Case 030Rebalancing and driftHard

Compare annual calendar rebalancing with 5-point threshold bands for a 60/40 portfolio over five given years of equity returns. Which rule trades more, which ends higher, and what does that tell you?

The situation

A model portfolio starts at Rs 100, 60% equity and 40% debt. Over five years equity returns plus 30%, minus 20%, plus 25%, plus 5% and minus 15%. Debt returns 7% every year.

Rule one, the calendar: at every year end, trade back to 60/40. Rule two, the band: at every year end, look at the equity weight and trade back to 60/40 only if it has moved outside 55% to 65%. Ignore costs and tax for the first pass.

Your task

Track the equity weight under each rule, count the trades, and give the ending value of each. Then say what the result does and does not prove.

Quick check

How many times does the band rule trade over the five years?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

The calendar trades 5 times and ends at 128.2; the band never trades and ends at 125.7. The zig-zag path rewarded the calendar: it sold equity after the rises and bought after the falls. That is a feature of this path, not proof the calendar is better. On a steady rising path the band trades less and ends higher. Bands trade when drift is large; calendars trade whether or not it is.

Step 1How do you track the weight without losing the thread?

Keep two numbers per year, equity and debt, and grow each by its own return. Year one: equity 60 becomes 78, debt 40 becomes 42.8, total 120.8, so equity is 64.6% of the portfolio. The calendar resets to 60/40 every year whatever the weight; the band looks at the weight and usually does nothing. A thermostat set to switch on only outside a comfort range runs less often than a timer that switches on every hour.

YearEquity returnCalendar weight before tradeCalendar tradeBand weightBand trade
1+30%64.6%5.5264.6%none
2-20%52.9%7.8357.7%none
3+25%63.7%4.7461.4%none
4+5%59.5%0.6261.0%none
5-15%54.4%7.2255.4%none
End value128.23125.72
Rs, from a start of Rs 100. The calendar makes 5 trades turning over Rs 25.9 and ends at Rs 128.23; the band portfolio stays between 55.4% and 64.6% equity, never trades, and ends at Rs 125.72.
Equity weight at each year end, before any trade50%55%60%65%StartY1Y2Y3Y4Y565% band edge55% band edgeCalendar: drifted weight, then reset to 60%. 5 tradesBand rule: 0 trades, never left the band
The calendar resets to 60% after every year, so it trades 5 times even when the drift is under half a point, while the band portfolio drifts between 55.4% and 64.6% equity and never leaves the 55% to 65% band.
Step 2Why did the calendar end higher here?

Look at its trades. After plus 30% it sold Rs 5.52 of equity; after minus 20% it bought Rs 7.83; after plus 25% it sold again. Rebalancing earns money when returns reverse, because it sells what just rose and buys what just fell. This path reversed almost every year, so the rule that traded most captured most. The band, holding a portfolio that drifted up and back, simply rode the zig-zag and finished Rs 2.51 lower.

Step 3Does that make the calendar the better rule?

No, and this is the step interviewers want to hear. Run the same rules on a path of plus 20% every year. With no reversals, every calendar trade sells a rising asset to buy a slower one: the calendar trades 5 times and ends at 199.4, while the band trades 2 times and ends at 200.6. The winner depends on the path, which nobody knows in advance. What the band reliably does is trade less, which matters once costs and tax on realised gains enter.

Which rule ends higher depends on the path, not the rulePath in the case: zig-zag128.2Calendar5 trades, 26 turned over125.7Bands0 trades, 0 turned overbars start at 120, not zeroContrast path: +20% every year199.4Calendar5 trades, 21 turned over200.6Bands2 trades, 16 turned overbars start at 195, not zero
On the case's zig-zag path the calendar ends at 128.2 against 125.7 for the band, but on a steady plus 20% path the band ends higher, 200.6 against 199.4, with 2 trades instead of 5: which rule wins is decided by the path.

Say the limitation of the setup too. Checking the band only at year ends is generous to the calendar; a band watched monthly would likely have fired inside year one or year two, when equity spent time above 65%. The practical answer for a client is a band checked often, with a calendar review as a backstop, so the portfolio trades when drift is large and never drifts unseen for long.

Where candidates lose it

The first loss is arithmetic: rebalancing the band portfolio in year one because 64.6% looks close to 65%. Close is not outside. Once you trade there, every later number is wrong.

The second is declaring a winner from one path. The calendar won here by Rs 2.51 because the returns zig-zagged. Say which kind of path helps each rule, and the interviewer hears judgement instead of a lucky number.

What the interviewer asks next

  • Add a 0.5% cost per rupee traded and 12.5% tax on realised equity gains. Does the calendar still win the zig-zag path?
  • Would a 3-point band have traded, and in which years?
  • How would you rebalance using new cash from the client instead of selling?
  • Why do some advisers rebalance only halfway back to the target?

Company names and figures are illustrative.