What rebalancing controls and what its return effect depends on

A portfolio with three per cent Bitcoin, reset to its target weights once a year in line with the rule, at times held 9.6% Bitcoin, more than three times the intended weight. Therein lies the real challenge for mandate management in practice: a rule can be formally satisfied while the actual structure of the portfolio is far from the agreed one.

The rebalancing rule therefore belongs to the mandate strategy and should be documented before the first investment: target weights, permitted deviations, review frequency and the procedure in the event of a breach, including the deliberate decision not to adjust. It should be oriented towards the structural requirements of the mandate, not towards the historically most profitable simulation. Which rule would have performed best in hindsight says little about which will perform best in future.

The previous issue of this newsletter, “How to check whether a new strategy diversifies a portfolio”, showed that the historical performance of a portfolio can depend considerably on rebalancing and on its rebalancing date. This technical article documents the study design, decomposition and counter-checks; the newsletter summarises the practical consequences. The example again comes from digital assets: because Bitcoin fluctuates so strongly, it makes particularly clear how far weights can drift. The questions behind it arise with any addition to a portfolio.

The example is a portfolio of 60% equities and 40% bonds, supplemented by three per cent Bitcoin. The three per cent are financed pro rata from both parts. The starting weights are thus 58.2% equities, 38.8% bonds and 3.0% Bitcoin, and are also the target weights. Three per cent is a deliberately chosen model case. The calculation is in euros with daily closing prices from 29 December 2017 to 30 September 2026, using a global equity ETF, a currency-hedged global bond ETF and Bitcoin. The two ETFs are real UCITS ETFs whose share classes are authorised for distribution in Germany; product names are not disclosed.

Five rebalancing rules are compared. The study does not recommend any of them for a mandate but shows which deviations and which further portfolio adjustments would have arisen from applying them. Three questions serve this purpose:

• How far and for how long do the weights deviate from the target weights under the rule?
• Which position triggers the adjustment, and which holdings are changed?
• What do the adjustments achieve compared with a clearly named alternative, and how dependent is the result on market path and implementation?

Key findings: The rules examined differ markedly in how far the Bitcoin weight strayed from the target weight; the largest interim losses, by contrast, were much closer together than the highest Bitcoin weights. With annual rebalancing, Bitcoin contributed 6.5 percentage points more to profit than with buy and hold, and yet the total return was 6.6 percentage points lower. Whether adjusting the Bitcoin weight raised or lowered the return depended on the start date.

A return disadvantage relative to buy and hold does not mean that a rule has failed in its task. Buy and hold keeps the initial holdings, not the agreed allocation; the return comparison alone therefore does not decide which rule suits a mandate.

What the rule controls

Rebalancing rules can be divided into two basic forms. Calendar rules reset the portfolio to the target weights on fixed dates, regardless of how far the weights have deviated. Band rules intervene only when a weight leaves a corridor defined in advance around its target weight.

Two variants of each are examined: quarterly and annual rebalancing, which reset on the last common trading day of the quarter or year respectively, regardless of price movements, and a narrower band of 2 to 4% and a wider one of 1.5 to 4.5% around the Bitcoin target weight. For the bands, only the Bitcoin weight triggers; equities and bonds have no thresholds of their own but are adjusted along with every Bitcoin trigger. The fifth rule is the deliberate decision not to adjust at all, buy and hold, which also serves as the benchmark. When an adjustment is made, all four other rules reset all positions to the target weights at the same closing price, so the bands do not merely reset to the band limit. The bands were fixed before the calculation.

An example: on 28 December 2020, the narrower band rule stood at 4.3% Bitcoin, 57.8% equities and 37.9% bonds. The reset means selling Bitcoin and buying equities and bonds until 3.0% Bitcoin, 58.2% equities and 38.8% bonds are reached again. The return of the band rules therefore does not depend on Bitcoin trading alone.

Checks are made only on trading days on which all three prices are available; on weekends and public holidays, when only Bitcoin trades, no check takes place. The reset takes place at the closing price of the same day.

The differences in allocation control are large. Under buy and hold, the Bitcoin weight rose as high as 12.4%, more than four times the target weight. With the two band rules, the highest observed weights were 4.3 and 4.9%, in each case just above the upper limit, because checks are made only at the closing price. Quarterly and annual rebalancing lay in between at 8.6 and 9.6%, with very different trading requirements: 34 adjustment dates against 8. At the highest Bitcoin weight, the bond weight was below the target weight of 38.8% under all five rules. Under the four rules with adjustment, the equity weight was also below its target of 58.2%; under buy and hold, it was clearly above that target, at 67.8%.

