Where is the portfolio inflection point?

[aloevera1]

This was probably asked a million times but I can't find any relevant threads...

For those of us who likes visualizing their portfolio growth.

At which invested portfolio size did you start seeing the exponential portfolio growth?

Obviously, there is the market noise but the overall trend should be visible anyway.

Yes, I am looking at my graph and playing a guessing game here. :D

[daverobev]

Do you mean exponential, or just that the portfolio is large enough that its size is moved more by its own growth than your contributions?

[aloevera1]

I mean exponential. It should be coming from the compounding effect from the portfolio...

I attached the picture from the internet to illustrate what I mean (the black circle on the graph).

[neo von retorch]

exponential

• Of or relating to an exponent.
• Containing, involving, or expressed as an exponent.
• Expressed in terms of a designated power of e, the base of natural logarithms.
• Pertaining to exponents; involving variable exponents.
  "an exponential expression; exponential calculus; an exponential function."
• Changing over time in an exponential manner, i. e. increasing or decreasing by a fixed ratio for each unit of time.
  "exponential growth; exponential decay"
• A curve whose nature is defined by means of an exponential equation.

inflection point

• A moment of dramatic change, especially in the development of a company, industry, or market.

For me, it started when I invested my first dollar in an account that grew in value over time, and periodically paid dividends.

Dramatic changes have been due to things like selling a house and capturing the equity, and then investing that into equities.

I think you need to revisit @daverobev suggestion that you mean the growth began to exceed your contributions over a time period.

Your drawing captures an arbitrary point of continued acceleration, but does not define "exponential" nor "inflection point."


I've attached my 8 year history of investing. The earliest drop was spending money on a down payment for a house. Then you start to see larger market movements have dramatic effects in 2020. The most recent jump in value was selling a house and being able to invest the proceeds. Overall movements are more dramatic as the balance grows, as they are more influenced by market value, and less influenced by my slow and continual contributions.

[reeshau]

Do you mean exponential, or just that the portfolio is large enough that its size is moved more by its own growth than your contributions?

^ I think exactly of this point as perhaps the first inflection point in investing: when your stache starts growing more than the new cash you are putting in.

I also distinctly remember hitting $1M.  That big, round number was a long way off, for a long time.

The numbers have kept rolling in, even after FIRE.  Milestones are to be celebrated, but not like that one.  I don't think it's being numb or taking them for granted; more like, they are on schedule.  "Well, of course that happened.  The others did too, and we haven't really changed much."

[vand]

Compounded returns are not the same as exponential returns - your rate of growth is not increasing just because you are compounding over time.

Time itself is the exponent when growing wealth. 

But in a real life case study many high-earning + high-saving types here are probably getting to FI (ie 4% WR) mainly from their own efforts (ie money they put in themselves) rather than from the compounding of the money they put it.

at 7% real growth and 50% saving rate you get to FI after 16 years having put in 54% of the portfolio value yourself
at 7% real growth and 60% saving rate you get to FI after 11 years having put in 65% of the portfolio value yourself
at 7% real growth and 70% saving rate you get to FI after 8 years having put in 73% of the portfolio value

I know we have had better than 7% real returns over the last decade and this changes the numbers somewhat, but not by as much as you think, eg even at 10% real growth and 50% saving rate you still only get to FI after 13 years with 48% of the portfolio coming from your own contributions

(https://www.getrichslowly.org/building-wealth/ is a good read)

Also, as ERN pointing out in one of his SWR series, this presents an interesting lopsided contrast then to the "living off your portfolio" challenge that awaits the FIREE thereafter.  Whilst with high saving rates and a fair market you can get to FI with as little as 30-50% of your pot coming from internal growth, if you have 40 or even 50yrs of retirement ahead of you the pot will need to then generate a total time weighted return of some 200-300% over that period in order to provide the income required over such a long timeframe (sounds scary, but can be as low as an annualised 3% or so real growth over that timeframe provided those returns are perfectly consistent)

[Heckler]

I also distinctly remember hitting $1M.  That big, round number was a long way off, for a long time.

My understanding is that $1M is the point you start really comprehending what compound growth is.

