# Regular amounts, a lump sum and rebalancing rules

> Investing at once vs in monthly parts, and rebalancing yearly, by a band or never: drift and drawdown.

- Course: [Long-Term Investing: Index Funds, Risk and Your Own Behavior](https://productovi.com/courses/long-term-investing.md)
- Module: Building the model portfolios
- Lesson 23/32, ~25 min
- Source: https://productovi.com/courses/long-term-investing/contributions-rebalancing

## All at once or bit by bit?

**Alex Tutor:** Early August at Zapas. The mixes are drafted, and now two practical rules are missing: how a user's first money goes in, and how each portfolio stays at its mix over the years.

**Ethan:** A beta user's two-year bank deposit just matured, and they want to put the \$12,000 in at once. Support says we should drip it in over a year to be "safe". Which is it?

**Grace:** I tested both on the Tessaro history. \$12,000 invested at once, or \$1,000 at the start of each of the first 12 months with the rest waiting in cash. Then ten years in world stocks.

**Grace:** Every start year from 1 to 31 gives one ten-year window, 31 windows in total. Money values are nominal.

**Dataset (CSV):** [Lump sum vs 12 monthly parts, 31 ten-year windows](https://productovi.com/datasets/long-term-investing/contributions-rebalancing/lump_vs_monthly.csv)

12,000 dollars at once vs 1,000 at the start of each of the first 12 months (the rest waits in cash at that year's cash rate); Tessaro World monthly returns, nominal; value after 10 years. lump_won = 1 if the lump sum ended higher. Synthetic data.

**Value after 10 years: lump sum vs 12 monthly parts**

| Start year | At once | Over 12 months |
| --- | --- | --- |
| 1 | 29896 | 26362 |
| 2 | 25301 | 27671 |
| 3 | 31277 | 31606 |
| 4 | 31242 | 31135 |
| 5 | 38956 | 35561 |
| 6 | 33848 | 33391 |
| 7 | 37013 | 34951 |
| 8 | 39345 | 39096 |
| 9 | 36085 | 31596 |
| 10 | 31136 | 31515 |
| 11 | 37683 | 37977 |
| 12 | 27622 | 25411 |
| 13 | 16876 | 16070 |
| 14 | 19102 | 17995 |
| 15 | 19254 | 19800 |
| 16 | 21692 | 19102 |
| 17 | 19019 | 17484 |
| 18 | 14525 | 15331 |
| 19 | 16501 | 15765 |
| 20 | 17869 | 17093 |
| 21 | 15117 | 17776 |
| 22 | 23649 | 27884 |
| 23 | 35023 | 29280 |
| 24 | 34694 | 32442 |
| 25 | 33516 | 33671 |
| 26 | 27982 | 28928 |
| 27 | 21064 | 21011 |
| 28 | 22788 | 22605 |
| 29 | 26713 | 24442 |
| 30 | 31936 | 31727 |
| 31 | 42069 | 38867 |

*x = the year the 12,000 dollars arrived (start of a ten-year window). Nominal dollars, synthetic Tessaro history.*

> **Exercise:** In 31 ten-year windows of the synthetic Tessaro history, investing \$12,000 at once ended higher than spreading it over 12 months in 21 windows. In what percent of the windows did the lump sum win? Round to one decimal.

**Sofia:** Two out of three for investing at once. Then why does spreading feel so much safer?

**Grace:** Because of the windows it wins. Look at a start in year 22, just before the bottom of the crash.

**Grace:** At once: \$23,649 after ten years. Spread over twelve months: \$27,884. And look at the first twelve months: the at-once money was down to about \$8,400, the spread money was close to \$10,000.

> **Exercise:** In the synthetic Tessaro history, \$12,000 that arrived at the start of year 22 was worth \$23,649 after 10 years if invested at once and \$27,884 if spread over 12 months. By how many dollars did spreading win in this window?

> **Exercise:** Which text can Zapas honestly show to a user who is about to invest \$12,000 in one go?

**Sofia:** And most users don't have a lump sum at all. They put in part of each salary.

**Grace:** Right, and for them there is no choice to make: the money arrives monthly, so it goes in monthly. The lump-sum question is only for people who already hold the cash today.

## Keeping the mix

**Ethan:** Fine. Second rule: rebalancing. I ran a 60/40 that was never rebalanced: \$23,453 after forty years. Rebalanced every year: \$19,960. Why would we rebalance at all?

**Grace:** Check what the never-rebalanced portfolio became. Stocks grew faster, so their share kept rising. By year 20 it was 81.8% stocks, by year 40 88.5%.

**Dataset (CSV):** [A 60/40 started with 1,000 dollars: three rebalancing rules](https://productovi.com/datasets/long-term-investing/contributions-rebalancing/rebalancing.csv)

Nominal, year-end. never = never rebalanced; yearly = back to 60/40 every year-end; band = back to 60/40 only when stocks are more than 5 points away from 60%. *_stocks_pct = stock weight at year-end before any rebalance; band_rebalanced = 1 if the band rule rebalanced that year. Synthetic data.