Deviation here covers overweights and underweights. For all rules the same corridor of 2 to 4% serves as the benchmark, including for the wider band, which was outside its own limits on 0.7% of days. Under annual rebalancing, the Bitcoin weight was above 4% on 38.2% of observation days and below 2% on 16.7%, that is, outside the corridor of 2 to 4% on 54.9% of days in total. Measurement is in each case before trading.

The longest continuous phase lasted 204 observation days; between the first and the last day of this phase lie 296 calendar days, and an unbroken breach duration cannot be determined from closing prices. The narrower band, by contrast, was outside on only 25 days, 1.1% of observation days, and never for longer than one day in a row.

The short duration under the narrower band is largely a consequence of the assumption that the reset takes place at the same closing price. If execution takes place only at the next closing price, the longest phase lasts up to two observation days, and the share of days outside rises to 1.7%.

Controlling the allocation is a component of risk management. However, the differences in maximum weight are not reflected to the same extent in the maximum portfolio loss. The maximum drawdown on a daily basis lay between −23.2% for buy and hold and −21.6% for the bands, annual volatility between 11.3% for buy and hold and 9.7 to 10.0% with adjustment.

To trigger trading, calendar rules need no ongoing monitoring of weights, whereas band rules do. If the mandate provides for investment limits, however, weights must be monitored under a calendar rule as well, because between two dates the Bitcoin weight can reach a multiple of the target weight.

Where the return comes from

Two measures must be distinguished. The profit contribution shows how much a single asset contributed to the total return, in percentage points of the initial value. The rule effect shows how much better or worse the whole portfolio performed with the rule than with buy and hold. The two can diverge: if Bitcoin is reset to 3% at year-end, the sale proceeds flow into equities and bonds, or a top-up purchase is financed from them. Their holdings change as a result, and so does everything they earn afterwards. A higher profit contribution of one asset therefore does not mean that the rule raised the total return.

How far the two can diverge is shown by a decomposition of annual rebalancing. For this, four portfolios with the same starting weights are compared. P0 adjusts nothing. P1 resets only the ratio of equities to bonds to 60 to 40 at year-end and leaves the Bitcoin holding unchanged. P2 resets only Bitcoin to three per cent; equities and bonds provide the offset pro rata, with their ratio to each other drifting freely. P3 resets all three positions to the target weights and corresponds to the annual rebalancing from the first part. This decomposition applies only to annual rebalancing; it does not explain the return differences between all five rules. The gaps to P0 show what the respective adjustment meant for the total return.

Each of these gaps applies individually against buy and hold: the equity–bond adjustment alone reduced the total return by 19.0 percentage points, the adjustment of the Bitcoin weight alone raised it by 14.5, the full adjustment reduced it by 6.6. The effects cannot simply be added, because the two rules interact: the Bitcoin rule continues with holdings that the equity–bond rule has previously changed, and vice versa. If the Bitcoin rule is added to the equity–bond rule (P3 versus P1), its effect is 12.4 rather than 14.5 percentage points. This difference is the interaction of −2.0 percentage points. It is not an unexplained residual but an expression of the interplay of the two rules.

The equity–bond adjustment reduced the return in a period in which equities rose considerably more than bonds; in phases of an increased equity weight, the reset reduced the equity share. According to a post hoc analysis, it was at the same time associated with lower volatility. This is a finding of this period and not a property of the method.

In P3, Bitcoin contributed 6.5 percentage points more to profit than under buy and hold. This higher Bitcoin profit contribution was more than offset by lower contributions from equities and bonds; the total return was 6.6 percentage points lower. How much the adjustment of one asset changes the profits of the others is shown by P2: Bitcoin contributed 6.6 percentage points more there, the equity contribution rose by 8.3, the bond contribution fell by 0.4. The effect of the Bitcoin rule on the overall portfolio, plus 14.5 percentage points, is therefore more than its additional Bitcoin profit. The rule effect cannot be read off the asset the rule targets.

What the result depends on

Start date

The main calculation begins on 29 December 2017. As a counter-check, annual rebalancing was started at five further year-ends, in each case running to 30 September 2026.