[MustacheAndaHalf]

I mean exponential. It should be coming from the compounding effect from the portfolio...

I attached the picture from the internet to illustrate what I mean (the black circle on the graph).

If you slice that graph into first and second half, both halves will have an inflection point.  You could then draw one black circle in each graph... or cut those in half.  Growing at a rate of 1.1x looks the same at each time scale.

[Alternatepriorities]

As others have pointed to my inflection point it was not a point at which the rate of growth changed, that has been consistent aside from "market noise".

If I graphed out my net worth it would look something like neo von retorch's just with my unique jumps and dips from life events. My inflection points were the times when life events really drove home the idea that investing really was making a huge difference in my life.

The first time I used market gains to buy something was a new (to me) vehicle two years after college. The market paid for 1/3 of my purchase after just two years of gains. Yes it was lucky timing, but it was also the gains that gave me the opportunity.

Hitting 100k felt like a huge milestone and that was went the gains/losses from "market noise" started to show up against the contributions I was making. Both of these were before I'd ever heard of FIRE when I was just doing my own thing and thought I was the only one. At that time 100k in retirement accounts before the age of thirty meant "I have enough invested for a regular age retirement, I won't be old and broke, now I just need to figure out how I will get there" 100k also gave me the confidence I now call "polite no thank you" money. It's not FU money, but it was a mental shift.

Several others mentioned the 1M  mark and that was one I did note. Although long before that the markets yearly "noise" completely drowns out my own contributions many years. Think about it a 20% market swing on a 500k portfolio moves it up or down 100k. I wasn't earning that much in a year let alone contributing it so the market was really pushing me around at that point, but I'd been at it long enough by then to just stay the course.

The final inflection point for me was when I realized I should really include expected capital gains on my surveys that ask about my income... (think credit card application)

[314159]

I mean exponential. It should be coming from the compounding effect from the portfolio...

I attached the picture from the internet to illustrate what I mean (the black circle on the graph).

If you slice that graph into first and second half, both halves will have an inflection point.  You could then draw one black circle in each graph... or cut those in half.  Growing at a rate of 1.1x looks the same at each time scale.

Yeah, I'm with you on this one. Mathematically, this question doesn't make sense. At what point does f(x)=1.1^x or 1.05^x or 2^x or 3^x or 10^x start growing exponentially? Well, they are all growing exponentially for every value of x—they're exponential functions!

OP, it sounds like you're not looking for a mathematical answer. What sort of answer are you looking for? Or can you rephrase your question?

[mistymoney]

I mean exponential. It should be coming from the compounding effect from the portfolio...

I attached the picture from the internet to illustrate what I mean (the black circle on the graph).

If you slice that graph into first and second half, both halves will have an inflection point.  You could then draw one black circle in each graph... or cut those in half.  Growing at a rate of 1.1x looks the same at each time scale.

Yeah, I'm with you on this one. Mathematically, this question doesn't make sense. At what point does f(x)=1.1^x or 1.05^x or 2^x or 3^x or 10^x start growing exponentially? Well, they are all growing exponentially for every value of x—they're exponential functions!

OP, it sounds like you're not looking for a mathematical answer. What sort of answer are you looking for? Or can you rephrase your question?

Yes!

Math nerds, I think this was referring to more of an emotional/experiencial inflection point rather than a request for an algebra 101 tutorial.

[secondcor521]

I understand and agree with the technical answer the math nerds have given already.

OP, maybe here's some ways to look at it:

For round numbers, let's say your investments are growing by 10% a year.  When will that seem big?  Well, when you have $1000 in your investment account, 10% is $100 a year:  enough for a fast food meal each month if you use the app.  When you have $10,000,000 in your investment account, 10% is $1M a year:  enough (for most folks) to live on, give generously, and have to figure out estate planning stuff.

I've been retired for 8 years, so I don't know what the number is today, but let's say you can save $20K into your 401(k) annually.  $20K is 10% of $200K, so when you get to $200K then in an average year the market would match your contributions.  So maybe $20K is the answer to your question as to when it feels real.