**Share of stocks in a 60/40: never rebalanced vs a 5-point band**

| Year | Never rebalanced | 5-point band |
| --- | --- | --- |
| 1 | 63.7 | 63.7 |
| 2 | 61.3 | 61.3 |
| 3 | 63.6 | 63.6 |
| 4 | 60.3 | 60.3 |
| 5 | 62.8 | 62.8 |
| 6 | 64.3 | 64.3 |
| 7 | 67.7 | 67.7 |
| 8 | 69.3 | 61.8 |
| 9 | 71.7 | 64.5 |
| 10 | 70.6 | 63.2 |
| 11 | 70.9 | 63.6 |
| 12 | 72.6 | 65.4 |
| 13 | 74.7 | 62.6 |
| 14 | 76 | 64.2 |
| 15 | 75.5 | 63.6 |
| 16 | 77.8 | 66.5 |
| 17 | 81 | 64.6 |
| 18 | 80.2 | 63.4 |
| 19 | 79.5 | 62.5 |
| 20 | 81.8 | 65.8 |
| 21 | 76.2 | 51.8 |
| 22 | 67.4 | 49.2 |
| 23 | 71.1 | 64.1 |
| 24 | 73.4 | 66.7 |
| 25 | 75.6 | 62.8 |
| 26 | 75.3 | 62.3 |
| 27 | 75 | 62 |
| 28 | 75.5 | 62.6 |
| 29 | 76.8 | 64.2 |
| 30 | 75.1 | 62.1 |
| 31 | 77.9 | 65.6 |
| 32 | 77.6 | 59.6 |
| 33 | 80.7 | 64.1 |
| 34 | 81.8 | 65.7 |
| 35 | 81.2 | 59.1 |
| 36 | 78.8 | 55.5 |
| 37 | 79.1 | 55.9 |
| 38 | 82.5 | 61.2 |
| 39 | 85.7 | 66.8 |
| 40 | 88.5 | 65.7 |

*Stock weight at each year-end before any rebalance. The target is 60%. Synthetic Tessaro history, years 1–40.*

> **Exercise:** A 60/40 portfolio started in year 1 and was never rebalanced. What share of it was in stocks at the end of year 40, in %?

**Sofia:** So the extra \$3,493 came from quietly holding a much riskier portfolio?

**Grace:** Yes. Its largest fall was −33.8%, against −22.8% for the rebalanced ones. The user picked 60/40 and got a different product.

![A 60/40 never rebalanced ends at 23,453 dollars but at 88.5% stocks and a −33.8% fall; rebalanced yearly or by a 5-point band it ends near 20,000 with a −22.8% fall.](https://productovi.com/courses/long-term-investing/diagrams/m6-l3-three-rules.png)

*The extra money came from a riskier mix than the one chosen.*

> **Exercise:** The never-rebalanced 60/40 ended with \$23,453 against \$19,960 for yearly rebalancing, so never rebalancing is the better rule for users who chose 60/40.

**Sofia:** But rebalancing means selling what has done well and buying what has lagged. Users will hate that.

**Grace:** That's exactly why the app should do it by rule, not by asking. In year 22 the band rule bought stocks near the bottom. Few people would press that button themselves.

**Ethan:** OK, we rebalance. But 39 trades in forty years means 39 rounds of spreads and possibly taxes. Isn't that a cost too?

**Grace:** It is. The 5-point band rebalanced only 10 times, when stocks moved more than 5 points from 60%. It ended with \$20,173 and the same −22.8% largest fall.

> **Exercise:** Zapas compares rebalancing rules for a 60/40. Which statements does the data support? Select all that apply.

**Ethan:** Fine. Write me the two rules for the product spec, so support stops improvising.

> **Exercise:** Write the two rules for Zapas's product spec in 3–4 sentences: (1) how a lump sum goes in, and (2) how portfolios are rebalanced. Back each rule with one number from this lesson's data.

**Grace:** That's the spec. Next we put it all together: three model portfolios and the questions that place each user.

> **Key ideas**
>
> - A lump sum invested at once ended higher in 21 of 31 ten-year windows (67.7%); spreading over 12 months mainly shrinks the worst early loss, as with a start just before the year-22 bottom (about −17% vs −30% after a year; \$27,884 vs \$23,649 after ten).
> - Mixes drift: a 60/40 never rebalanced reached 81.8% stocks by year 20 and 88.5% by year 40.
> - Never rebalancing ended higher only by becoming riskier: largest fall −33.8% vs −22.8%.
> - A 5-point band kept the same risk as yearly rebalancing with 10 trades instead of 39.
> - Make both rules automatic; neither should depend on a forecast.

> **Educational, not advice**
>
> This lesson explains how investing works; it doesn't tell you what to buy. Investments can fall and you can get back less than you put in. Check the current rules where you live or ask a licensed professional.

- Previous lesson: [Stocks vs bonds: risk capacity, tolerance and the job you have](https://productovi.com/courses/long-term-investing/stocks-bonds-mix.md)
- Next lesson: [Case: three model portfolios and the onboarding questions](https://productovi.com/courses/long-term-investing/case-model-portfolios.md)

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