The effect of the equity–bond adjustment was negative at all six starts, between −3.3 and −21.6 percentage points. This is a sign-stable finding in the variants examined, not a general property. The effect of the Bitcoin adjustment, by contrast, changed sign and ranged from −26.5 to +14.5 percentage points. With a start at the end of 2018, the full adjustment reduced the total return by 50.9 percentage points; with a start at the end of 2021, it raised it by 0.3. The starting point shapes the result; the numbers alone do not show why. All six start dates are given in Appendix C.

Subperiods and rebalancing date

A division of the period also shows how much the result depends on the chosen time window. If it is split on 30 December 2022 into two subperiods, each with fresh target weights, the effect of the Bitcoin adjustment in the first was positive for all twelve possible month-end rebalancing dates and in the second negative for all twelve. The subperiods are of different lengths and are not independent samples. The rebalancing date alone can flip the sign of the overall effect: with a reset on the last trading day in March, the full adjustment was 5.2 percentage points above P0; with a reset in December, 6.6 below. Of twelve rebalancing dates, only March was positive. The individual values are in Appendix D (rebalancing dates) and Appendix E (subperiods).

End date with a fixed start

The following figure varies the end date with a fixed start on 29 December 2017. For each trading day, it shows how far the portfolio value of each rebalancing variant lay above or below that of buy and hold. From May 2019 to early February 2024, all four rebalancing variants were consistently ahead of buy and hold. After that, the gaps changed sign several times; at the end, all four were below. The figure supplements the study of different start dates but does not replace it: it does not start new subperiods with fresh target weights.

Execution

Execution also shifts the numbers. If the reset takes place only at the next closing price, the total return under annual rebalancing rises from 114.1 to 116.6%, under the narrower band it falls from 108.1 to 102.8 and under the wider band from 108.6 to 105.3%. The highest Bitcoin weight rises from 4.3 to 4.6% under the narrower band and from 9.6 to 11.1% under annual rebalancing; even with this execution, the highest Bitcoin weights under the band rules remain clearly lower. A general superiority of one rule does not follow: the differences between them depend on window, rebalancing date and execution. The counter-check is shown in Appendix F.

What remains

Rebalancing controls the allocation. Whether it raises or lowers the return depends on the market path and on implementation, and a higher profit contribution of one asset is not yet a return advantage of the rule. What matters for the mandate is that target weight, permitted deviation, trigger and trading scope fit together and that the return effect of a rule is assessed against a clearly named alternative.

Three questions for your own rebalancing rule

The study yields three questions that can be put to any rebalancing rule.

1. How far does the portfolio deviate? Recalculate the rule on historical prices: how high and for how long were positions outside the intended ranges, and what monitoring, response and escalation does the mandate provide for a breach?

2. What is traded in total? For a typical trigger day, list all purchases and sales and check them against the mandate requirements. Whether only the triggering position or all building blocks are reset is part of the rule.

3. Against which alternative is the return effect measured? In the performance discussion, state the benchmark explicitly, for example buy and hold. Selecting a rule by its backtest return does not hold up: if the sign changes when the start or the implementation shifts, a return advantage or disadvantage cannot be generalised.

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Context and limitations

The study design and evaluation rules were set down in writing before the calculations of this issue and frozen on 15 October 2026. The author was aware of earlier own calculations on rebalancing with other weights and other rules; they are not included in this issue. Fixed in advance were the weight, the five rules, the metrics, the four comparison portfolios, the subperiods, the twelve rebalancing dates, the five additional start dates and the counter-check on execution. Post hoc are the statement on the volatility of the equity–bond adjustment, the figures for the equity and bond weights at the highest Bitcoin weight, and the descriptive analysis of the return gaps with a fixed start and varying end date; no new portfolios were calculated for these. Compared with the issue “How to check whether a new strategy diversifies a portfolio”, currency (euros instead of US dollars), data frequency (daily instead of monthly data) and maximum drawdown (daily values instead of month-end levels) differ.

On the data basis: an accumulating global equity ETF without currency hedging, an accumulating, currency-hedged global bond ETF and the Bitcoin price in euros, in each case as daily closing prices. ETF returns are after fund costs, the Bitcoin series without assumed product costs. In the export of the bond series, five trading days in May 2019 were missing; the prices were supplemented from the exchange’s price history, and the cause of the gap is unresolved.

The calculations answer a question of allocation and return over a completed period. They are not a model allocation for a client portfolio and take into account neither implementability nor liquidity. The calculation includes the fund costs reflected in the ETF prices but no additional transaction costs and taxes of rebalancing. It shows trading volume and historical effects, but not the economically best way of implementation. Execution at the closing price of the trigger day is an idealised assumption. ETF and Bitcoin closing prices do not represent the same valuation point in time; even the counter-check with execution at the next closing price does not remove this. The twelve rebalancing dates and the start dates are not independent samples, and no statistical proof can be derived from a period of about nine years with few Bitcoin cycles.