Or maybe you have some other anchor in your mind - maybe you paid $10K for your first car.  The market sometimes goes up 1% in a day.  So one day you'll have $1M in your portfolio and you'll be "up a car".

Or maybe you make $5K a month and the market goes up 2% in a day (it happens sometimes).  At $250K, the market went up that day by what you make in a month.

[roomtempmayo]

Charlie Munger famously said that it takes $100k to get started, and the first $100k is the hardest.

Another way to ask the question is when a portfolio starts generating "real money" (scare quotes around deliberately subjective term) on its own. 

[aloevera1]

Thank you everyone. This is very helpful to refine my thinking. For some reason, this question has been bugging me for a while.

I agree with the technical definition that the average rate of growth does not change over time. The closest way to reframe the question was something @roomtempmayo wrote:

when a portfolio starts generating "real money" (scare quotes around deliberately subjective term) on its own. 

I think I am getting to getting some closure on this now.

There were also couple of more technical thoughts but I realize that my approach was wrong.  It's really good to talk things over rather than stew on them in my head.

1) Given that I reinvest the dividends, the growth of the portfolio should not be linear. Right now it roughly does look linear because it consists mostly of my contributions. I am aware that distribution of dividends should cause stock price to drop at the time so it should not matter but I am not fully sure what the impact of reinvestment would be on portfolio growth.

2) The compounding formula for the single $1 is (1+0.07)^t assuming 7% return. Mathematically, this graph looks like the one I posted. Yes, time will be the exponent, I am well aware of it. But I extrapolated that the whole portfolio chart would follow the same pattern.

However, if I am thinking about multiple contributions, I get the sum of various X1*(1+r1)^(time for this compunding) + X1*(1+r2)^(time for this compunding) + .... etc. So perhaps it is unreasonable to expect the smooth plot out of my portfolio.

Anyway.

Maybe the better way to think about inflection is what has been suggested in this thread: think about market gains and what I could have bought with them rather than staring at the chart :D My portfolio gains would have been enough to pay for a trip to Japan which I really would like to take...

@vand

But in a real life case study many high-earning + high-saving types here are probably getting to FI (ie 4% WR) mainly from their own efforts (ie money they put in themselves) rather than from the compounding of the money they put it.

Dammit. I thought I could just put in $100k and be done. :D

[314159]

However, if I am thinking about multiple contributions, I get the sum of various X1*(1+r1)^(time for this compunding) + X1*(1+r2)^(time for this compunding) + .... etc. So perhaps it is unreasonable to expect the smooth plot out of my portfolio.

I'll let others speak to the rest of your post, but yes, there is a closed-form formula for compounding with regular contributions. Before you type it out into your spreadsheet, though, you can just use your spreadsheet's built in version, =FV(rate,nper,pmt,[pv],[type]). (Google Sheets, Apple Numbers, LibreOffice Calc, or any other spreadsheet also has this function).

And yes, it is more linear-looking than the non-contribution graph: here's an example where you start with 0 and invest $20k annually at 7%: https://www.desmos.com/calculator/4hi3hafdck

[secondcor521]

1) Given that I reinvest the dividends, the growth of the portfolio should not be linear. Right now it roughly does look linear because it consists mostly of my contributions. I am aware that distribution of dividends should cause stock price to drop at the time so it should not matter but I am not fully sure what the impact of reinvestment would be on portfolio growth.

Many investors, myself included, just look at total return, which is essentially the dividend or interest income plus the change (hopefully increase) in asset value.  So if you're getting a 2% dividend and the stock (or whatever) grows 5%, then that is 7% and you can plug that into either the simple compounding formula or the FV() function.

[Telecaster]

1) Given that I reinvest the dividends, the growth of the portfolio should not be linear. Right now it roughly does look linear because it consists mostly of my contributions. I am aware that distribution of dividends should cause stock price to drop at the time so it should not matter but I am not fully sure what the impact of reinvestment would be on portfolio growth.

The stock price is indeed adjusted downward to account for the dividends, but the adjustment is smaller than normal variation in the stock price, so you can't see the dividend dates in the chart of stock prices.   

