Is "compounding" the right/best word to describe equity/index fund growth

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Is "compounding" the right/best word to describe equity/index fund growth

Post by coachd50 »

Apologies for the previous thread- with a poorly premised title. Thank you to those that replied.

When discussing investing, particularly index fund/mutual fund or ETF investing I have often seen the following phrase "invest early and let compounding work its magic".

My question- is it really compounding? Is this the best word or appropriate word for this?

When discussing rudimentary personal finance, compound interest is almost always a topic. We often see the basic example of $100 @10% results in $10 earned yr 1, but $11 earned yr 2. The $1 being the result of "compounding. The interest paid yr 2 on the interest earned year 1.

This is different than growth on index funds isn't it? So should their be a different word, particularly when teaching the beginning elements of personal finance and index fund investing?
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by make_a_better_world »

Returns on equities are not interest but the concept of compounding is the same. If you invest money into a profitable business, the idea is the company takes this capital and deploys it and ultimately produces earnings. These earning are given back to the investors via stock price appreciation or as a dividend payment. If you re-invest these earnings into the business as they are received, and the business is still able to take new capital and deploy it to generate earnings, then you will generate compounding returns over time. Time and reinvestment are the critical factors. It is very similar to the concept of compound interest, but of course, the earnings are not guaranteed or on a predestined schedule.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by LadyGeek »

This is a continuation from No Dividends = No compounding ?, but rephrased with a better title.

coachd50 has worked with the moderators to start a new discussion.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by dbr »

coachd50 wrote: Fri Nov 26, 2021 2:03 pm Apologies for the previous thread- with a poorly premised title. Thank you to those that replied.

When discussing investing, particularly index fund/mutual fund or ETF investing I have often seen the following phrase "invest early and let compounding work its magic".

My question- is it really compounding? Is this the best word or appropriate word for this?

When discussing rudimentary personal finance, compound interest is almost always a topic. We often see the basic example of $100 @10% results in $10 earned yr 1, but $11 earned yr 2. The $1 being the result of "compounding. The interest paid yr 2 on the interest earned year 1.

This is different than growth on index funds isn't it? So should their be a different word, particularly when teaching the beginning elements of personal finance and index fund investing?
There is no difference between compounding interest at a fixed rate on a savings account and using the idea of compounding for growth of index funds as long as you can accept the idea that return can vary from period to period, even be negative, and the idea still applies. Return is defined in the way it is so that this concept works.

In the previous thread I wrote this all out in algebra to explain the concept so I'll just paste that here:

The definition of annual return is that it is the increase of value of the holdings in a year including capital gain (price increase), which can be positive or negative, and dividends reinvested, then divided by the starting value and expressed as a percent.

In a succession of years there will be an annual return each year. The formula for the value at the end of several years is:

End Value = Starting Value * (1 + R1/100) * (1 +R2/100) * . . . . * (1 + Rn/100) where the Rx are the annual (or any other period) returns

In mathematics that is called a compound growth model. If no dividends are paid there are still returns. To say this is not compounding would be an odd thing to say, but the math is a well defined model that is conventional to the field. Sometimes people want to claim that if all the Rx are not the same then it isn't compounding, but math is seldom obligated to be that narrow minded.

Note that for two years, for example, the multiplied out expression is 1 + r1 + r2 + r1 * r2 (where rx = Rx/100) The interpretation is that r1 refflects the return in year one, r2 reflects the return in year two, and r1 * r2 reflects the return in year two on the return earned in year 1. This least term is what is normally understood to be compounding.

If you can compute a value R that substituted for all the Rx then that number is called the CAGR, which is a kind of average for a growth model like this. The CAGR is also the value R you get if you take the geometric average of the (1 + Rx/100) and subtract 1 and multiply the 100. The messing around with terms of 100 is to convert between decimal units and percent units. The adding and subtracting of one converts between a return and a compound growth factor.

Also note that this means the growth over time is (1+CAGR)/100^N where N is the number of years. Also that if the return is the same everyyear then the the growth is (1 + r)^N This last result would correspond to something like interest compounded annually, and so on.

