# Registered always-long volatility-sizing study v1

## Hypothesis and distinction

Test whether reducing BTC exposure when realized volatility rises, and allowing mild leverage when it is low, improves after-cost returns relative to both spot BTC hold and fixed exposure. This is a distinct sizing hypothesis, not another flow entry/exit filter or a scaled version of the original trend/macro bot. Previous leverage studies and directional volatility discovery remain relevant negative evidence. All historical periods are explored; no holdout or automatic promotion claim.

## Signals and cadence

Use the exact previously frozen old/recent BTC price inputs, with full warmup before account slicing. Realized volatility is sample standard deviation of log close returns over N exact contiguous four-hour intervals, multiplied by sqrt(365.25*6). Lookbacks of 14/30/60 days mean 84/180/360 returns and require N+1 price bars. A missing price interval invalidates the feature until the complete lookback is available; no imputation or treating a longer gap as one ordinary four-hour return.

Five volatility candidates: annual volatility budgets 40%,60%,80% with a 30-day lookback; 60% with 14-day and 60-day lookbacks. Exposure is clamp(budget / observed volatility, 0.25, 1.50). Exactly zero volatility gives the cap; missing/warmup volatility gives 1.00. Sixth candidate uses 60%/30 days with an otherwise identical 1.00 cap. Four controls: daily constant exposures 0.75,1.25,1.50, and 1.00 buy-once BTC. Ten models total. Controls bracket exposure; none is described as exactly matching a candidate's realized risk.

Update the desired target only at UTC 00:00 candle closes, holding it between daily observations. Every account schedules an initial allocation using the already-warmed target at its first row, then rebalances only from daily 00:00 decisions. Constant-exposure controls have the same initial/daily schedule. BTC buys once at the same initial execution delay and retains its quantity. All fills occur after {1,3} four-hour bars; missed exact fill timestamps expire rather than moving to the next bar. No intraday target refresh or opportunistic trade-frequency tuning.

## Hypothetical financing account

Start each account with $10,000 cash. Borrowing is represented only by a negative USD cash balance, not by real margin access or a perpetual contract. Charge simple interval interest on that outstanding debt at APR {5%,10%,20%} times elapsed seconds / (365.25*86400), including gaps. Debited interest becomes part of debt for later intervals. Positive cash earns zero. These are fixed sensitivity assumptions, not observed borrowing quotes. Do not apply perpetual funding as though it were the same instrument.

Trading costs {6,30} bps per dollar traded. Solve exact post-fee target exposure for targets up to 1.50, keeping BTC quantity fixed between transactions. Costs, turnover, interest, P&L and balances must reconcile. Primary case: 10% borrowing APR, 6 bps trading cost, four-hour execution delay. No terminal sale. Record actual mean exposure and annualized observed account volatility; higher return versus 1x BTC alone does not establish sizing value.

For a borrowed long, use a hypothetical 25% maintenance equity/notional requirement. Before any closing-price rebalance, debit the full elapsed interval's interest and check the current supplied candle low against maintenance. If breached, force-close at that low less 50 bps adverse slippage, plus ordinary trading costs and an additional 100 bps liquidation fee. This deliberately adverse within-bar execution assumption does not claim a venue's actual rules or the exact price/time of a historical forced sale. Suppress scheduled entry on that same bar. Later scheduled decisions may reopen if capital remains positive. Record every liquidation and its assumed execution details.

If liquidation produces nonpositive equity, stop the account and retain its negative/zero ending equity, drawdown and debt shortfall; do not delete the failed case or reset to a new bankroll. CAGR/return-volatility ratios are unavailable for a nonpositive account. Ongoing interest after the account has stopped is outside this finite experiment. Data gaps leave unobserved intrabar risk unresolved; zero detected liquidations would not prove actual liquidation safety. Preserve prior frozen price sanitization and never clean data based on this result.

## Matrix and interpretation

Use the same 17 windows as breakout robustness, including full history, early/late eras, annual slices, 2017/2019 onward and the separate recent replay. 10 models x 17 windows x 2 costs x 2 execution delays x 3 borrowing APRs = 2,040 cases. All retained. Report returns/CAGR, maximum observed-close drawdown including initial capital, realized volatility, mean exposure, trading costs, borrowing charges and liquidation/insolvency counts.

Show all five budgets/lookbacks and the unlevered sibling against all constant controls. Report how frequently a candidate beats both BTC and the fixed 1.25x/1.50x controls in full history, 2019 onward, 2023 onward and recent windows across all sensitivity cases. Those are descriptive comparisons, not p-values or a winner-selection rule. Do not choose the best leverage/volatility budget or imply a guarantee. Forward adoption would require a separately versioned paper registry and additional evidence; the current fourteen-model journal is frozen.

## Verification

Verify frozen source/input identities and 23,600 canonical decisions. BTC buy-once must reproduce all 68 matching prior curves (17 windows x 2 costs x 2 execution delays); borrowing APR cannot change those no-debt results. Preserve all current account/feature traces with hashes. Test exact fee accounting above 1x, financing over elapsed gaps, daily rebalance schedules, delayed fills, candle-low liquidation before scheduled fills, insolvency retention, zero/missing-volatility fallbacks, future-input/account-prefix invariance and source scale invariance. Run focused tests then full discovery, archive reproducible evidence and back up. The performance-improvement goal remains active until actually achieved.