[nereo]

Charlie Munger famously said that it takes $100k to get started, and the first $100k is the hardest.

When rapper Drake posted on then-Twitter “the first million is the hardest”, Texas billionaire and oil tycoon T Boone Pickens responded “the next billion is a helluva lot harder RT @Drake”

https://x.com/boonepickens/status/207984741260070914?lang=en

[VanillaGorilla]

I haven't noticed any inflection points, just a series of goals that were nice to hit and an ever-increasing sense of retrospective awe.

I remember desperately wanting to finish school, and the incredible relief to have found a good job. I remember having enough to buy a house, and being so proud of myself for having bought one.

Then I wanted to have enough to pay the house off - that was big. Then I found FIRE and set my sights on having enough to provide the passive income I lived off in school. Then $1M net worth, then $1M with no mortgage, etc, etc.

Now I'm looking forward to the next arbitrary milestone, and when I regularly look at my historical numbers and marvel how I just followed the advice of some random dude on the internet who claimed to have a way to get rich, and it worked.

Ok fine, one fun inflection point is when I could open my Vanguard chart and see that my returns were greater than my contributions.

[Wintergreen78]

The first big milestone for me was seeing annual returns exceed my annual contribution. Looking back, it was the year after I passed $100k invested. The next big milestone was seeing over $100k in returns for a year, which was a little after passing $500k. The next was seeing a drop of over $100k, which was somewhere around $800-900k.

[waltworks]

I think we should revisit this thread when we eventually get a really solid 30-50% crash, which comes along every once in a while.

Personally, I loaded up my beater station wagon with Costco rice during the GFC because I thought the world was ending, even though I was in fine shape (the local food bank was the eventual beneficiary, so it all worked out...) And I consider myself pretty rational and was a statistician!

-W

[SeattleCPA]

This was probably asked a million times but I can't find any relevant threads...

For those of us who likes visualizing their portfolio growth.

At which invested portfolio size did you start seeing the exponential portfolio growth?

Obviously, there is the market noise but the overall trend should be visible anyway.

Yes, I am looking at my graph and playing a guessing game here. :D

I wonder if you're scaling your chart in a less than useful way. If you use logarithmic scaling, you don't have the hockey stick show up.

A few years ago, I did a blog post that plotted how a portfolio of stocks would grow historically in about a dozen different countries if you start with 1000 local currency units and "get" the historical returns. You can skim through those charts here, Rate of Return of Everything Charts, but basically you don't see an inflection point in any of them.

E.g., here's the line chart for Australia showing returns from stocks, housing and bonds over last 150 years:

[FireLane]

I'm going to take a different tack on this one: exponential growth is something you see in retrospect.

When I check my investments from week to week or month to month, I don't see huge changes happening before my eyes. Sometimes it goes up by a few thousand (yay!), sometimes it goes down (boo!). But the swings rarely feel large relative to the size of my portfolio.

But when I look back at a graph of my portfolio values over several years, then the difference becomes dramatic. What seemed like a towering peak when I hit it the first time now looks like a little foothill.

[Alternatepriorities]

Dammit. I thought I could just put in $100k and be done. :D

Oddly enough this was my plan before I found MMM and I had already reached it when I did. My logic was to invest 100k before the age of 30 and then stop worrying about retirement. The money would grow to an inflation adjusted 1 mil by then and I'd be fine. If i kept working and saving that would be great, but if I wanted to spend time as a vagabond in my 30s I could without worrying about being destitute in my 70s... At 31 I spent one year traveling the world with nothing but a carry on backpack. The next year I found MMM while feeling frustrated about sitting in and office again and decided to aim for FIRE.

[Taran Wanderer]

Over the years I have found that the inflection point has been about halfway from where I started to where I am when I look at the graph, at least after the first five years or so. It’s most visible if you have at least 40 points on the line or bars in the graph.  So with 5 years of data, you need to look at months.  With 10 years of data, look at quarters.

In practical terms, things started to take off when the stash hit $300k to $400k and earnings began exceeding contributions. That has only gotten more pronounced since then.

[vand]

This was probably asked a million times but I can't find any relevant threads...

