Keeping the mix where the plan put it
Markets move the allocation for you. Rebalancing trades it back, and the trade size is the gap between what the client holds and what the target says on today's value.
- Compute the drifted weight after a market move
- Size the trade that restores the target
- Find the new money that rebalances without selling
- Find the equity return that triggers a rebalancing band
The intuition
A client's 60/40 portfolio has a good year: equities rise 20%, bonds go nowhere. Nobody traded, but the portfolio is now 64/36. The client did not decide to take more risk; the market decided for them. Rebalancing is the discipline of trading back to the agreed mix, which means selling what has done well and buying what has done badly. It feels wrong, which is exactly why it has to be a rule rather than a judgment call.
The arithmetic is two lines. Grow each sleeve by its return; the drifted weight is equities over the new total. The trade is what is held less what the target weight says on the new total. Two refinements matter in practice: new contributions can close the gap without selling anything (cheaper in a taxable account), and a band turns the rule into a trigger: rebalance when the weight drifts more than so many points, which the same arithmetic run backwards turns into the equity return that trips it.
Drifted weight = equities after the move ÷ total after the move. Trade = equities held − target weight × total (positive means sell equities). New money to rebalance without selling = the total at which the overweight sleeve is exactly on target, less today's total. Equity return that drifts the weight from w to w + b with bonds flat = (w + b)(1 − w) ÷ (w(1 − w − b)) − 1.
Why it works
- The conventions here: two sleeves start exactly on target; each earns a stated return over the period; no income, tax or trading costs. Rebalancing restores the target weights on the new value. Cash-flow rebalancing adds money only to the underweight sleeve. The band ask holds bonds flat and uses a five-point band.
- Rebalancing is about risk, not forecasts. Selling equities after a rise is not a prediction that they will fall; it is keeping the risk where the plan put it. Buying after a fall is the same rule in the other direction.
- The trade is a gap on today's value. Target equity is the target weight times the new total, not the old one. A common slip is to rebalance to the old dollar amounts.
- New money rebalances without a sale. Hold the overweight sleeve fixed and ask what total would make it exactly its target weight; the difference is the contribution needed. It takes more money than the sale would, so contributions close small drifts, not large ones.
- Bands turn a chore into a trigger. Rebalance when the weight is more than so many points off target. Bonds flat, the equity return that trips a band comes from the ratio of the two sleeves: the ratio needed over the starting ratio, less one.
- Weights near 50% drift fastest per unit of relative performance, so the same five-point band is reached after a smaller move for a 50/50 portfolio than for a 70/30 one.
| Equities: $600,000 × 1.20; bonds: $400,000 | $720,000 and $400,000, total $1,120,000 |
| Drifted weight: 720,000 ÷ 1,120,000 | 64.29%, 4.29 points overweight |
| Trade: 720,000 − 60% × 1,120,000 | sell $48,000 of equities, buy bonds |
| New money instead: 720,000 ÷ 60% − 1,120,000 | $80,000 into bonds |
| Equity return that trips a 5-point band: (65% × 40%) ÷ (60% × 35%) − 1 | 23.81% |
The contribution route needs $80,000 against a $48,000 sale, because it can only add to the underweight sleeve.
The formulas
Grow each sleeve, add them up.
Equities over the new total.
Held less target on today's value; positive means sell equities.
The total at which the overweight sleeve is on target, less today's total.
The ratio of sleeves needed over the starting ratio.
Worked example
Target equity is the target weight times today's total. The trade is what is held less that. The follow-up is the client's objection, and the answer.
See it move
Same client and the same target. Change each sleeve's return over the year, the target weight and the size of the portfolio.
- Raise the equity return. The drifted weight rises and the trade grows: more to sell, or less to buy.
- Raise the bond return. The drifted equity weight falls, because the other sleeve grew.
- Set the two returns equal. The drifted weight lands exactly on the target and the trade is zero: drift comes from the difference between the sleeves, not from the market as a whole.
- Change the size of the portfolio. The weights and the band trigger stay where they are; the dollar figures scale.
Run it backwards
The policy says rebalance when the equity weight drifts five points above target. Bonds flat, what equity return trips it?
With bonds flat the weight depends only on the ratio of the sleeves. The ratio at the trigger weight over the starting ratio is the growth factor equities need; less one, it is the return.
The follow-up compares two targets: the same band trips after a smaller move for a 50/50 portfolio than for a 70/30, because weights near a half move fastest.
Traps
Say it in the interview
“Why rebalance, and how do you decide the trade?”
Check yourself
4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.
Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.
- Drifted weight = equities after the move ÷ total after the move.
- Trade = held − target weight × today's total.
- New money rebalances without selling, but needs more dollars than a sale.
- A band is a trigger: bonds flat, it converts into an equity return.