This is the math, which if one wants to ignore it will probably leave only confusion.
Last edited by dbr on Fri Nov 26, 2021 2:30 pm, edited 1 time in total.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by HomerJ »

coachd50 wrote: Fri Nov 26, 2021 2:03 pm Apologies for the previous thread- with a poorly premised title. Thank you to those that replied.

When discussing investing, particularly index fund/mutual fund or ETF investing I have often seen the following phrase "invest early and let compounding work its magic".

My question- is it really compounding? Is this the best word or appropriate word for this?

When discussing rudimentary personal finance, compound interest is almost always a topic. We often see the basic example of $100 @10% results in $10 earned yr 1, but $11 earned yr 2. The $1 being the result of "compounding. The interest paid yr 2 on the interest earned year 1.

This is different than growth on index funds isn't it? So should their be a different word, particularly when teaching the beginning elements of personal finance and index fund investing?
Normally you re-invest the dividends and gains back into the same index fund.

So an index fund that goes up 10% one year, and 10% the next year, does indeed increase the value of your investment 11% in that second year, since the first year's dividends and gains ALSO go up 10%.

Even if there is no dividends, the increase in your fund's value still goes up 11% in the second year because 10% added to 1.10 is 1.21.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by Nate79 »

I don't like the idea of using generalized terms that give new investors a misconception of how investing in equities really work. It leads to questions like "I was told that VTSAX compounds at 8% per year but my balance lost money last month. Is my broker stealing my money?"
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by Silk McCue »

With equity the compounding effect comes from capital appreciation and dividend reinvestment which provides us with total return. I think that compounding is a concept that folks generally understand.

If more explanation is needed by someone use my first sentence, some other sentence, a paragraph, a chapter or book.

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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by LadyGeek »

dbr wrote: Fri Nov 26, 2021 2:29 pm If you can compute a value R that substituted for all the Rx then that number is called the CAGR, which is a kind of average for a growth model like this...
Background info: Compound Annual Growth Rate (CAGR)

CAGR is the best way to make "apples-to-apples" comparisons between any two investments.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by dbr »

Nate79 wrote: Fri Nov 26, 2021 2:33 pm I don't like the idea of using generalized terms that give new investors a misconception of how investing in equities really work. It leads to questions like "I was told that VTSAX compounds at 8% per year but my balance lost money last month. Is my broker stealing my money?"
Yes, but the fallacy is not in saying that the investment compounds but in adding the wrong statement "at 8% per year." The FIRST statement that is needed is that stock annual returns are variable, including that they are often negative. It goes back to whether or not a person can make a small step and accept that compounding is an idea that works just fine when the returns are variable. That means savings account compounding is a special case of a general idea. Maybe it depends on a person's ability to recognize something as a special case of something more general or not being able to do that.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by dbr »

LadyGeek wrote: Fri Nov 26, 2021 2:38 pm
dbr wrote: Fri Nov 26, 2021 2:29 pm If you can compute a value R that substituted for all the Rx then that number is called the CAGR, which is a kind of average for a growth model like this...
Background info: Compound Annual Growth Rate (CAGR)

CAGR is the best way to make "apples-to-apples" comparisons between any two investments.
Actually there is a mathematical definition of a "general average" and that concept is that for any set of data and a function of that data the general average is the number that substituted in the function for all the individual instances and gives the same result is the "average."

In the case of arithmetic average the function that applies is just adding up the data. If the function is multiplying the data you get the geometric average. For CAGR the function is the growth formula for a consecutive series of returns.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by GP813 »

Yes, my example of this is Amazon as a business and stock that I own. Despite not paying a dividend Jeff Bezos and company have certainly compounded the money they've raised and earned into their various businesses under the Amazon company to great effect.

An equity/index fund is an even clearer example, you are taking all or a broad number of all the publicly traded businesses and the new successful products and services they offer, labor cost reductions, productivity gains, technological advancements, and capital appreciation and balancing against all the stuff that can go wrong and over time this has been very effective to compound your invested money.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by dbr »

Well, compounding can also apply to a failing company where the negative returns appear year after year and the investment "spirals" down to nothing. Another case of compounding would be the drawing down of a retirement portfolio where the change in value originates from the return minus the withdrawal. In some years one exceeds the other and the net growth could be positive or negative.