For those of us who likes visualizing their portfolio growth.

At which invested portfolio size did you start seeing the exponential portfolio growth?

Obviously, there is the market noise but the overall trend should be visible anyway.

Yes, I am looking at my graph and playing a guessing game here. :D

I wonder if you're scaling your chart in a less than useful way. If you use logarithmic scaling, you don't have the hockey stick show up.

A few years ago, I did a blog post that plotted how a portfolio of stocks would grow historically in about a dozen different countries if you start with 1000 local currency units and "get" the historical returns. You can skim through those charts here, Rate of Return of Everything Charts, but basically you don't see an inflection point in any of them.

E.g., here's the line chart for Australia showing returns from stocks, housing and bonds over last 150 years:

Yes. Log scale is essential if you are visualizing rates of return.

Also, the fixation on round numbers... Obvious going from 900k to 1m is much less work than going from 100k to 200k, yet we seem to keep each 100k as a landmark in our own mental accounting.

[lcmac32]

I do enjoy this thread (math nerds and thoughtful introspection responses. It is more about what people have done and provides inspiration to me that it can be done.

When I got my first professional level job, I decided that my inflection point was this definition of wealth.  I defined it as when my investments can earn more for me than I can working.  (caveat:  anything invested and you lose a job or can't work would by the definition = being wealthy.  I exclude that $0.00 income scenario from the definition).   

I have yet to reach that point, but this year was pretty close so far.  I have gone to a 2x higher paying job so of course my task got much harder, but for a very good reason. 

It isn't exactly a FIRE definition b/c by frugality the FIRE moment can be much sooner than investments earning more than one's income from working.  I still am keeping with that definition as the inflection point for myself, but am simultaneously working on getting my FIRE number down as low as possible.

Definitely 1st world type discussions, which I am grateful to have the luxury to induldge in.

[vand]

I do enjoy this thread (math nerds and thoughtful introspection responses. It is more about what people have done and provides inspiration to me that it can be done.

When I got my first professional level job, I decided that my inflection point was this definition of wealth.  I defined it as when my investments can earn more for me than I can working.  (caveat:  anything invested and you lose a job or can't work would by the definition = being wealthy.  I exclude that $0.00 income scenario from the definition).   

I have yet to reach that point, but this year was pretty close so far.  I have gone to a 2x higher paying job so of course my task got much harder, but for a very good reason. 

It isn't exactly a FIRE definition b/c by frugality the FIRE moment can be much sooner than investments earning more than one's income from working.  I still am keeping with that definition as the inflection point for myself, but am simultaneously working on getting my FIRE number down as low as possible.

Definitely 1st world type discussions, which I am grateful to have the luxury to induldge in.

Yeah, likewise..  I'm waiting for the day my portfolio earns more from it's own internal growth at a reasonable and sustainable rate of return   (not the silly 20-25% of the last 12-18 months)... than I can add to it in ongoing contributions... and that day is still not there as I've worked a bit on myself and been fortunate enough to have increase my income quite a bit in the last couple of years..
see also https://forum.mrmoneymustache.com/welcome-to-the-forum/career-progression-compounding-of-your-earning-capacity/

[reeshau]

I do enjoy this thread (math nerds and thoughtful introspection responses. It is more about what people have done and provides inspiration to me that it can be done.

When I got my first professional level job, I decided that my inflection point was this definition of wealth.  I defined it as when my investments can earn more for me than I can working.  (caveat:  anything invested and you lose a job or can't work would by the definition = being wealthy.  I exclude that $0.00 income scenario from the definition).   

I have yet to reach that point, but this year was pretty close so far.  I have gone to a 2x higher paying job so of course my task got much harder, but for a very good reason. 

It isn't exactly a FIRE definition b/c by frugality the FIRE moment can be much sooner than investments earning more than one's income from working.  I still am keeping with that definition as the inflection point for myself, but am simultaneously working on getting my FIRE number down as low as possible.

Definitely 1st world type discussions, which I am grateful to have the luxury to induldge in.

