Both paths over your horizon: the piece net of carry and exit toll, against the same money in the market. The gap at the right edge is the price of the position — or its prize. Hover to explore.
Two paths for the same money. The market path: the price compounds at your market assumption; with the tax chip on, the gain pays your ordinary capital-gains rate at the end. The piece: the price compounds at the appreciation you believe in, the exit toll (auction or dealer commission) comes off the sale, US federal tax takes up to 28% of the collectible gain when the chip is on — and every year’s insurance and storage compounds against you at the market rate, because money spent on the vault also missed the market. The hurdle line prints the appreciation at which the piece ties the market after all of it.
Authentication and restoration surprises, fashion risk (the market for the thing existing at exit), and the joy of ownership — unpriced, unpriceable, and often the real return. State tax on the sale varies; the chip’s 28% is the federal collectible maximum. And unlike an index fund, one piece is one piece: the dispersion around any average is enormous, in both directions. The instrument prices the position; the object is your department.
market = price × (1+r)^n − tax on the market gain
piece = price × (1+a)^n × (1 − exit%) − 28% tax on the gain
carry = Σ (insurance + storage) compounded at r
verdict = piece − carry, against market · hurdle: the a where they tie