A classic example of constant compound negative growth would be the radiation output of a mass of radioactive material as the number of undecayed nuclei shrinks while the probability of decay of a nucleus is constant. See also the solution to the differential equation dx/dt = -a*x(t)

But compounding is a mathematical concept that can be applied to any time sequence of data by an appropriate definition of the rate in a period. The model is more useful and meaningful in some cases than in others, but it certainly applies well to investment results in successive periods.

I am not sure if trying to apply the concept to something like a periodic up and down signal would be useful -- just ruminating on something where you would not use the idea.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by 02nz »

After skimming the two threads it's not clear to me what the OP is really asking, but here's the simplest way I can put it:

If you have A number of dollars in a savings account yielding B%, after C years you'll have D dollars.

Now imagine instead those same A dollars were invested in stocks (whether paying dividends or not, so long as the dividends are reinvested) with a CAGR of B%, after C years you'll also have D dollars.

There's no difference in the math. And so I don't see why there would be any difference in terminology.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by LadyGeek »

Another example of compounding in the negative direction is the Assets Under Management (AUM) fee charged by a financial advisor. Subtract the AUM fee (percentage) directly from your return (percentage).
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by firebirdparts »

I posted in the other thread, but anyway I say no; there is such a thing as organic growth of a business, but that growth doesn’t always compound. Sometimes it does, but the factors that cause that are explicit, and usually they are limited by addressable market and competition, both in-kind competition and the competition of other lifestyles that eschew your product.

Making money from money is 100 times easier than making money by meeting human needs. A large number of companies make their money by meeting human needs. The assumption of unlimited human need does not always hold.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by delamer »

I find “compounding” misleading in this context too.

There are 2 ways the value of a stock-based asset can grow — through an increasing share price and through revinvesting any dividends.

Reinvesting dividends bears resemblance to compounding. Just like compound interest on a savings account means that your interest ends up earning more interest, reinvested dividends means that your dividends end up earning more dividends.

But an increasing share price doesn’t compound. It just goes up. So a stock that doesn’t pay dividends isn’t affected by compounding,

And you certainly don’t want to select investments based on dividend yields. A stock that pays dividends isn’t a better choice than one that doesn’t just because of compounding. Reinvesting dividends isn’t an advantage over share price growth (and may be a disadvantage in a taxsble account).

(CAGR is just a math term for geometric growth, calculated after-the-fact. It doesn’t literally mean that the growth was achieved by reinvesting dividends.)
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by Nate79 »

Yes, just because you can calculate a CAGR doesn't mean in any way that the investment actually compounded.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by dbr »

Note the OP asks about using the word to describe equity growth. It is certainly true that return and derived values such as CAGR are commonly used to describe equity growth, that is, compounding is used for that purpose. Is there some way in which this is a wrong way to describe equity growth or is there an alternative description that is better? (Which is what the OP is asking.)

If one wants to elicit a cause for why the value of equity holding grows then compounding would not be an explanation all by itself. In the first place one needs to explain why return is even positive on average, let alone that it does or doesn't compound. After all there are plenty of examples where compounding is a description of or even a cause of decay or decline.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by coachd50 »

delamer wrote: Sat Nov 27, 2021 9:53 am I find “compounding” misleading in this context too.



Reinvesting dividends bears resemblance to compounding. Just like compound interest on a savings account means that your interest ends up earning more interest, reinvested dividends means that your dividends end up earning more dividends.
This is thought process behind my original (but poorly titled) thread on this subject.

(CAGR is just a math term for geometric growth, calculated after-the-fact. It doesn’t literally mean that the growth was achieved by reinvesting dividends.)
This is the basis of my question.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by coachd50 »

dbr wrote: Sat Nov 27, 2021 10:49 am

If one wants to elicit a cause for why the value of equity holding grows then compounding would not be an explanation all by itself.
Yes, this is also one of the main focuses of my question.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by AnnetteLouisan »

I’ll take a stab, since I had a similar question when I looked at my Fidelity statement recently. Nothing was credited, just a value was stated.