Yeah, likewise..  I'm waiting for the day my portfolio earns more from it's own internal growth at a reasonable and sustainable rate of return   (not the silly 20-25% of the last 12-18 months)... than I can add to it in ongoing contributions... and that day is still not there as I've worked a bit on myself and been fortunate enough to have increase my income quite a bit in the last couple of years..
see also https://forum.mrmoneymustache.com/welcome-to-the-forum/career-progression-compounding-of-your-earning-capacity/

Everyone has their own point where they feel comfortable.  But this seems like risking over-saving, to me.  You don't have to generate your salary in FIRE, just your expenses.  And for a mustachian, those numbers are very different.  I would think this is closer to an end point, or beyond, than an inflection point, I.e. some milestone in the middle.

[vand]

I do enjoy this thread (math nerds and thoughtful introspection responses. It is more about what people have done and provides inspiration to me that it can be done.

When I got my first professional level job, I decided that my inflection point was this definition of wealth.  I defined it as when my investments can earn more for me than I can working.  (caveat:  anything invested and you lose a job or can't work would by the definition = being wealthy.  I exclude that $0.00 income scenario from the definition).   

I have yet to reach that point, but this year was pretty close so far.  I have gone to a 2x higher paying job so of course my task got much harder, but for a very good reason. 

It isn't exactly a FIRE definition b/c by frugality the FIRE moment can be much sooner than investments earning more than one's income from working.  I still am keeping with that definition as the inflection point for myself, but am simultaneously working on getting my FIRE number down as low as possible.

Definitely 1st world type discussions, which I am grateful to have the luxury to induldge in.

Yeah, likewise..  I'm waiting for the day my portfolio earns more from it's own internal growth at a reasonable and sustainable rate of return   (not the silly 20-25% of the last 12-18 months)... than I can add to it in ongoing contributions... and that day is still not there as I've worked a bit on myself and been fortunate enough to have increase my income quite a bit in the last couple of years..
see also https://forum.mrmoneymustache.com/welcome-to-the-forum/career-progression-compounding-of-your-earning-capacity/

Everyone has their own point where they feel comfortable.  But this seems like risking over-saving, to me.  You don't have to generate your salary in FIRE, just your expenses.  And for a mustachian, those numbers are very different.  I would think this is closer to an end point, or beyond, than an inflection point, I.e. some milestone in the middle.

I'll be the first to admit that the biggest thing that has inflated faster than the CPI is my personal FI number over the last few years haha

Not that I'm apologizing for it.. I think it's fine to have moderate ambition and I'm rather enjoying reaping the benefits of these latter stage career moves.

I do plan to spend more in retirement than I do at the moment, plus I'm doing the anti-Ramsey thing and will carry a huge mortgage into retirement and use my pot to eventually pay down, so that needs to be factored in

[shuffler]

I defined it as when my investments can earn more for me than I can working.
...
I have yet to reach that point, but this year was pretty close so far.  I have gone to a 2x higher paying job so of course my task got much harder, but for a very good reason. 

Yeah, likewise..  I'm waiting for the day my portfolio earns more from it's own internal growth at a reasonable and sustainable rate of return   (not the silly 20-25% of the last 12-18 months)... than I can add to it in ongoing contributions... and that day is still not there as I've worked a bit on myself and been fortunate enough to have increase my income quite a bit in the last couple of years.

I did the little bit of algebra for this a few years ago.
With assumptions, I found it to be when you have a stash of ~5x your annual income.

"When our investments gains start outpacing our deposits" is a natural metric I would use, too.

Except most people's income and savings don't stay constant over the years, so I'd choose to state it in terms of present-day stash and present-day income.

If we assume:
  *  10% annual return on investments (note that this is intentionally not adjusted for inflation)
  *  50% savings rate (we're reasonably decent mustachians)
  *  Income of $x.
  *  Stash of $s.

... then every year we'll be depositing 0.5x.
... and every year our stash will grow by 0.1s.
... and "when our investments gains start outpacing our deposits" is when 0.1s = 0.5x ... or ... s = 5x

In other words:
    When our stash is 5 times our annual income.

Feel free to adjust the assumption percentages for your own savings and investment-return rates.

