Somewhere in the 7th tab of my 2nd spreadsheet, I realized that cutting back to part-time at work would still grow my portfolio at 2/3 the rate of remaining full-time. Is this even a thing, or is my math beyond saving?
Eventually, the market will grow your portfolio faster than you can.
Coast FI
Coast FI (Financial Independence) is a version of FIRE (Financial Independence Retire Early) where someone stops actively saving for retirement and only works enough to cover expenses. No more saving. This process has the market growing an existing retirement portfolio over time until it reaches the standard 25x target annual expenses.
Suppose you’re 0 < q \leq 1 percent of the way to covering your annual expenses, E, with your retirement portfolio \mathbb{X}.
\mathbb{X} = q\cdot25\cdot ELet’s expect it’ll take N years for that to grow at an inflation-adjusted annual rate of r.
\begin{darray}{rcl}25\cdot E &=& \mathbb{X}\cdot(1+r)^N\\\\&=&q\cdot 25\cdot E\cdot(1+r)^N\\\\\iff\hspace{1cm}\frac{1}{q} &=&(1+r)^N\\\\\iff\hspace{1cm}N&=&\frac{-\ln(q)}{\ln(1+r)}\end{darray}Simplifying things slightly, let’s again use continuously compounding interest.
\frac{1}{q} = e^{r\cdot N}~~\iff~~N=-\frac{1}{r}\ln(q)~~~~~\Leftarrow\textrm{Coast FI time estimate}Notice that as q\to1, the time estimate N\to0 exactly as you’d hope.
q-FI
We already discussed an example in an earlier post about reaching “Half FI”. Let’s further overthink the concept and generalize it. We’ll be able to use the resulting math as a comparison to the Coast FI equation above. This will give us a framework to better decide when it’s time to shift into neutral.
Recall that the savings rate p can be recovered from a savings ratio R as the following.
p=\frac{R}{R+1} = \frac{\textrm{savings}}{\textrm{savings}+\textrm{expenses}} = \frac{\textrm{savings}}{\textrm{net income}}When your portfolio frees up \mathbb{X}/25 = q\cdot E every year, then your savings increases by that amount. Your effective savings rate updates to reflect that in a very natural way.
p'=\frac{R+q}{R+1} = \frac{\textrm{total savings}}{\textrm{original savings}+\textrm{expenses}} = \frac{\textrm{total savings}}{\textrm{net income}}When you’re half FI, you’re exactly in the q=\frac{1}{2} case using the terminology above. Our earlier treatment claimed the effective savings rate for q=\frac{1}{2} was p'=\frac{1+p}{2} or the weighted average of your actual savings rate and 100\%. Using the effective savings rate update above, we can now prove it.
p'=\frac{R+q}{R+1} = \frac{\frac{p}{1-p}+q}{\frac{p}{1-p}+1} = \frac{\frac{p}{1-p}+q\cdot\frac{1-p}{1-p}}{\frac{p}{1-p}+\frac{1-p}{1-p}} = p + q(1-p) = q + (1-q)pThus, when you’re q-FI, your current approach needs only N more years to reach full 100\%-FI.
\begin{darray}{rcl}N &=& -\frac{1}{r}\cdot\ln\left(\frac{R+q}{R+1}\right)\\\\&=&-\frac{1}{r}\ln(q+(1-q)p)~~~~~\Leftarrow\textrm{Full FI time estimate with any }R\end{darray}Talk about pretty; what happens when R=0=p? When you’re beyond saving, the equation collapses into the coast FI estimate N=-\frac{1}{r}\ln(q).
Shifting Gears
Ok, the easy part is done. We can estimate time to completion for both your status quo savings rate and switching to coast FI. Using r=4\% everywhere, we can think in more concrete terms. When is the right point in the journey (if any) to make the switch? Stay on the current path for this long?
N_R=-25\ln\left(\frac{R+q}{R+1}\right)Or switch to a much less demanding gig that barely covers the current bills (switch to R=0) for this long?
N_0=-25\ln(q)Horseshoes and hand grenades
How much time does making this switch add to your journey? It’s not obvious just from looking at the equations. The savings ratio R really complicates this question. Let’s look at comparisons for a few values of R.