If you are used to bank savings and CDs, or even bonds, you are familiar with interest being credited and locked in and compounded every day, month, quarter or semiannual period, as the case many be. There’s a satisfaction in that regularity.

Fund growth has dividends that get credited but the main benefit is that the price per share (hopefully) goes up. Yet it is recorded on your statement but the gain is not locked in and credited as a gain to you like typical compounding until you sell.

Somewhat like real estate: values can soar but they can also fall and you will scramble for what you had when you never really had it since you never locked it in. Maddening but generally still much more profitable in the long run than savings or bonds.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by dbr »

A more fundamental concept about what compounding is would be that growth is compound when the rate of growth is proportional to the size of what is growing. When you hold a savings account paying interest at a certain rate this is true by definition, especially if you can get it continuously compounded. Mathematically this is represented by the differential equation dx(t)/dt = ax(t) where t is time. As is known the solution to that equation is x(t) = e^at, meaning exponential growth. Thus compound growth is exponential growth. Of course the process is disrupted if the interest rate is changed.

That leads to how we would apply this concept to stock values (including dividends invested back in). If you believe that by and large the rate of growth of a stock holding over time is always proportional to the value at any time, then you are saying the growth is compound growth. The idea that one would calculate a CAGR implements that thought. But we know stock value growth rates vary all the time. In spite of that variation we do believe that on average those growth rates gather around a central growth constant called the expected return. If you think expected return is a meaningful idea then you mean that equity growth is compound growth with a lot of noise superimposed on it. That bank account when the interest rate changes is not different in that respect either.

The question why the growth rate of equities is proportional to the currently achieved value is a different problem that perhaps stands as a mystery. One should note that over long times many stock markets are linear on a log-linear plot, meaning the time dependence is exponential with a fixed rate constant. Thus empirically stock market growth is compound growth.

What people want to make of this is up to them. The investment industry obviously has adopted this model as a way to report investment results else we would not have defined the concepts of return, expected return, and CAGR.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by MIretired »

It is a mistake to simply say that the price of a stock or fund is purely speculative. Because the price is relative to expected future earnings per share, and earnings growth rate.
And earnings growth is mostly possible because of compound growth of earnings. Consider growth in earnings year over year at a rate of 10% indefinitely.
You say, 'but that price change is not defined by compounding'. But if the investment has a growth rate, then it is exponentially growing in price. Or compounding. (10% x 10% ...).
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by MIretired »

True, the buy and hold investor's return is only the dividends kept, the dividend growth rate, and the final sale of the whole investment. But that doesn't mean the value of the investment cannot compound in positive direction (dividends reinvested or not.) Kind of a double statement of the growth rate.

The earnings grow at a rate, not just in one fell swoop. Hence, compounding growth. More money to reinvest in growth each period.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by etfan »

This seems like a matter of "medium". We always say money is fungible but it does come in different forms.

A company that gives you dividends, thus allowing you to purchase more shares, makes it easy to perceive the growth acceleration and positive feedback effect (more shares => more dividends => even more shares etc.)

But a company that re-invests its gains in itself is still increasing the rate of its own growth (by expanding into new markets, creating new products, etc). So the rate of return of your still single share in that company could still be accelerating exponentially in value if not in quantity.

So the medium of the compounding effect in the first case is in the quantity of the shares you own, while the medium of the same effect in the second case is manifesting only in the medium of the the value of the single share you own.

The only real difference between these and a Savings account is the fact that Savings accounts only go up in value. But I suppose compound growth could also be negative. Just like upward growth can be exponential, downward shrinking is also potentially exponential.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by 000 »

It's not an ideal term but it is technically correct, insofar as equities experience internal variable compounding.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by nisiprius »

I don't think it's an accurate term. It affects me like a fingernail on a blackboard. But I don't know anything better so I have to tolerate it.

