings, rent or interest — its long-run return comes from price change alone, historically trailing productive assets. Blending 10% of a 7% expected-return portfolio into 5% gold mechanically subtracts 0.2 points. Whether that insurance premium is worthwhile depends on how much you value the smoother ride the correlation provides.