The trade formula on one portfolio after a good year, rebalancing with new money instead of selling, a 5-point band, and what rebalancing did through a 30 per cent fall.
To rebalance, multiply each target weight by the portfolio's current total and trade the difference from what you hold. A 100,000 portfolio set at 60 per cent stocks and 40 per cent bonds, after stocks rise 20 per cent and bonds 2 per cent, is worth 112,800 with 63.83 per cent in stocks: sell 4,320 of stocks and buy 4,320 of bonds. Or put 7,200 of new money into bonds and sell nothing.
Worked in full in Stock Market Investing for Beginners by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A 60/40 split is a decision about risk. Markets change it without asking: every year in which stocks beat bonds moves the portfolio towards stocks, and after a long run of good years a 60/40 investor can be holding 75/25 without having decided to. Rebalancing is the trade that puts the decision back. The arithmetic is short, and worth doing once by hand.
| Input | Value |
|---|---|
| Starting value | 100,000 |
| Target: stock index fund | 60%, 60,000 |
| Target: bond index fund | 40%, 40,000 |
| Stock return over the year | +20% |
| Bond return over the year | +2% |
| Tolerance band | 5 points either side |
Stocks: 60,000 × 1.20 = 72,000
Bonds: 40,000 × 1.02 = 40,800
Total: 112,800, a 12.8 per cent year
Stock weight: 72,000 ÷ 112,800 = 63.83%; bond weight 36.17%
Trade = target weight × current total − current holding
Stocks: 0.60 × 112,800 − 72,000 = 67,680 − 72,000 = −4,320 (sell)
Bonds: 0.40 × 112,800 − 40,800 = 45,120 − 40,800 = +4,320 (buy)
Excel, holdings in B2:B3, targets in C2:C3: =C2*SUM($B$2:$B$3)-B2, filled down
The two trades always sum to zero: the money from the sale buys the other fund. A positive number means buy, a negative one sell. After the trade the portfolio is 67,680 and 45,120: 60/40 again, at the new total.
Selling can trigger tax and dealing costs. A saver adding money anyway can send it to the underweight fund. The amount needed solves (bonds + X) = 40% × (total + X):
X = (target weight × total − holding) ÷ (1 − target weight)
= (0.40 × 112,800 − 40,800) ÷ 0.60 = 4,320 ÷ 0.60 = 7,200
New total 120,000: 72,000 stocks and 48,000 bonds, exactly 60/40
Note that it takes 7,200 of contributions to do the work of a 4,320 switch, because new money also raises the total. For a small drift, a few months of contributions usually suffice.
Rebalancing every month is busywork, and costs money. A common rule is to act only when a weight leaves a band, here 55 to 65 per cent in stocks. The table applies it to five possible years from the same 100,000 start.
| Stocks / bonds | Total | Stock weight | Stock trade to 60% | Outside 55 to 65? |
|---|---|---|---|---|
| +10% / +2% | 106,800 | 61.80% | −1,920 | no |
| +20% / +2% | 112,800 | 63.83% | −4,320 | no |
| +30% / +2% | 118,800 | 65.66% | −6,720 | yes |
| −20% / +2% | 88,800 | 54.05% | +5,280 | yes |
| −30% / +3% | 83,200 | 50.48% | +7,920 | yes |
On the band rule the worked year, at 63.83 per cent, would wait; an annual-date rule would trade it. Both are defensible. What matters is choosing the rule before the market moves, so the decision is not made in the moment.
The last row is the hard one. Stocks have fallen 30 per cent, and rebalancing means buying 7,920 more of them. Suppose stocks then recover the 42.86 per cent needed to get back to where they started, and bonds earn another 3 per cent.
| Policy | Stocks after the fall | Bonds after the fall | Value after recovery |
|---|---|---|---|
| Hold, no rebalancing | 42,000 | 41,200 | 102,436 |
| Rebalance to 60/40 at the bottom | 49,920 | 33,280 | 105,593 |
The rebalanced portfolio ends 3,157 ahead, because it bought stocks cheaply and sold bonds that then rose only 3 per cent. It also ends at 67.54 per cent stocks and would rebalance again, this time selling. If stocks had fallen a further 20 per cent instead of recovering, the rebalanced portfolio would have been 1,822 behind. Rebalancing does not know which way the market goes next. It keeps the mix you chose, which is why it is best written as a rule in advance.
Trade = target weight × total − holding: on 112,800 that is a 4,320 switch from stocks to bonds, or 7,200 of new money into bonds. Choose an annual date or a band, write it down, and follow it in both directions. The book's rule for a falling market, written before the fall, is one of the twelve working documents on the free companion page for this book.
Once a year, or when a weight drifts outside a band, are the two common rules. With a 5-point band on a 60/40 target, a 100,000 portfolio rebalances when stocks pass 65 or fall below 55 per cent: a 30 per cent rise in stocks takes the weight to 65.66 per cent and triggers it; a 20 per cent rise, at 63.83, does not.
Yes, by directing new contributions to the underweight asset. The amount is (target weight x total minus holding) divided by (1 minus target weight). In the worked example bonds at 40,800 of 112,800 need 7,200 of new money to return to 40 per cent, which avoids selling and any tax on the gain.
Not reliably. It controls risk by keeping the mix you chose. In a fall and full recovery it helps: in the illustration the rebalanced portfolio ends at 105,593 against 102,436. If stocks keep falling instead, a further 20 per cent drop leaves it 1,822 behind. Its purpose is to keep the risk you signed up for.
This article is one calculation from Stock Market Investing for Beginners. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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