Python to generate the above
import matplotlib.pyplot as plt
from math import log as ln
step = .001
x = [x * step for x in range(1,int(1/step))]
def fi(x, R=0): return [-25*ln((R+q)/(R+1)) for q in x]
fig, ax = plt.subplots()
ax.plot(x, fi(x), ‘k–‘, label=’Coast FI, R=0’)
for R in [0.1, 0.25, 0.5, 0.75, 1, 1.5, 2, 2.9, 3]:
ax.plot(x, fi(x, R), label=(‘R=%3.2f’%R))
legend = ax.legend(loc=’lower left’, fontsize=’x-large’)
plt.ylabel(‘Years till Full FI’)
plt.xlabel(‘Values of q’)
plt.axis((0,1,0,10))
plt.show()
As you can see, the time difference for the higher savings ratios compared to coast FI (e.g. bottom line R=3 vs top dashed line R=0) is quite large. In those cases, your hard work and willingness to sacrifice a ton of present-day consumption is doing most of the heavy lifting in growing your portfolio. Giving up your fire hose of savings every month really sets you back a long time.
On the other hand, someone with a relatively low savings rate relies on the market to do most of the heavy lifting over time so an eventual switch to coast FI has a much smaller impact. This is a relatively unsatisfying place to be, however, since a very small R value isn’t a very big difference compared to shifting to R=0. But at least the change in time to completion is smaller (e.g. top solid line R=0.10 to top dashed line R=0)
So nobody wins. High savers are stuck. Low savers can’t go much lower.
People and places
Nonsense! These are options, and often good options. If the current job sucks, these estimates show for sufficiently large q, changes in your savings rate no longer matter. Grind in the beginning so you can coast eventually.
Looking again, the difference between R=0.1 and R=0 is pretty short. It’s under a year for everything visible on the plot. Alternatively, the difference between R=3 and R=2.9 is almost too small to perceive. As usual, a high savings rate buys you a ton of flexibility. Accepting a more enjoyable job for a bit of a pay cut no longer moves the needle as your q begins approaching 100%.
Time and tempo
If you like your current job, but it’s just too much, then you have other options. Switching to part-time frees up a ton of time during the week and probably provides the majority of what most FIRE folks are seeking. Contractors can work fewer hours. People who are paid piecemeal can work at a more relaxed pace and better enjoy the journey. You can negotiate fewer responsibilities or more vacation time for lower pay.
Business owners can cut the 80% of their customers that typically result in 20% of the total profit or the 10% of their customers that result in 90% of the headaches. Or both!
Compared to the beginning
As q gets larger, p' = q + (1-q)\cdot p is dominated by the q term while (1-q)\cdot p matters less and less. Contrast that to the beginning of your journey, where q was small and the calculation of p' was dominated by the (1-q)\cdot p term. Large savings rates are hugely beneficial in the beginning, but they matter substantially less near the end. Grind in the beginning so you can coast later.
Post-FI
We have still more use cases. Suppose you’re already at lean FI, but decide you want more for your future self. You can coast FI your way out of lean FI into a fatter FI with at least a 4% pay increase every year. You’re beyond saving but still growing your future.
Another variation is at the next market crash. Rather than drawing from your portfolio at lower valuations, get back to work. If you coast FI during the lower period, then you’re supercharging your future returns. With a deep and protracted enough market downturn, you could turn lean FIRE into chubby FIRE by simply coasting.
The reason we use conservative withdrawal rates like 4% is because of the risk of market downturns (sequence of returns risk). Anyone willing to switch gears back to coast FI during a downturn can almost certainly utilize a higher withdrawal rate in good times.
Summary
Both high and low savers can make small changes. Given your q value is what it is, simply plug in the proposed R or p values (even 0) to compare your options.
\begin{darray}{rcl}N&=&-25\ln\left(\frac{R+q}{R+1}\right)\\\\&=&-25\ln(q+(1-q)p)\end{darray}Usually, I reserve the phrase “beyond saving” for my self-deprecating humor, but in this case, it’s a very cozy place to be. The working world provides a wealth of benefits when you’re there by choice. You can comfortably choose roles that align with your interests, skills, values, schedule, friends, hobbies, location, investment objectives, and on and on. Given that, you’ll often find yourself in a position to provide much more value to your organization than anyone who’s in constant fear for their job.
For anyone embarking on the journey to achieve their own financial independence, they’ll find a maze of options in front of them. One of those options is to eventually relax and let Mr. Market complete the task.