The Cost of Manufacturing Convexity: Tracking Error, Trading Frictions, and the Limits of Synthetic Protection

Convexity can be purchased through options or manufactured through dynamic trading.This paper decomposes the manufacturing residual and tests whether synthetic savings survive risk adjustment.Itô’s formula supplies the exact benchmark: continuous feedback produces a terminal profile only after accounting for continuous quadratic variation and jump charges. Exact stock-and-bond replication requires those charges to be spanned, so incompleteness and implementation error remain distinct. We attribute implementation error sequentially todiscretisation, transaction costs, signal lag, and jumps. The leading discretisation variance declines inversely with the number of rebalancing intervals, making it tracking risk rather than cost. Transaction costs admit the Leland effective-volatility approximation. For affine feedback, the expected lag gain residual equals minus the feedback slope times a laggedproduct density; nonlinear rules retain a state-dependent local-slope term.Jumps create the central asymmetry. In Monte Carlo experiments, a log-return variance proxy is held fixed while variation is shifted from diffusion to jumps. Mean short-and-hedge surplus rises from essentially zero to 1.7 percent of the option price at a 13 percent jump share and 4.7 percent at a 38 percent share, but dispersion nearly triples, while adverse-tail losses deteriorate sharply. A transparent reproducible four-benchmark decomposition separates pricing-model and hedge-rule effects from remaining finite-grid/jump-market residuals. Path-level bootstrap intervals confirm that these Monte Carlo effects are not simulation noise, while remaining explicitly calibration- and model-dependent. Combining the components with a downside expected-shortfall penalty produces a rebalancing program in which trading frequency rises with aversion to manufacturing failure.Under the benchmark calibration, local manufacturing-cost estimates are of the same order as commonly reported index variance premia. Synthetic protection is therefore not generically cheap: its apparent advantage can result from comparing expected costs while ignoring tracking dispersion and crash-state failure. Purchased and manufactured convexity are near-substitutes in average exposure but materially different insurance contracts in discontinuous markets.