Stocks rise and their portfolio weight exceeds the amount you originally agreed to hold. You hesitate to sell a winner but worry about the next decline. In another month, new money changes the weights without any sale. Should either event automatically cause a trade?
Rebalancing asks whether holdings still match the policy and how to restore them at acceptable cost. Give the same account two rules written in advance, follow twelve periods, and compare their trading dates, fees, and remaining deviations.
Check whether the policy still applies
You will distinguish weight drift from a changed target, calculate a rebalance including costs, and save a timed decision-and-execution record for two rules. Targets should come from a prior policy such as G47's. This example supplies separate teaching weights, selected without using the later returns.
Rebalancing adjusts an allocation that has drifted from its agreed state. Investor.gov describes calendar-based and preset-deviation checks and explains that different growth rates can change portfolio risk.1 This does not guarantee a higher return from every sale of a winner and purchase of a laggard.
First check purposes. Near-term payments, less reliable income, or changed loss capacity can require a new household and portfolio policy before restoring an old allocation. Market drift and changed needs can occur together; record their reasons separately.
Give both rules the same complete inputs
C3-50-v1 uses synthetic dollars and twelve equally long teaching months, M1–M12, with no actual ETF or calendar dates. Initial holdings are stocks $6,000, bonds $3,000, and cash $1,000: equity $10,000. This is an existing-position snapshot, without an extra initial purchase fee. Targets are 60%, 30%, and 10%, not recommended allocations.
All returns below are total returns including reinvested distributions. Cash earns zero. Do not add dividend cash again.
| Month | Stock return | Bond return | Cash return | Outside contribution at start |
|---|---|---|---|---|
| M1 | 5% | 1% | 0% | $0 |
| M2 | −8% | −2% | 0% | $0 |
| M3 | 3% | 0.5% | 0% | $0 |
| M4 | 6% | 0% | 0% | $0 |
| M5 | −4% | −1% | 0% | $0 |
| M6 | 2% | 1% | 0% | $0 |
| M7 | 1% | 0.5% | 0% | $1,000 |
| M8 | −12% | −4% | 0% | $0 |
| M9 | 4% | 1% | 0% | $0 |
| M10 | 3% | 0.5% | 0% | $0 |
| M11 | −2% | 0% | 0% | $0 |
| M12 | 5% | 0.5% | 0% | $0 |
The only outside flow is $1,000 added to cash at the start of M7, after M6's execution window and before M7's returns. No withdrawal occurs, and the contribution has no fee. It is not investment profit and does not create an immediate contribution-day trade. It enters the next scheduled month-end check.
Rule A, quarterly: check and restore the allocation after M3, M6, M9, and M12. The calendar triggers it even for a small deviation; a zero difference creates no trade.
Rule B, threshold: check every month-end. Trigger if any asset's absolute weight difference from target is at least five percentage points, including equality. Check cash as well as stocks and bonds. Once triggered, both rules adjust stocks and bonds together, not only the asset crossing the boundary.
Five percentage points is not 5% of the target. Moving stocks from 60% to 65% is a five-point deviation. Five percent of 60% would instead be three percentage points, a different rule.
The original specification in Chinese, inputs, 24-row ledger, and trade list preserve full precision. G93's return calculations and G51's attribution use this same account, not a replacement series.
Valuation comes before a separate execution window
Each period starts from the previous post-execution balances. Record beginning equity before the external flow, add that period's cash contribution, apply the returns, and form the month-end valuation and decision. Trades occur afterward in a distinct window Wm. The exercise assumes no extra price change between valuation and execution, ample liquidity, and complete fills.
That assumption isolates arithmetic; it does not guarantee a real fill at the same close after complete closing information is known. Actual price changes, halts, or delayed cash require recalculated quantities and recorded delays. Do not improve results by rewriting the decision time. W12 also executes; terminal value is after W12 costs, without forced liquidation.
Every nonzero stock or bond purchase or sale costs five basis points of its absolute traded value, or 0.0005 times that amount. There is no minimum commission, additional spread, slippage, tax, or management fee. Holdings are ideally continuously divisible, with no whole-share rounding. Use 28-significant-digit Decimal arithmetic, without rounding each transaction to cents. Displayed approximations do not replace calculation inputs.
