Get a cup of coffee.
In this thread, I'll walk you through 8 key concepts related to compounding and exponential growth.
To be a successful Jedi Knight, one must deeply understand the Force.
To be a successful investor, one must deeply understand the "force" of compounding.
In this thread, I'll walk you through 8 key concepts related to compounding and exponential growth.
To be a successful Jedi Knight, one must deeply understand the Force.
To be a successful investor, one must deeply understand the "force" of compounding.
Key Concept #1
What is Compounding?
Compounding means our WEALTH grows *exponentially* with TIME.
That is, if we wrote a formula for our WEALTH as a function of TIME, that formula would have TIME in the *exponent*.
Like so:
What is Compounding?
Compounding means our WEALTH grows *exponentially* with TIME.
That is, if we wrote a formula for our WEALTH as a function of TIME, that formula would have TIME in the *exponent*.
Like so:
Key Concept #2
The biggest benefits of compounding come towards the end.
For example, take a savings account that starts with $1 and earns 10% per year -- compounded for 100 years.
In the FIRST 10 years, the account grows by ~$1.59.
In the LAST 10 years, it grows by ~$8,468.
The biggest benefits of compounding come towards the end.
For example, take a savings account that starts with $1 and earns 10% per year -- compounded for 100 years.
In the FIRST 10 years, the account grows by ~$1.59.
In the LAST 10 years, it grows by ~$8,468.
This is because wealth curves that grow exponentially are *non-linear* -- in fact, *convex* -- with respect to time.
For the SAME incremental time spent, we get a LARGER incremental wealth benefit the FURTHER along we are in the process.
Like so:
For the SAME incremental time spent, we get a LARGER incremental wealth benefit the FURTHER along we are in the process.
Like so:
Here's another example of such "back loaded" benefits:
Suppose Mike saves $50K/year for 30 years.
And at the end of each year, Mike takes his $50K of savings and puts it into his portfolio.
And the portfolio compounds capital at 10% per year.
Suppose Mike saves $50K/year for 30 years.
And at the end of each year, Mike takes his $50K of savings and puts it into his portfolio.
And the portfolio compounds capital at 10% per year.
Then, after 30 years, Mike will have an ~$8.22M nest egg.
But ~40% of that nest egg will have come in the LAST 5 years.
That is, the LAST ~16.67% of the TIME spent accounts for ~40% of the WEALTH gained.
That's convexity in compounding.
But ~40% of that nest egg will have come in the LAST 5 years.
That is, the LAST ~16.67% of the TIME spent accounts for ~40% of the WEALTH gained.
That's convexity in compounding.
As Morgan Housel explains beautifully in The Psychology of Money, this convexity applies to Warren Buffett as well:
Key Concept #3
A FASTER compounder (eg, a 15% per year grower) will *always* eventually overtake a SLOWER compounder (eg, a 10% per year grower) -- EVEN IF the latter has a huge head start.
This seems rather obvious.
But this simple fact has so many investing implications.
A FASTER compounder (eg, a 15% per year grower) will *always* eventually overtake a SLOWER compounder (eg, a 10% per year grower) -- EVEN IF the latter has a huge head start.
This seems rather obvious.
But this simple fact has so many investing implications.
For example, suppose a company has 2 lines of business.
Line 1 is 90% of revenues now, but only grows at 5% per year.
Line 2 is only 10% of revenues now, but it grows at 50% per year.
Then, in ~6 short years, Line 2 will overtake Line 1.
Line 1 is 90% of revenues now, but only grows at 5% per year.
Line 2 is only 10% of revenues now, but it grows at 50% per year.
Then, in ~6 short years, Line 2 will overtake Line 1.
As investors, we often underestimate the speed with which fledgling new lines of business can grow to dominate our portfolio companies' economics.
Apple was once (mostly) just selling Macs and iPods. A few short years later, the iPhone dwarfed everything else.
Apple was once (mostly) just selling Macs and iPods. A few short years later, the iPhone dwarfed everything else.
This principle also applies to position sizes within our portfolio.
For example, suppose we build an equal weighted portfolio of 10 stocks.
And suppose 9 of these 10 stocks grow at 5% per year, but 1 lucky hit proceeds to deliver 25% per year growth.
For example, suppose we build an equal weighted portfolio of 10 stocks.
And suppose 9 of these 10 stocks grow at 5% per year, but 1 lucky hit proceeds to deliver 25% per year growth.
If we just leave our portfolio as is (ie, no re-balancing), in less than 13 years, the 25% grower will account for more than half our portfolio.
Thus, over time, the power of compounding can wash away our mistakes and let our superstars shine. What an agreeable dynamic!
