Portfolio rebalancing calculator

How do you calculate rebalancing trades?

Add up what you hold, add any new cash, and multiply the total by each target weight. That gives each holding's target value. The trade for each holding is target value - value now: a positive number is a buy, a negative one a sale.

The default portfolio is worth $100,000: US stocks $54,000, international stocks $16,000, bonds $22,000 and cash $8,000, against targets of 50%, 20%, 25% and 5%. With $5,000 of new cash the total becomes $105,000, so the target values are $52,500, $21,000, $26,250 and $5,250.

Sales of $4,250 plus the $5,000 of new cash pay for $9,250 of buys, and every holding lands exactly on its target. With no new cash the same portfolio needs $7,000 of sales and $7,000 of buys. The targets in every example on this page are illustrations: the calculator works with whatever weights you set and does not suggest any.

Rebalancing with new cash only: no sales

Selling has costs, and in a taxable account it can create a gain to report. The alternative is to send new money only to the holdings below target. Choose New cash only and the calculator works out each holding's shortfall against its target and splits the cash across those holdings in proportion to their shortfalls, so every underweight holding closes the same share of its gap.

On the default portfolio, international stocks are $5,000 short and bonds $4,250 short, a total shortfall of $9,250. The $5,000 of new cash covers 54.05% of it: $2,702.70 goes to international stocks and $2,297.30 to bonds. Nothing is sold, so US stocks and cash stay where they are.

After the purchases the weights are 51.43%, 17.81%, 23.14% and 7.62%. The largest drift falls from 4.00 points to 2.62 points, now in cash, which only a sale or more new cash for the other holdings can reduce. The headline shows the share of the gap closed; the table shows the purchase for each holding.

How much new cash would rebalance without selling?

Enough to make the most overweight holding, measured against its own target, fit. Each holding needs a total portfolio of at least value now / target weight before it is at or under target. The largest of those figures, minus what you hold now, is the new cash that would rebalance everything with no sales.

On the default portfolio those figures are $108,000 for US stocks ($54,000 / 0.50), $80,000 for international stocks, $88,000 for bonds and $160,000 for cash ($8,000 / 0.05). The cash holding sets the bar: the portfolio would need to grow to $160,000, so $60,000 of new money. Enter 60,000 in the cash field on the New cash only tab and every target is reached exactly.

Notice why. A small target magnifies drift: cash is only 3 points over its 5% target, but it is 60% above its target value. When one holding has a 0% target and still holds money, no amount of new cash is enough, and the calculator says so.

What is portfolio drift, and when do portfolios get rebalanced?

Drift is the gap between a holding's weight now and its target, in percentage points. It appears because holdings grow at different rates: if shares rise faster than bonds, the share weight creeps up without you buying anything. The calculator shows the largest drift before and after the trades.

The SEC's Beginners' Guide to Asset Allocation, Diversification, and Rebalancing defines rebalancing as bringing your portfolio back to your original asset allocation mix. It describes two ways people time it: on a regular calendar interval, such as every six or twelve months, or only when an asset class's weight moves more than a set percentage. It also lists three ways to do it: sell what is overweight and buy what is underweight, buy more of what is underweight, or direct continuing contributions to the underweight categories.

The arithmetic of a percentage rule is easy to check here. In the default portfolio no holding has drifted by more than 4 points, so a rule that waits for a 5-point move would do nothing yet, while a 3-point rule would already act on US and international stocks.

Worked example in pounds: shares and bonds

A UK investor holds £70,000 in a shares fund and £30,000 in a bond fund, with targets of 60% and 40%. The mix has drifted 10 points. Rebalancing what is held means selling £10,000 of the shares fund and buying £10,000 of the bond fund.

Add £6,000 of new cash on the Buy and sell tab and the portfolio becomes £106,000: the targets are £63,600 and £42,400, so the trades shrink to a £6,400 sale and a £12,400 purchase. On the New cash only tab the whole £6,000 goes to the bond fund. That closes 48.39% of the £12,400 shortfall and leaves the bond fund at 33.96%, 6.04 points under target.

To rebalance fully with no sale, the portfolio would have to grow to £70,000 / 0.60 = £116,666.67, so £16,666.67 of new money. The same steps work in euros, dirhams or any of 24 currencies; values you type in the holdings list are never rescaled when you switch currency.

What if my target weights do not add up to 100%?

The calculator still works. It divides each target by their total so they share the whole portfolio, and a note under the result says so. For example, €30,000 in an equity fund, €15,000 in a bond fund and €5,000 in a money market fund, with targets of 50%, 30% and 10%, add up to 90%. Scaled, the targets become 55.56%, 33.33% and 11.11% of the €50,000.

The trades are then a sale of €2,222.22 from the equity fund and purchases of €1,666.67 and €555.56. If the missing 10% was meant to stay in cash, add a cash row with a 10% target instead, and the trades change to match what you meant. The table under the calculator always shows the targets it actually used.

How to calculate rebalancing in Excel or Google Sheets

Put the values in B2:B5, the target percentages in C2:C5 and any new cash in E1. Then, filled down from row 2:

• Target value: =C2/SUM($C$2:$C$5)*(SUM($B$2:$B$5)+$E$1)
• Trade: =D2-B2, where D2 holds the target value; negative means sell.
• Shortfall for the no-sales method: =MAX(0,D2-B2) in column F.
• Purchase with new cash only: =F2*MIN(1,$E$1/SUM($F$2:$F$5))

For the cash that would rebalance without selling, put =B2/(C2/SUM($C$2:$C$5)) in column G and use =MAX(G2:G5)-SUM(B2:B5). On the default portfolio these give the same figures as the calculator: sales of $4,250, buys of $9,250, purchases of $2,702.70 and $2,297.30 with cash only, and $60,000 for a no-sale rebalance.

Costs and tax when you rebalance

The SEC's guide says to consider whether the method of rebalancing you choose will trigger transaction fees or tax consequences. Every sale on the Buy and sell tab is a disposal: in a taxable account it can produce a capital gain, and the tax depends on your country and the account. The capital gains tax calculator estimates it for the United States, the United Kingdom, Canada and Australia.

Commissions, spreads and fund dealing charges also come off each trade. Small trades can cost more in charges than the drift they correct. The New cash only tab avoids sales altogether, and the fund fee calculator shows what the yearly charges on the funds themselves add up to over time.

Common mistakes and what this calculator leaves out

• Leaving new cash out of the total. Targets apply to the portfolio after the cash goes in.
• Reading drift as a percentage of the holding. A 3-point drift on a 5% target is a 60% overshoot in value.
• Forgetting holdings outside the account. If your targets cover several accounts, list every holding.
• Treating a sale as free. Charges and tax can make the cash-only method the cheaper route.
• Using stale values. Prices move; enter values from the same day.

The calculator rounds nothing, so a fund that trades in whole units will land slightly off target. It holds no prices and does not fetch your holdings, it does not model charges or tax on the trades, and it says nothing about what your targets should be. Those are yours to set.

Glossary

Target weight: the share of the portfolio you intend a holding to have. Asset allocation: how a portfolio is divided between kinds of investment. Drift: weight now minus target weight, in percentage points. Rebalancing: trading back to the target weights. Shortfall: how far a holding's value is below its target value. Overweight and underweight: above or below target.

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