The reason I don't think it is accurate is that to me, "compounding" is short for "compound interest" and I don't think it should be used as a synonym for geometrical growth, or exponential growth.

Originally, there was simple interest and there was compound interest. Compound interest refers to the practice of a lender adding unpaid interest to a loan and charging interest on the interest. In the 1800s at some times and place it was considered usurious and unenforceable in law. If a borrower owed you $100 on a 5% loan and didn't pay it, you could sue him for $100 but you couldn't add it to the loan, charge interest on the interest, and sue him for $105. If there's nothing in the picture that can be called "interest" and nothing that can be called "interest on the interest," I don't think you have "compounding."

At least one dictionary defines compound interest as
Interest computed on the accumulated unpaid interest as well as on the original principal.
It also defines the verb to compound as
To compute (interest) on the principal and accrued interest.
These definitions don't apply to anything but debts and interest and don't make sense in the context of stocks. When a stock investment "compounds" what is the "principal," what is the "accrued interest," what is the interest rate, and what are you "computing?"

Certainly, it is important for investors to understand exponential growth and compound interest, although I don't think it is quite the miracle it is sometimes made out to be.

But it's not worth fighting over.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by 000 »

nisiprius, what about equity in a bank which holds debentures on its balance sheet? :wink: :D
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by nisiprius »

000 wrote: Sat Nov 27, 2021 8:28 pm nisiprius, what about equity in a bank holding debentures on its balance sheet? :wink: :D
I have no clue what you're talking about so let's just say you're right.

(Rise to bait. Pause for attempt to air-quotes 'think.') Wouldn't that only work if those are the only things on its balance sheet? Even then I'm a little queasy if we are talking about a collection of debts each of which is "compounding" at a different rate, because the whole collection will not grow at a constant compound rate.

How about an ETF whose only holding is a single bond?
Last edited by nisiprius on Sat Nov 27, 2021 8:47 pm, edited 1 time in total.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by nisiprius »

Show of hands. Has this fund been "compounding? Is this what you think of as "compounding?"

Image

Yes, you get the balance at the end of each year by adding the product of the previous end-of-year balance and that year's total return to the previous end-of-year balance.

Yes, during the next year you get return on the previous year's return. Not interest on interest, but return on return.

Yes, the performance of the fund is equal to that of a bank account growing at 0.42% compound interest per year.

But is this "compounding?"
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by 000 »

I guess one could argue the semantics both ways.

Equity growth is not compound interest.

But could it still be compound something?

If the term compound itself simply refers to 'growth on growth' and equity firms are using their profits to invest to make more profits, isn't that compounding?

Then again, what the OP actually asked was, is compounding the best word to describe equity growth? And if people are getting it confused (whether reasonably or not) with compound interest, then maybe it isn't. All that equity growth can go away if valuations change. But bonds can also go down if valuations change. The concept really only perfectly fits non-marketable interest bearing products.

As far as this.....
nisiprius wrote: Sat Nov 27, 2021 8:41 pm Show of hands. is this what you think of as "compounding?"
Maybe this is one of those cases where sometimes the 'compounding' was negative, just like sometimes the SCV 'premium' is negative. :mrgreen:
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by MIretired »

I would side with neg. growth not being compounding, which probably throws out the whole comparison. But I've been thinking of compounding as the non-continuous form of exponential growth. Probably mistakenly mathematically, even.

Too bad only 4% of companies account for stock market growth net.

Eta: I would agree if you said compounding is not a growth rate.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by willthrill81 »

We can measure stocks' rate of growth over time. I don't know of a better word to describe that long-term growth rate other than a compound growth rate, so that makes it the best word by default unless someone can think of a more accurate one. Years with negative growth merely bring down the compounded growth rate, nothing more and nothing less.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by MIretired »

willthrill81 wrote: Sat Nov 27, 2021 9:30 pm We can measure stocks' rate of growth over time. I don't know of a better word to describe that long-term growth rate other than a compound growth rate, so that makes it the best word by default unless someone can think of a more accurate one. Years with negative growth merely bring down the compounded growth rate, nothing more and nothing less.
Is compounding not a growth rate? Stock market returns are a growth rate, +/-. But compounding is a different series in which you alternately add a money return and multiply by a rate of return.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by MIretired »

MIretired wrote: Sat Nov 27, 2021 9:21 pm I would side with neg. growth not being compounding, which probably throws out the whole comparison. But I've been thinking of compounding as the non-continuous form of exponential growth. Probably mistakenly mathematically, even.