Thus, over time, the power of compounding can wash away our mistakes and let our superstars shine. What an agreeable dynamic!
Key Concept #4
Interruptions can be costly.
As Charlie Munger says, the first rule of compounding is to never interrupt it unnecessarily.
For example, let's revisit Mike's example above. But this time, we'll throw in a few interruptions to his compounding and see what happens.
Interruptions can be costly.
As Charlie Munger says, the first rule of compounding is to never interrupt it unnecessarily.
For example, let's revisit Mike's example above. But this time, we'll throw in a few interruptions to his compounding and see what happens.
As before, Mike sets out on a 30-year "save and invest" journey -- saving $50K per year, and investing these savings at a 10% per year return.
But during this 30-year stretch, suppose Mike loses his job 3 times -- once every 10 years. Each "jobless" period lasts about a year.
But during this 30-year stretch, suppose Mike loses his job 3 times -- once every 10 years. Each "jobless" period lasts about a year.
During "jobless" years, Mike does not save $50K.
Instead, he *withdraws* $100K from his portfolio to support himself.
This interrupts his compounding engine.
The question is: what's the ultimate impact of these interruptions on Mike's nest egg at the end of Year 30?
Instead, he *withdraws* $100K from his portfolio to support himself.
This interrupts his compounding engine.
The question is: what's the ultimate impact of these interruptions on Mike's nest egg at the end of Year 30?
*Without* these interruptions, we said Mike's nest egg will be worth ~$8.22M.
*With* these interruptions, this drops to ~$6.57M.
Thus, the interruptions reduced Mike's nest egg by ~$1.65M, or ~20%.
And that's for "missing" only 3 out of 30 years -- or only 10% of the time.
*With* these interruptions, this drops to ~$6.57M.
Thus, the interruptions reduced Mike's nest egg by ~$1.65M, or ~20%.
And that's for "missing" only 3 out of 30 years -- or only 10% of the time.
Key Concept #5
The Rule of 72
Most of us have a hard time doing the *math* of compounding in our heads.
We are wired to think *linearly*. This often leads us astray in *exponential* settings.
The Rule of 72 is an *approximation* to help with this:
The Rule of 72
Most of us have a hard time doing the *math* of compounding in our heads.
We are wired to think *linearly*. This often leads us astray in *exponential* settings.
The Rule of 72 is an *approximation* to help with this:
The Rule of 72 gives us a way to do *exponential* math in our heads -- by focusing on how long the process of compounding takes to *double* our wealth.
For example, suppose we buy a stock and it quadruples in 10 years. That's a "double every 5 years".
For example, suppose we buy a stock and it quadruples in 10 years. That's a "double every 5 years".
Applying the Rule of 72, our return on this stock is roughly 72/5 = 14.4% per year.
For more:
For more:
https://twitter.com/10kdiver/status/1340366623425761280
Key Concept #6
Turning capital more quickly leads to faster compounding.
That is, it's better to earn 10% on our capital every 6 months than to earn 20% on our capital every year.
Calculations:
Turning capital more quickly leads to faster compounding.
That is, it's better to earn 10% on our capital every 6 months than to earn 20% on our capital every year.
Calculations:
This has important investing implications.
For example, businesses that turn inventory quickly may be able to earn good returns for their owners -- even with low margins.
But there may be a law of diminishing returns at play here. For more:
For example, businesses that turn inventory quickly may be able to earn good returns for their owners -- even with low margins.
But there may be a law of diminishing returns at play here. For more:
https://twitter.com/10kdiver/status/1409171698532847616
Key Concept #7
Compounding CANNOT go on forever.
As with most fast growing phenomena, nature has a way of inhibiting growth once we reach a certain size.
For example, a recent college graduate can usually double their net worth more easily than someone like Jeff Bezos.
Compounding CANNOT go on forever.
As with most fast growing phenomena, nature has a way of inhibiting growth once we reach a certain size.
For example, a recent college graduate can usually double their net worth more easily than someone like Jeff Bezos.
By the same token, it may be easier for a $1B market cap company to grow to $2B, than for a $100B company to grow to $200B.
As Buffett likes to put it, size is often an anchor of investment returns.
As Buffett likes to put it, size is often an anchor of investment returns.
So, sooner or later, compounding will have to either slow down or come to a complete stop -- at virtually ANY business.
The *time frame* of this slow down/stop can play a BIG role in helping us decide, as investors, what price we can prudently pay to acquire a business.
The *time frame* of this slow down/stop can play a BIG role in helping us decide, as investors, what price we can prudently pay to acquire a business.
For example, suppose we have 2 businesses: A and B.
They both have $5B of capital. And they both earn 20% on capital. So, both will earn $1B this year.