Boris Jurczyk is the founder of 21Nexus Capital and is therefore economically connected to the topic of digital assets. 21Nexus Capital acts as adviser to a fund that invests, among other things, in digital assets.

This article is for information purposes only and constitutes neither investment advice nor a recommendation to buy or sell financial instruments or crypto assets. Crypto assets are subject to substantial price fluctuations; a total loss of the capital invested is possible. The figures shown refer to the period December 2017 to September 2026. Past performance is not a reliable indicator of future results.

Appendix A: Definitions

Total return: change in portfolio value from the start day to 30 September 2026, as a percentage of the initial value. Return per year: based on 8.75 years for the full period, otherwise on calendar days divided by 365.25.

Volatility: standard deviation of daily returns, multiplied by the square root of 252.

Maximum drawdown: largest decline in portfolio value from a previously reached peak, measured on daily values. The figure is not a loss relative to the initial capital.

Highest Bitcoin weight: largest weight of Bitcoin on all observation days, in each case before any trading on that day.

Observation days: trading days on which prices are available for the equity ETF, the bond ETF and Bitcoin (2,216 days, 2,215 daily returns). Rules are checked only on these days.

Adjustment dates: number of days on which a rule resets. No reset takes place on the last day of the period.

Turnover p.a. (share of the portfolio reallocated per year, one-sided turnover): sum of the amounts bought in adjustments across all three assets, that is, including equities and bonds, in each case as a percentage of portfolio value at the time of adjustment, converted to one year. The initial investment is not counted; the sales are of equal size and are not counted additionally.

Deviation duration: share of observation days on which the Bitcoin weight before trading was outside the corridor of 2 to 4% or 1.5 to 4.5% respectively, and the longest continuous sequence of such days. Calendar days are the span from the first to the last day of the sequence, not an unbroken breach duration.

Profit contribution: holding of an asset times price change, summed over all days, in percentage points of the initial value. The contributions add up to the total return. Rule effect: difference in total return relative to buy and hold, in percentage points.

Interaction: total return with full adjustment minus return of the equities-and-bonds-only variant minus return of the Bitcoin-only variant plus return under buy and hold.

Appendix B: Metrics of the five rules

Appendix C: All start dates

Appendix D: Twelve rebalancing dates

Appendix E: Subperiods

Subperiod A runs from 29 December 2017 to 30 December 2022, subperiod B from 30 December 2022 to 30 September 2026. Both begin with fresh target weights.

Appendix F: Execution at the next closing price

As a counter-check, a triggered trade is executed only at the next common closing price. At most one triggered adjustment order is held open at a time, and it is executed irrespective of the weight then current.

Appendix G: Risk metrics of the four comparison portfolios

This analysis was added after the protocol was fixed and is post hoc. In this period, the equity–bond adjustment was associated with lower volatility; this is a finding of this period and not a property of the method.

Appendix H: Data check

Data basis: daily closing prices of an accumulating global equity ETF without currency hedging, an accumulating, currency-hedged global bond ETF and the Bitcoin price in euros. ETF returns are after fund costs, the Bitcoin series without assumed product costs. Over the period, equity prices rose by 185.5%, bond prices fell by 3.9% and Bitcoin rose by 472.8%.

Common trading days: 2,216 days from 29 December 2017 to 30 September 2026. Rules are checked only on these days.

Data gap: In the export of the bond series, five trading days from 27 to 31 May 2019 were missing. The prices were supplemented from the exchange’s price history. The cause of the gap in the export is unresolved.

Checks performed: The buy-and-hold series was reconstructed directly from the prices; the deviation from the calculation series is zero. The sum of the profit contributions equals the total return. Return, volatility, maximum drawdown, highest Bitcoin weight, adjustment dates and share of days outside the corridors were recalculated as spreadsheet formulas from the daily series and do not deviate from the script values. Purchase volume, longest sequences outside the corridors, profit contributions, rebalancing dates, start dates and the execution counter-check were checked in an independent recalculation. All table values of this appendix were reconciled in full with the verification sheet.

Limits: The reset logic is implemented in the calculation script, not in spreadsheet formulas. The verification sheet contains the daily Bitcoin weights of the five rules, not the complete holdings and weights of all three assets.