Gold vs “Digital Gold” — correlation, quanto, and a simple barbell
Insurance assets aren’t identical. Gold is physical and sovereign-agnostic; Bitcoin is digital and adoption-driven. This lab lets you show the differences with clean numbers—then structure around them.
Tip: paste your own series below (CSV, two columns: date,price) to replace demo data.
1) Quanto forward uplift (USD investor on XAU)
Under USD measure, lognormal gold (XAU) with FX converts to USD quanto forward:
\[ F_{\text{quanto}}(0,T)= S_0\exp\!\big((r_{\text{USD}}-q-\rho\,\sigma_{\text{XAU}}\sigma_{\text{FX}})T\big) \]
Results
| Plain forward (no quanto term) | — |
| Quanto forward | — |
| Quanto uplift (annualized drift adj) | — |
If ρ < 0 (gold up, USD up tends to be opposite), the quanto forward rises vs the plain forward by $-\rho\,\sigma_{\text{XAU}}\sigma_{\text{FX}}$ each year. That’s supportive for USD-quanto calls on gold.
2) Barbell — Gold (insurance) + BTC (convex tail)
Use demo monthly series or paste your own below. Rebalance keeps the convex leg from running away in calm regimes.
Quick stats
| Gold (ann. μ / σ) | — |
| BTC (ann. μ / σ) | — |
| Barbell (ann. μ / σ) | — |
| Rolling 95% drawdown (barbell) | — |
These are simple arithmetic estimates from the loaded series; use your own book data for proper risk.
Cumulative growth
3) Rolling correlation and left-tail beta (vs SPX)
Paste CSV for each series (two columns: date,price). We’ll compute monthly log returns, 6-month rolling corr, and tail beta vs SPX for the lowest 20% SPX months.
Dates must align reasonably; we’ll inner-join on month.
Rolling 6-month correlation
Left-tail beta (20% worst SPX months)
| Gold tail beta vs SPX | — |
| BTC tail beta vs SPX | — |
Tail beta = OLS slope of asset returns on SPX returns restricted to bottom 20% SPX months. Lower (or negative) is better as insurance.
Takeaways for clients
- Insurance ≠ identical behavior: Gold’s left-tail co-move with SPX is typically lower than BTC’s; BTC brings convex upside in “risk-on” windows.
- Quanto matters for USD buyers of gold: With negative ρ (gold vs USD), quanto forward is higher than plain forward by \( -\rho\sigma_{\text{XAU}}\sigma_{\text{FX}} \), supportive for USD-quanto calls.
- Barbell clarity: Keep the majority in the physical-style insurance leg (gold), then overlay a disciplined BTC call allocation (rebalance).
This page is an educational lab. Use dealer curves, house vol surfaces, and production data for decisions. Not investment advice.