But A has *25* years of re-investment funded growth via compounding ahead of it. Whereas B only has *10* years.
They both have $5B of capital. And they both earn 20% on capital. So, both will earn $1B this year.
But A has *25* years of re-investment funded growth via compounding ahead of it. Whereas B only has *10* years.
Suppose we want a 10% per year return on our investments.
Then, we can afford to pay ~$88B for A.
But only ~$24B for B.
Because A has a much longer *runway* for compounding capital.
Then, we can afford to pay ~$88B for A.
But only ~$24B for B.
Because A has a much longer *runway* for compounding capital.
Key Concept #8
Compounding seldom happens at a steady rate.
Stocks often go up and down. Businesses earn different returns on their capital during good times and bad. Etc.
So, the rate at which our wealth compounds will fluctuate from month to month, year to year, etc.
Compounding seldom happens at a steady rate.
Stocks often go up and down. Businesses earn different returns on their capital during good times and bad. Etc.
So, the rate at which our wealth compounds will fluctuate from month to month, year to year, etc.
Sequence Risk (also called Path Dependence) can play a major role in such situations.
The idea here is: if we're *neither* adding nor removing capital from a portfolio, the *order*/*sequence* of returns earned by our portfolio does NOT matter.
The idea here is: if we're *neither* adding nor removing capital from a portfolio, the *order*/*sequence* of returns earned by our portfolio does NOT matter.
For example, a 20% UP year followed by a 10% DOWN year has the *exact* same effect on our portfolio as a 10% DOWN year followed by a 20% UP year.
But this "invariance to sequence" does NOT hold true if we're adding or removing capital each year from our portfolio.
But this "invariance to sequence" does NOT hold true if we're adding or removing capital each year from our portfolio.
Typically, during the years we earn and save, we regularly *add* capital to our portfolios.
And in retirement, we regularly *remove* capital from our portfolios.
The *order*/*sequence* of returns tends to affect us differently in these situations.
And in retirement, we regularly *remove* capital from our portfolios.
The *order*/*sequence* of returns tends to affect us differently in these situations.
If we're going to have both GOOD and BAD years anyway, here's the general rule:
If we're *adding* capital, we should hope for the BAD years to hit us first, followed by the GOOD years.
And the other way round if we're *removing* capital.
For more:
If we're *adding* capital, we should hope for the BAD years to hit us first, followed by the GOOD years.
And the other way round if we're *removing* capital.
For more:
https://twitter.com/10kdiver/status/1353169429287211009
Here's a summary of the key concepts in this thread:
1) Compounding = Exponential growth of wealth,
2) The biggest benefits of compounding come towards the end -- ie, compounding is *convex*,
3) A faster compounder will eventually overtake a slower compounder,
1) Compounding = Exponential growth of wealth,
2) The biggest benefits of compounding come towards the end -- ie, compounding is *convex*,
3) A faster compounder will eventually overtake a slower compounder,
4) Interruptions to compounding can be costly,
5) The Rule of 72 can help us do compounding math mentally,
6) Turning capital more quickly leads to faster compounding,
7) Compounding CANNOT go on forever, so we should be careful what price we pay for businesses, AND
5) The Rule of 72 can help us do compounding math mentally,
6) Turning capital more quickly leads to faster compounding,
7) Compounding CANNOT go on forever, so we should be careful what price we pay for businesses, AND
8) Compounding at a *steady* clip is almost always impossible, so we should be aware of and plan for Sequence Risk.
As investors, we need to cultivate strong familiarity with the fundamentals of compounding and exponential growth. I hope this thread helped with that.
As investors, we need to cultivate strong familiarity with the fundamentals of compounding and exponential growth. I hope this thread helped with that.
For a more wide-ranging discussion of the principles of compounding and how they apply to investing, please join me at 1pm ET tomorrow (Sun, Jan 16) for a new Money Concepts episode via @getcallin.
Hope to see you there!
Link: callin.com/link/XKLdBajHda
Hope to see you there!
Link: callin.com/link/XKLdBajHda
Thank you very much for reading all the way to the end.
Please stay safe. Enjoy your weekend!
/End
Please stay safe. Enjoy your weekend!
/End
ERROR:
Folks, I made a mistake in the "compounding is convex" picture above. Here's the corrected picture. Apologies for the confusion.
The description in the text is still correct -- the benefits of compounding do tend to be back loaded.
(h/t @austraind for catching this!)
Folks, I made a mistake in the "compounding is convex" picture above. Here's the corrected picture. Apologies for the confusion.
The description in the text is still correct -- the benefits of compounding do tend to be back loaded.
(h/t @austraind for catching this!)
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