Too bad only 4% of companies account for stock market growth net.

Eta: I would agree if you said compounding is not a growth rate.
Edit: Or I was thinking of compound growth as the non-continuous example of continuous compound growth. ha-ha.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by MIretired »

And then we say: 'is compound growth the same as compound interest?'.
Compounding monthly a non additive or subtractive bank account:
(P+rate/12)^12 <> (P+(n√rate))^12

But, annually, compound annual growth = compound annual yield.

But it is no longer compound interest, but compound yield.
Last edited by MIretired on Sat Nov 27, 2021 10:48 pm, edited 1 time in total.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by mikeyzito22 »

nisiprius wrote: Sat Nov 27, 2021 8:41 pm Show of hands. Has this fund been "compounding? Is this what you think of as "compounding?"

Image

Yes, you get the balance at the end of each year by adding the product of the previous end-of-year balance and that year's total return to the previous end-of-year balance.

Yes, during the next year you get return on the previous year's return. Not interest on interest, but return on return.

Yes, the performance of the fund is equal to that of a bank account growing at 0.42% compound interest per year.

But is this "compounding?"
"During the period from 2009 to 2017, we faced a significant challenge navigating a speculative market environment." Hussman. You betcha, not compounding and definitely not growing :sharebeer
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by MIretired »

Compound growth <> compound interest, but = compound yield.

Yield defined per duration.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by pascalwager »

No, I don't think "compounding" is correct. Compounding refers to an increase due to principle + interest as in a bank savings account. A stock fund share price is not composed of principle + interest.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by Beensabu »

nisiprius wrote: Sat Nov 27, 2021 8:41 pm Show of hands. Has this fund been "compounding? Is this what you think of as "compounding?"

Image
That is the saddest portfolio growth chart I've ever seen. :shock: It's a tale of options gone wrong...
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by Ferdinand2014 »

nisiprius wrote: Sat Nov 27, 2021 8:41 pm Show of hands. Has this fund been "compounding? Is this what you think of as "compounding?"

Image

Yes, you get the balance at the end of each year by adding the product of the previous end-of-year balance and that year's total return to the previous end-of-year balance.

Yes, during the next year you get return on the previous year's return. Not interest on interest, but return on return.

Yes, the performance of the fund is equal to that of a bank account growing at 0.42% compound interest per year.

But is this "compounding?"
That’s one rather embarrassing fund. Compounding positive for a while and compounding negatively for a while.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by lws »

In compounding, must the value of the ith period depend on the value of the (i-1)th period?
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by coachd50 »

willthrill81 wrote: Sat Nov 27, 2021 9:30 pm We can measure stocks' rate of growth over time. I don't know of a better word to describe that long-term growth rate other than a compound growth rate, so that makes it the best word by default unless someone can think of a more accurate one. Years with negative growth merely bring down the compounded growth rate, nothing more and nothing less.
You can also measure the growth of a human over time. Would you say that is also "compounding"? Honestly asking, not a sarcastic or argumentative reply.

Is it wrong to say define "compounding" is the "growth of the growth"? That extra $1 paid on the $10 earned.
As someone pointed out, just because one can calculate a CAGR mathematically, does that accurately describe how that growth occurred?

Again, my question is asked in reference to a comment made in another post --"live below your means, start investing early, and watch the magic of "compounding".
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by Silk McCue »

coachd50 wrote: Sun Nov 28, 2021 12:22 am [

You can also measure the growth of a human over time. Would you say that is also "compounding"? Honestly asking, not a sarcastic or argumentative reply.
Honestly replying, that is sarcastic and argumentative.