At a trigger, freeze pretrade equity E. Set stock value to 0.6E and bond value to 0.3E, both using that same E. Signed trade is target minus existing value: positive buys, negative sells. Cash absorbs both signed amounts and fees. Thus stock and bond amounts reach prefee targets, while fees reduce final equity and leave slight weight differences. Do not submit repeated corrective trades to eliminate the last displayed digit.
The ideal amount model completes sales before purchases and checks final cash is nonnegative. This does not establish actual settlement or financing feasibility. All supplied ledger periods pass that simplified cash check; a real account needs its own conditions.
Recalculate the surprisingly small M3 trade
After the first three returns, stocks are $6,000 × 1.05 × 0.92 × 1.03 = $5,969.88. Bonds are $2,984.247 and cash remains $1,000. Pretrade equity is $9,954.127. The quarterly calendar triggers a rebalance.
Stock target is $5,972.4762, requiring a $2.5962 purchase. Bond target is $2,986.2381, requiring $1.9911. Total traded value is $4.5873 and fee is $0.00229365, less than one cent. The exercise permits that outcome because it has no minimum charge or quantity unit.
Cash becomes approximately $995.4104 and post-fee equity approximately $9,954.1247. The reduction in the combined assets is exactly the fee, not another unexplained loss. Retain exact amounts in the ledger instead of carrying those rounded values forward.
The threshold account does not trade here because deviations are small. Both outcomes follow their registered rules. If such a tiny transaction is undesirable, introduce a minimum trade or tolerance band in a new version before evaluating its outcomes. Do not silently delete the quarterly trade after noticing its fee.
New money changes the denominator and the next check
The threshold account ends M6 at approximately $10,180.3975. Add $1,000 before M7 returns, then apply the 1% stock and 0.5% bond returns. At M7's end, stocks are approximately $6,258.4134, bonds $2,998.8683, and cash $2,000, totaling $11,257.2817.
Cash weight is approximately 17.7663%, or 7.7663 percentage points above its 10% target, so the rule triggers. This is a contribution effect, not performance from cash “doubling.” Buy approximately $495.9556 in stocks and $378.3162 in bonds, pay approximately $0.4371, and retain approximately $1,125.2910 cash.
New contributions can fill underweight categories and reduce some sales without guaranteeing cost-free adjustment. They also cannot share a second assignment as existing emergency reserves. A real distribution paid in cash needs its own ledger route; do not combine a dividend-inclusive return with another credit for the same payment.
FINRA describes redirecting money, adding to underweight categories, and selling overweight holdings, alongside trading costs and potential taxable-account consequences.2 This example's tax exclusion does not establish that actual rebalancing is tax-free.
Compare all twelve periods, including nontrade checks
Quarterly rebalancing executes in W3, W6, W9, and W12. The threshold rule executes only in W7. These are all nonzero asset adjustments, with dollars displayed to four decimal places:
| Rule/window | Signed stock trade | Signed bond trade | Total fee |
|---|---|---|---|
| Quarterly W3 | 2.5962 | 1.9911 | 0.0023 |
| Quarterly W6 | −90.8475 | 68.2086 | 0.0795 |
| Quarterly W9 | 737.9607 | 215.9797 | 0.4770 |
| Quarterly W12 | −133.9740 | 92.1226 | 0.1130 |
| Threshold W7 | 495.9556 | 378.3162 | 0.4371 |
Quarterly produces eight asset trades, gross traded value of approximately $1,343.6805, and total fees of $0.6718. Threshold produces two asset trades, approximately $874.2718 traded and $0.4371 in fees. Gross traded value sums absolute purchases and sales. Without an equity denominator, it is an amount, not a turnover percentage.
After W12, quarterly equity is approximately $11,053.9253 and threshold equity $10,984.3270. Both include the outside $1,000. Net investment profit/loss is therefore approximately +$53.9253 and −$15.6730, not gains of $1,053.9253 and $984.3270. G93 handles return percentages under these flow boundaries; first reconcile the money.
