Methodology

Underlying total return

For each trading date t, the underlying return is r_t = (C_t − C_t−1 + D_t + G_t) / C_t−1, where C is the close and D and G are cash dividend and capital-gain events recorded on that exact date. The resulting path compounds as U_t = U_t−1(1 + r_t). Split-normalized closes already reflect splits, so split events are never applied a second time.

Synthetic leveraged return

The reconstruction applies the fund’s signed daily leverage L to each underlying total return: s_t = max(-1, Lr_t − e/252 − (L − 1)(f_t + b)/252), then compounds S_t = S_t−1(1 + s_t). Here e is the annual net expense ratio, f is the DFF rate, and b is the category borrowing coefficient. DFF is the latest observed federal-funds rate no more than seven calendar days before the trading date. Broad-index 2× and 3× products use a 1% annual category coefficient; single-stock 2× products use 13.5%. The 252 divisor converts annual assumptions to a daily amount. A return cannot fall below −100%; once the reconstructed value reaches zero, it remains zero.

Cash events belong to the underlying total-return calculation. The synthetic path does not create a separate payout, and it does not model intraday rebalancing, spreads, taxes, or issuer-specific swap mechanics.

Launch date and live history

Before a fund’s launch date, the chart is a counterfactual: it shows what the formula would have produced from the available underlying or documented proxy. From launch onward, the chart uses the fund’s evidenced close history when it can be continuously rebased to the reconstructed path. If that path was already wiped out, the actual comparison is unavailable rather than shown with a false zero anchor. A proxy is disclosed because its return may differ from the fund’s stated underlying.

Average Difference

Average Difference is the mean absolute percentage error on exact common dates only. Both actual and synthetic paths are rebased to the first common date, that anchor date is excluded, and each remaining error is |(S_t/S₀) − (A_t/A₀)| / (A_t/A₀). It is unavailable without at least one post-anchor common date or when the synthetic value at the anchor is zero, because the paths cannot be rebased continuously.

No guarantees

Reconstructed results are synthetic and for research and education only. They are not investment advice, actual historical performance, or a guarantee of future results.