Rebalancing premium is the additional compounded growth attributed to maintaining target portfolio weights as assets move relative to one another. For a quant, its meaning depends on the comparator: growth above the weighted growth of the constituent assets and outperformance of a buy-and-hold portfolio are different quantities. A positive first quantity does not guarantee a positive second one.
Rebalancing restores the allocation; the premium concerns its return consequences. A constant-mix strategy repeatedly restores fixed portfolio weights, while a buy-and-hold strategy lets them drift. The following ledger shows why that difference can help, and why it can also hurt.
Two flat assets, a growing portfolio
Start with one unit of capital, split equally between fictional assets A and B. Assume fractional holdings, reinvested distributions, no external flows, no costs or taxes, and a reset at unchanged prices after the first period. Returns are simple total returns over two equal-length periods; no annualisation is implied. The alternating example is adapted from Willenbrock (2011), §3.
| Asset | Period 1 | Period 2 | Two-period return |
|---|---|---|---|
| A | +25% | −20% | 0% |
| B | −20% | +25% | 0% |
Each asset ends where it started because . Buy and hold therefore finishes with the original one unit. The constant-mix portfolio earns
so its terminal wealth is : a 5.0625% cumulative return, or 2.5% compounded per period.
The reset is the crucial transaction:
| Holding value | After period 1 | Trade | After reset |
|---|---|---|---|
| A | 0.6250 | −0.1125 | 0.5125 |
| B | 0.4000 | +0.1125 | 0.5125 |
| Total | 1.0250 | 0 | 1.0250 |
Selling A funds buying B; the reset creates no wealth at execution. It changes the capital exposed to period 2: more is now in B before its recovery. One-way turnover, using pre-trade wealth, is . Counting both purchase and sale gives approximately 21.95% gross traded value relative to wealth. Neither percentage is a fee rate.
Change the second period and buy and hold wins
Keep the first period unchanged. Now let A rise 25% again and B fall 20% again. Resetting to 50/50 still earns 2.5% in each period, so constant mix again finishes at 1.050625. But buy and hold finishes at
a 10.125% cumulative return. The initial A holding grows into a larger portfolio weight, and its second gain benefits more capital. Rebalancing sold part of that continuing winner.
Original endpoint comparison with one costless 50/50 reset after period 1. The alternating scenario is adapted from Willenbrock (2011), §3; the persistent-return counterexample changes the second period. Connecting segments show period endpoints, not observed intraperiod prices.
The constant-mix advantage against buy and hold changes from +5.0625 to −5.0625 percentage points. This is a change in the supplied return path, not a different rebalancing rule. Neither scenario estimates expected alpha. Bernstein’s “Rebalancing: Practical Issues” likewise distinguishes a return increment above averaged asset growth from an actual comparison with an unrebalanced portfolio.
What “excess growth” measures
There is an exact finite-period log-growth identity behind the intuition. For fixed nonnegative weights summing to one and asset returns , define
The inequality follows from concavity of the logarithm. Summing over periods gives the constant-mix portfolio’s total log return minus the fixed-weight average of the assets’ total log returns. That reference is a weighted geometric basket of asset wealth relatives. It is not the wealth of the buy-and-hold portfolio, which is the weighted arithmetic sum of those wealth relatives. The persistent-return counterexample can therefore have positive log-growth gaps while constant mix underperforms buy and hold.
In a frictionless continuous-path diffusion model, Fernholz and Karatzas, equations (1.12)–(1.13), express the corresponding instantaneous log-growth drift as
Here is asset ’s instantaneous log-growth drift, and is its instantaneous covariance rate with asset . The second sum is portfolio variance per unit time. The excess growth rate is nonnegative for long-only weights; it can be zero when the assets have identical return shocks. It compares portfolio log growth with weighted asset log growth, and is not risk-free excess return or guaranteed benchmark outperformance.
This diffusion identity is exact within its model. Replacing its variance rates with sample variances of finite-period simple returns gives an approximation, not an exact backtest decomposition. Lower correlation, holding asset volatilities and weights fixed, can enlarge the excess-growth term; it does not settle the buy-and-hold comparison.
The premium must survive implementation
A usable claim states the assets, starting weights, horizon, reset schedule, return convention, comparator and cost basis. Persistent relative trends can favour drifting weights; reversals can favour the reset. Changing the rebalance frequency changes the trades and the return path sampled. More frequent trading does not establish a larger net premium.
Spreads, commissions, market impact and realised taxes can consume a gross benefit. Costs paid from the portfolio also reduce the capital available for subsequent returns, so the costless ledger cannot simply be treated as a net result. Transaction Costs and Implementation develops linear costs and no-trade regions; its public page is a preview and the full lesson requires membership. The relevant decision is whether restoring the chosen exposure justifies the trades under those constraints, rather than assuming that every reset earns a bonus.
Sources
- Scott Willenbrock — Diversification Return, Portfolio Rebalancing, and the Commodity Return Puzzle (2011), §§2–4: periodic constant weights, the alternating two-asset example, and the distinction from buy and hold. The ledger and counterexample above independently expand the example.
- Robert Fernholz and Ioannis Karatzas — Stochastic Portfolio Theory: an Overview (10 January 2008), Chapter I, equations (1.9)–(1.17): self-financing portfolios, covariance rates and the continuous-time excess-growth decomposition.
- William J. Bernstein — Rebalancing: Practical Issues (1997), “When It Doesn’t Work” and the closing frequency/cost discussion: the comparator, allocation drift and implementation trade-offs. Its historical tax rates and backtest returns are not used as current assumptions here.