Quarterly ends closer to target, with maximum absolute weight deviation of approximately 0.0009204 percentage points. Threshold's maximum end deviation is approximately 0.3541899 percentage points, below five, so it keeps the allocation. A small post-fee difference is not an error, and within-threshold drift is not a forgotten trade.
Quarterly has the higher terminal value on this path. Its different holdings and extra costs both contribute; the fee difference alone does not explain the entire final gap. Another return path, threshold, spending pattern, or cost model can change the comparison. Do not declare the observed winner an optimal frequency after seeing the twelve periods.
A trigger still needs cash and policy approval
M8 supplies simultaneous adverse returns of −12% for stocks and −4% for bonds. Nominal cash is unchanged in this model without a promise of unchanged purchasing power. Rebalancing reshapes exposure according to policy; it does not remove joint risk.
A real minimum payment-cash requirement needs a posttrade check. If unmet, pause, reduce the order, or use a registered exception. A target weight does not permit using living reserves. Cash insufficiency cannot silently create borrowing in a long-only, unlevered account.
Real shares or minimum fund purchases may leave residuals. Follow the registered quantity algorithm, then recheck cash and concentration. Rounding every original ledger amount to cents creates another model; it is not faithful reproduction of this continuous version.
SEC's fee guidance distinguishes transaction and ongoing expenses and points to actual disclosures.3 Small synthetic charges do not establish that real implementation differences are negligible. A cost already included in a net return should not be deducted a second time.
Test a boundary rather than approving by appearance
Explain. Why does a stock weight of 65% trigger the five-point rule? Why is the quarterly account's $1,053.9253 balance increase not its investment profit?
Reference answers · reveal
Answer. Subtract 60% from 65% for five percentage points, rather than calculating relative weight growth. The balance increase includes the $1,000 contribution; investment profit is approximately $53.9253. The contribution cannot be counted as earnings as well as cash.
Transfer. In an independent decision snapshot, equity is $10,000, with stocks $6,500, bonds $2,500, and cash $1,000. Keep targets and fees. Does threshold trigger, what trades result, and what are post-fee cash and equity? If another policy requires cash of at least $1,000, may the unchanged proposal execute?
Answer. Stock and bond deviations are exactly +5 and −5 points, so it triggers. Sell $500 stocks, buy $500 bonds, and charge $0.50 on $1,000 gross trades. Cash becomes $999.50, equity $9,999.50. Stock and bond values remain $6,000 and $3,000, slightly above 60% and 30% of the lower post-fee equity. Do not secretly add corrective orders.
The $1,000 cash floor fails. Pause or recalculate under a previously permitted order-reduction method. The $0.50 is not irrelevant because it is small, and the floor cannot be rewritten afterward. Triggering and execution approval are separate decisions.
Save a reproducible rebalancing rule
Record target provenance, weight denominators, dates or exact threshold definition, assets checked, assets adjusted after a trigger, external-flow timing, execution window, quantity precision, fees, minimum cash, and exception priorities. State which fields a tool actually exports rather than assuming it supplies them.
Attach original returns and flows, each pretrade valuation, decision, order, fee, post-fee equity, and residual. Reconcile each period as beginning equity before flow + outside flow + net investment profit/loss = ending equity. Verify that information precedes trades and preserve checks even when no trade triggers.
Restore a policy that still fits the purpose, not a set of visually tidy percentages. Apply the same registered checks to price drift and new money, respect cash and execution constraints, and compare complete ledgers. A contribution is not profit, and one synthetic path cannot establish the best rebalancing frequency for every investor.
References
- Investor.gov: Asset Allocation and Diversification, drift, restoring allocations, and calendar/deviation approaches.
- FINRA: Asset Allocation and Diversification, “Role of Rebalancing,” funding routes, costs, and taxable-account considerations.
- Investor.gov: How Fees and Expenses Affect Your Investment Portfolio, July 23, 2025. Transaction/ongoing charges and disclosures; five basis points is this exercise's input.
Editorial status
AI-assisted draft synchronized to the accepted second-round Chinese source. C3-50 is a synthetic mechanism packet, without real ETF materials or verified real trading. See the author review. A separate AI reviewer has completed an independent full-text and bilingual review. Human financial review and target-reader testing have not been performed and are not scheduled for this edition.