Cheers
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by LadyGeek »

coachd50 wrote: Sun Nov 28, 2021 12:22 am Again, my question is asked in reference to a comment made in another post --"live below your means, start investing early, and watch the magic of "compounding".
That's an excellent point. The wiki uses compound interest to explain why it's important to save early.

See: Importance of saving early

The wiki article compares the growth of a portfolio to earning compound interest. It's not the math, but the idea that the effects of compound interest are multiplied over time. So... the sooner you start saving, the more you'll have for retirement.

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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by coachd50 »

Silk McCue wrote: Sun Nov 28, 2021 6:43 am
coachd50 wrote: Sun Nov 28, 2021 12:22 am [

You can also measure the growth of a human over time. Would you say that is also "compounding"? Honestly asking, not a sarcastic or argumentative reply.
Honestly replying, that is sarcastic and argumentative.

Cheers
I don’t believe it is- and this is why: - I can see an answer of yes being given depending on the interpretation of the word “compounding.

Is compounding “growth over time” or is it “growth due to growth”?

That is at the crux of my question. Is the moving from 5’11 (1.8 m) to 6 foot (1.82 m) considered “compounding” because that 2.5 cm growth is on top of the say 130 cm someone has grown through their lifetime?

My entire question is about what is compounding and if that word should be used when discussing what is illustrated in Lady Geek’s post above
Last edited by coachd50 on Sun Nov 28, 2021 7:38 am, edited 1 time in total.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by coachd50 »

Edit- messed up formatting
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by investorpeter »

coachd50 wrote: Sun Nov 28, 2021 7:11 am
Silk McCue wrote: Sun Nov 28, 2021 6:43 am
coachd50 wrote: Sun Nov 28, 2021 12:22 am [

You can also measure the growth of a human over time. Would you say that is also "compounding"? Honestly asking, not a sarcastic or argumentative reply.
Honestly replying, that is sarcastic and argumentative.

Cheers
I don’t believe it is- and this is why: - I can see an answer of yes being given depending on the interpretation of the word “compounding.

Is compounding “growth over time” or is it “growth due to growth”?

That is at the crux of my question. Is the moving from 5’11 (1.8 m) to 6 foot (1.82 m) considered “compounding” because that 2.5 cm growth is on top of the say 130 cm someone has grown through their lifetime?

My entire question is about what is compounding and if that word should be used when discussing what is illustrated in Lady Geek’s post above
Actually I think human growth is a really interesting analogy that illustrates the confusion over this discussion of compounding. On first blush, it would seem that human growth is not a good example of compounding, because human growth rate obviously slows down over time - otherwise, we would all be towering giants when we retire. As you point out, there is no "growth upon growth" of human height which is the core feature of compounding. But at a cellular level, during certain periods of human development, and in certain organ systems, cells proliferate in a way that could be construed as "compounding". One cell divides into two, and those two divide into four cells, and on and on. Interestingly (and perhaps aptly applied to equities as well), such growth rates are not sustainable over time, nor are they constant except during very short periods of time. Unconstrained cellular growth is basically cancer, which will eventually kill the organism. Sustainable biological systems must develop ways to constrain that growth, without snuffing it out, so as to be able to call upon that ability to grow when needed, such as during early development or in response to injury.

So, the answer is yes and no. Human growth over time does not compound, but when you take a closer look, there are processes underlying human growth that do show features of compounding, but they are counterbalanced by other forces that constrain that growth. I think a similar phenomenon occurs with the overall stock market. In certain parts of the stock market, we can see obvious compounding growth (tech sector, perhaps?), but that rate of growth is not sustainable over time.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by nisiprius »

coachd50 wrote: Sun Nov 28, 2021 12:22 am...You can also measure the growth of a human over time. Would you say that is also "compounding"?...
The initial stages of an embryo, after fertilization, begin with a single cell dividing into two, then the two almost simultaneously dividing into four, then the four into eight. They're mostly just dividing, not growing, and I don't know offhand how the volume weight increases, but that's certainly a kind of exponential growth, the number of cells being 2n where n is the number of divisions. A division is on the order of 15 hours or so but they don't take equal amounts of time. Somewhere around 16 or 32 they quit being synchronized and the general shape quits being a round ball or blastula, and it starts looking more and more like some tiny salamander or something.

