Math for investing.
Savings rate to 25X expenses:
| Savings Rate(%) | Time in years |
|---|---|
| 5 | 66 |
| 10 | 51 |
| 15 | 43 |
| 20 | 37 |
| 25 | 32 |
| 30 | 28 |
| 35 | 25 |
| 40 | 22 |
| 45 | 19 |
| 50 | 17 |
| 55 | 14.5 |
| 60 | 12.5 |
| 65 | 10.5 |
| 70 | 8.5 |
| 75 | 7 |
| 80 | 5.5 |
| 85 | 4 |
| 90 | 3 |
| 95 | 2 |
| 100 | 0 |
source Assumptions: 5% real CAGR, 25X expenses
In Reddit format:
Savings Rate: Time in years
- 100%: 0 years
- 95%: 2 years
- 90%: 3 years
- 85%: 4 years
- 80%: 5.5 years
- 75%: 7 years
- 70% 8.5 years
- 65% 10.5 years
- 60%: 12.5 years
- 55% 14.5 years
- 50% 17 years
- 45%: 19 years
- 40%: 22 years
- 35%: 25 years
- 30%: 28 years
- 25%: 32 years
- 20%: 37 years
- 15%: 43 years
- 10%: 51 years
- 5%: 66 years
Expenses by withdrawal rate(WR):
The math: 1 / %WR * 100
4% WR: 1/4*100 = 25
Example in the table below is for $30,000/yr in retirement expenses
| Withdrawal Rate(%) | Expense Multiple | Example($30k) |
|---|---|---|
| 2% | 50 | $1,500,000 |
| 2.5% | 40 | $1,200,000 |
| 3% | 33.4 | $1,002,000 |
| 3.5% | 28.6 | $858,000 |
| 4% | 25 | $750,000 |
4%WR has historically been fine for US based retirements w/ a 60/40 AA for a 30 year long retirement, see Trinity Study & William Bengen's work.
Equities vs Bonds
Since 1794 to today over various time periods, equities have a X% chance of beating bonds[0]:
- 1 year: 56.2%
- 5 years: 61.7%
- 10 years: 65.0%
- 20 years: 65.7%
- 30 years: 68.0%
- 50 years: 68.4%
source: McQuarrie, Edward F., Stocks for the Long Run? Sometimes Yes. Sometimes No. (July 23, 2021). Available at SSRN: https://ssrn.com/abstract=3805927 or http://dx.doi.org/10.2139/ssrn.3805927
Calculating rate of return
use Modified Dietz
Expected Returns
A "normal" view, not including countries that lost a major world war, etc:
A quick look at one of the Credit Suisse Yearbooks yielded the list of ten countries below — showing real (inflation-adjusted), geometric average returns from 1900 to 2016:
| Stocks | Bonds | |
|---|---|---|
| Australia | 6.8% | 1.7% |
| Canada | 5.7% | 2.2% |
| Ireland | 4.4% | 1.6% |
| New Zealand | 6.2% | 2.1% |
| Norway | 4.3% | 1.8% |
| Spain | 3.6% | 1.8% |
| Sweden | 5.9% | 2.7% |
| Switzerland | 4.4% | 2.3% |
| United Kingdom | 5.5% | 1.8% |
| United States | 6.4% | 2.0% |
| AVERAGE | 5.3% | 2.0% |
So expecting 4-5%/yr real in equities and about half that in bonds seems reasonable. Or they way I say it, expect a touch above inflation for bonds and about 2X more in equities.
Personal Inflation Rate
I think calculating a PIR is interesting and can be useful for planning purposes in retirement.
Here is how I do it:
- Add up expenses from last year, labeled: last_year_expenses
- Add up expenses from this year, labeled: this_year_expenses
- Calculate the dollar amount difference you spent between the two years: this_year_expenses - last_year_expenses labeled: diff
- PIR = diff / this_year_expenses