The time that it takes someone to reach financial independence (FI) depends on heavily on 3 factors:
- savings rate
- portfolio returns
- accepted safe portfolio withdrawal rate
So why doesn’t it depend on how much income you make or how much you spend? I think the best way to explain this with some math. The time taken to reach financial independence can be defined by the following formula:
(Note 1)
For a household with the following information:
| Post tax income | $100,000 |
| Cost of living | $40,000 |
| Yearly savings | $60,000 |
| Safe withdrawal rate | 4% |
| Portfolio return | 7% |
We have:
Something to notice is that cost of living is divided by the yearly savings in dollars as shown below. This is why how much you earn doesn’t matter, it only matters what your cost of living is relative to your yearly savings i.e., savings rate. So, given the same savings rate the equation would yield the same number of years to FI regardless of whether income was $50,000, $100,000 or $10M. Of course, there’s a whole other topic about how much money is required for a ‘comfortable life’ and how higher incomes facilitate higher savings rates.
The following table shows the times taken to reach financial independence using a safe withdrawal rate of 4% for a given set of portfolio returns and savings rates. Disclaimer: the tables do not take into account transaction fees; portfolio management fees, inflation or taxes.
Observations
A household’s savings rate has a massive effect on the time it takes to reach financial independence. At a savings rate of 10% it would take about 40 years to reach financial independence at a portfolio return of 7.5% or 45.9 years at 6.00%.
Portfolio returns matter less as savings rates increase. At a 70% savings rate the difference in time taken to reach financial independence for portfolio returns of 1% p.a. vs 15% p.a. is less than 3.5 years (10.23 years vs 6.86 years).
Implications
If your savings rate is at the lower end of the scale (< 20%) then working to increase it will provide the most benefit from a risk to reward ratio. For example, a household with a savings rate of 10% with a portfolio return of 6% will take 45.9 years to achieve FI; by increasing their savings rate to 20% their time to reach FI drops by 12.5 years to 33.4 years with no additional investment risk. If this household wanted to make a similar time saving by increasing their portfolio returns only, they would need a return of about 10% and be subjected to far greater investment risk. As a reminder, more risk tends to imply a greater chance of failure.
If your savings rate is already high (>70%) then chasing higher portfolio returns yields minimal benefit for reducing your time to reach FI. Conversely there are minimal consequences to chasing higher returns as well, this gives you the option of putting a portion of your funds towards riskier investment options.
Safe withdrawal rates
As I’ve talked about before, a 4% safe withdrawal rate is based on numerous studies that show very high likelihoods (>95% chance) of diversified stock/bond portfolios lasting 30 years. If you are willing to accept more longevity risk, it is possible to reduce your time to FI by using a higher withdrawal rate. A study published in 1998 by Cooley, Hubbard and Walz found that a 75/25 stock/bond portfolio had an 86% chance lasting 30 years. This would mean that for a household with a 60% savings rate and 7% portfolio return they would be able to reach FI in 9.74 years vs 11.43 years in the previous example. The following table shows the years to FI at a 5% withdrawal rate:
Concluding thoughts
Hopefully these tables can provide you with a sort of quick reference guide to the time taken to reach financial independence. When looking at your own journey, remember that parameters like savings rates and portfolio returns are not set in stone, which means that you should model for a variety of different outcomes.
Engineer your freedom
References
Cooley, P, Hubbard, C, and Walz, D, 1998, Retirement Savings: Choosing a Withdrawal Rate That is Sustainable, Bierwirth Vol 10(1)
Notes
1. Formula is derived by solving for n in a geometric series