Population biologists studied this around the 1800s and I think they may have been the ones to formulate a simple model for exponential growth with a constraint on it. Yep. The model is called the logistic equation and it's a symmetrical S-shaped curve that starts out exponential, slows, reaches an inflection point, curves down, and approaches an upper limit whose approach is a decaying exponential.

Some kinds of growth of individual organisms actually have a decent fit to a logistic curve.

I think economists and financial people hate the idea of any kind of limit to exponential growth and I don't think I've ever heard it referred to in investing discussions. Companies, of course, compete like predators and prey and might be better modeled by the Lotka-Volterra models and equations that emerged in the early twentieth century...

There has long been much debate about whether world human population is following a logistic curve and, if so, where the inflection point and upper limit might be.

In biology, it's not rare to refer to unconstrained exponential growth as "following a compound-interest law" and draw distinctions between "logistic growth" and "compound-interest growth."

To me, personally, the necessary conditions for calling something "compounding" is that a) there is an obvious mechanism in which the expected percentage growth is a percentage of the current size (not the original size), and that the percentage growth rate be constant, or at least very stable and predictable.

Obligatory. I think the "Fidelity Fiduciary Bank" song? monologue? from Mary Poppins is... wonderful. (If you invest your tuppence wisely in the bank--safe! and! sound! Soon that tuppence safely invested in the bank Will! Com! Pound! ... you'll be part of railways through Africa, dams across the Nile, fleets of ocean greyhounds, majestic, self-amortizing canals [fanfare] PLANTATIONS OF RIPENING TEA!!!! "While stand the banks of England, England stands" says a doddering Dick van Dyke as he topples over.)
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
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Re: Is "compounding" the right/best word to describe equity/index fund growth

Post by dbr »

coachd50 wrote: Sun Nov 28, 2021 12:22 am
willthrill81 wrote: Sat Nov 27, 2021 9:30 pm We can measure stocks' rate of growth over time. I don't know of a better word to describe that long-term growth rate other than a compound growth rate, so that makes it the best word by default unless someone can think of a more accurate one. Years with negative growth merely bring down the compounded growth rate, nothing more and nothing less.
You can also measure the growth of a human over time. Would you say that is also "compounding"? Honestly asking, not a sarcastic or argumentative reply.

I would say no because at maturity human growth stops, well it stops for height but maybe not for weight :shock: During the period of time that a human is growing you could express the growth in a compound growth model if you want to, but it would be at a decreasing rate of growth where the growth rate reaches zero in finite time. Examples where we would want to describe growth as compound would not usually include the case where the growth rate drops to zero and stays there.

Is it wrong to say define "compounding" is the "growth of the growth"? That extra $1 paid on the $10 earned.
As someone pointed out, just because one can calculate a CAGR mathematically, does that accurately describe how that growth occurred?

A compound growth model for two periods looks like this:

End Value = Beginning Value * (1 + growth rate 1) * (1 + growth rate 2)

If you multiply that out you get

End Value = BV + BV * gr1 + BV * gr2 + BV * gr1 * gr2

So compounding includes a term which is growth rate 2 applied to the result of growth rate 1, but the essential idea of the concept is multiplication of period 1 result by something to get the period 2 result rather than to think if growth as adding something.

The essence if the description is that it is a description. Whether or not one wants to use that description depends.

For example, take simple rather than compound interest. The value of the investment after some time is

End Value = BV + BV * gr1 + BV * gr2 for two periods.

You can rewrite this as

End Value = BV * (1+ gr1 + gr2)

So the difference is that compound growth is a growing product of a simple sum and simple growth is a simple product of a growing sum.


Again, my question is asked in reference to a comment made in another post --"live below your means, start investing early, and watch the magic of "compounding".

I think statements like this are silly, or perhaps they can be used usefully if taken to be references to a more developed discussion.
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