[Wintergreen78]

I defined it as when my investments can earn more for me than I can working.
...
I have yet to reach that point, but this year was pretty close so far.  I have gone to a 2x higher paying job so of course my task got much harder, but for a very good reason. 

Yeah, likewise..  I'm waiting for the day my portfolio earns more from it's own internal growth at a reasonable and sustainable rate of return   (not the silly 20-25% of the last 12-18 months)... than I can add to it in ongoing contributions... and that day is still not there as I've worked a bit on myself and been fortunate enough to have increase my income quite a bit in the last couple of years.

I did the little bit of algebra for this a few years ago.
With assumptions, I found it to be when you have a stash of ~5x your annual income.

"When our investments gains start outpacing our deposits" is a natural metric I would use, too.

Except most people's income and savings don't stay constant over the years, so I'd choose to state it in terms of present-day stash and present-day income.

If we assume:
  *  10% annual return on investments (note that this is intentionally not adjusted for inflation)
  *  50% savings rate (we're reasonably decent mustachians)
  *  Income of $x.
  *  Stash of $s.

... then every year we'll be depositing 0.5x.
... and every year our stash will grow by 0.1s.
... and "when our investments gains start outpacing our deposits" is when 0.1s = 0.5x ... or ... s = 5x

In other words:
    When our stash is 5 times our annual income.

Feel free to adjust the assumption percentages for your own savings and investment-return rates.

I’m telling you, the inflection point is not when you see it go up by more than you make in a year, but when you see it go down by more than you make in a year. That is when you know that returns have gotten big enough to really matter!

[Radagast]

Here's a couple snips of various accounts and subtotals I track as well as my total net worth, so you can see all the break points I see.

[aloevera1]

Thank you everyone for responding, this thread gave me a lot to think about. Always good to learn new stuff. I love how the responses covered both math and emotional rationale. To be honest, I am stuck in the boring middle of accumulation so finding new ways to think about portfolio and play with spreadsheets is very satisfying.

However, if I am thinking about multiple contributions, I get the sum of various X1*(1+r1)^(time for this compunding) + X1*(1+r2)^(time for this compunding) + .... etc. So perhaps it is unreasonable to expect the smooth plot out of my portfolio.

I'll let others speak to the rest of your post, but yes, there is a closed-form formula for compounding with regular contributions. Before you type it out into your spreadsheet, though, you can just use your spreadsheet's built in version, =FV(rate,nper,pmt,[pv],[type]). (Google Sheets, Apple Numbers, LibreOffice Calc, or any other spreadsheet also has this function).

And yes, it is more linear-looking than the non-contribution graph: here's an example where you start with 0 and invest $20k annually at 7%: https://www.desmos.com/calculator/4hi3hafdck

This is super helpful, thank you! :) I immediately included it in my planning spreadsheet. Something to aspire to :)

I wonder if you're scaling your chart in a less than useful way. If you use logarithmic scaling, you don't have the hockey stick show up.

I was not using logarithmic scale but it's an interesting idea to try. Agree, will not get the hockey stick there...

When I got my first professional level job, I decided that my inflection point was this definition of wealth.  I defined it as when my investments can earn more for me than I can working.  (caveat:  anything invested and you lose a job or can't work would by the definition = being wealthy.  I exclude that $0.00 income scenario from the definition).   

I have yet to reach that point, but this year was pretty close so far.  I have gone to a 2x higher paying job so of course my task got much harder, but for a very good reason.

It isn't exactly a FIRE definition b/c by frugality the FIRE moment can be much sooner than investments earning more than one's income from working.  I still am keeping with that definition as the inflection point for myself, but am simultaneously working on getting my FIRE number down as low as possible.

Definitely 1st world type discussions, which I am grateful to have the luxury to induldge in.

I like this perspective a lot. If portfolio is generating enough capital gains to cover expenses, that's a first major milestone. If portfolio is generating enough to replace the income, that's a second very satisfying milestone.

@Radagast, thanks for sharing the plots! I find that my graphs look similar so that seems validating :) 

[EliteZags]

my returns on the year are already close to doubling my annual (mid-6figure) salary