When do you notice the compounding at work?

[mx711yam]

I have about 180k in our retirement accounts. I haven't seen much growth at all in these accounts over the last year or two apart from my contributions. At what point or dollar range do you start to actually see the magic of compounding work?

Assume I have a basic three fund portfolio.

Thanks

[BahamaMan]

I have about 180k in our retirement accounts. I haven't seen much growth at all in these accounts over the last year or two apart from my contributions. At what point or dollar range do you start to actually see the magic of compounding work?

Assume I have a basic three fund portfolio.

Thanks

At the Very end of a Bull Market.

[goingup]

In a flat market, all you're getting is about 2% investment yield. So for now your contributions far outpace the compounding. At $500,000 you'll start to pick up steam, even at 2%. Of course, we're all hoping for better than 2% returns.

[dbr]

I see it any time I want to compare the value of an investment at one time to the value at another time and notice that the new value is obtained by the value of the old value multiplied by (1+return) or by adding the old value * return to the old value.

If what you mean is when do you feel good about the fact that investments change in value over time, the answer is when there has been a period of strong positive returns. For young savers this begins to make an impression when gains due to returns become significantly larger than contributions. In the meantime returns may be small or to various degrees negative, and then one does not feel so good if one is inclined to have feelings about the state of their investments.

[MIretired]

You have to have consecutive growth, on par, to have compounded growth (growth on growth; qty. = CAGR.)
For instance, 12% * 2 yrs. in a row is (p)*1.12*1.12=(p) * 1.12^2= (p) * 1.2544 ; CAGR = avg. = 1.1272 /yr.

Whereas (p) * (1 + 2*(.12 + .12)) = (p) * 1.24 (no compounding of growth)( ie: if you took out your gains from first year and 2nd year at the ends of these yrs.) , (p) * .24 , avg. for 2 yrs. = .24/2 = 1.12 / yr. (income not compounded.)

[Snowjob]

once your returns are far in excess of your contributions

[dbr]

once your returns are far in excess of your contributions

Succinctly stated.

A consideration is that one also notices compounding when returns are losses large compared to contributions and/or withdrawals.

[Kevin M]

I think you're really looking at rate of return vs. savings rate, since it takes some years for compounding to make much difference. For just the compounding effect, you can compare simple interest on the original amount to compound interest. The longer the time and the higher the rate, the more you notice it.

At a rate of 2% over 10 years, it looks like this:

Code: Select all

Period   Simple  Compound
------   ------  --------
0        10,000  10,000
1        10,200  10,200
2        10,400  10,404
3        10,600  10,612
4        10,800  10,824
5        11,000  11,041
6        11,200  11,262
7        11,400  11,487
8        11,600  11,717
9        11,800  11,951
10       12,000  12,190

At 10% over 10 years:

Code: Select all

Period    Simple    Compound
------    ------    --------
0         10,000    10,000
1         11,000    11,000
2         12,000    12,100
3         13,000    13,310
4         14,000    14,641
5         15,000    16,105
6         16,000    17,716
7         17,000    19,487
8         18,000    21,436
9         19,000    23,579
10        20,000    25,937

Using examples above, if you're saving $10K per year, the increase from savings obviously will dwarf the increase from rate of return or compounding, more so in earlier years and with lower return rates.

Kevin

[dbr]

I think you're really looking at rate of return vs. savings rate, since it takes some years for compounding to make much difference. For just the compounding effect, you can compare simple interest on the original amount to compound interest. The longer the time and the higher the rate, the more you notice it.

At a rate of 2% over 10 years, it looks like this:

Code: Select all

Period   Simple  Compound
------   ------  --------
0        10,000  10,000
1        10,200  10,200
2        10,400  10,404
3        10,600  10,612
4        10,800  10,824
5        11,000  11,041
6        11,200  11,262
7        11,400  11,487
8        11,600  11,717
9        11,800  11,951
10       12,000  12,190

At 10% over 10 years:

Code: Select all

Period    Simple    Compound
------    ------    --------
0         10,000    10,000
1         11,000    11,000
2         12,000    12,100
3         13,000    13,310
4         14,000    14,641
5         15,000    16,105
6         16,000    17,716
7         17,000    19,487
8         18,000    21,436
9         19,000    23,579
10        20,000    25,937

Kevin

In the case where the returns are variable and the range of variation is three or four times the size of the average (imagine a distribution looking rather like a normal distribution with a standard deviation, or some measure of width, three or four times the mean, or some measure of central tendency), it is hard to say just how or when one would notice the difference between compounded and simple growth and when return would become more noticeable than contributions and/or withdrawals.

[Dutch]

Not apropos of the OP, but I always have a "problem" with applying the term compounding to stocks, or anything else that has a variable principal balance.

Sure, after the fact you can express any price appreciation as a compounded return, but I'm not sure if that really is the magic of compounding at work.

[packet]

You notice more as you look less.

:beerCheers,
packet

[LateStarter1975]

You notice more as you look less.

:beerCheers,
packet

+1
I've learned to check my balances much less now, from weekly to monthly, now to quarterly. I've realized I always get a pleasant surprise on the balance whenever I look these days (quarterly) even though the market has been flat and I'm in my very early years of accumulation. For me, savings rate is all that matters now. In 10 years, I'll start looking out for the compounding...

[The Wizard]

Not apropos of the OP, but I always have a "problem" with applying the term compounding to stocks, or anything else that has a variable principal balance.

Sure, after the fact you can express any price appreciation as a compounded return, but I'm not sure if that really is the magic of compounding at work.

Correct.
This is my usual comment in threads having to do with compounding.

From early 2008 until March, 2009, my portfolio balance "compounded" from something well over $1M to something less than $1M.
But at least the # of shares I had increased...

[dbr]

Not apropos of the OP, but I always have a "problem" with applying the term compounding to stocks, or anything else that has a variable principal balance.

Sure, after the fact you can express any price appreciation as a compounded return, but I'm not sure if that really is the magic of compounding at work.

Correct.
This is my usual comment in threads having to do with compounding.

From early 2008 until March, 2009, my portfolio balance "compounded" from something well over $1M to something less than $1M.
But at least the # of shares I had increased...

This issue arises on about any thread beginning with references to compounding. It is a fair statement that the image of compound growth at a steady rate of compounding is not what one gets with an investment portfolio of stocks, or containing any significant fraction of stocks. In the case of the OP, the question is about notice, and for stocks the idea the OP is looking at doesn't exactly apply.

A more general notion of compounding is simply growth where some factor is applied in each successive step to the previous result. The meaning of compound is that the factor is being applied to the result of all the previous applications of some factor causing the successive factors to multiply each other in an increasingly large (in number) set of terms with time. When the factor applied in each step is some sort of sample from some sort-of distribution of possible factors, then you get what stocks do, but the result can be wild and not look very much like the picture of constant compounded growth. I think it is definitely meaningful to continue to use the notion, but one surely cannot expect the results to be that simple.

[sls239]

Personally I felt it was a turning point approximately when a 1% swing in stock prices resulted in difference in value of a full month of income.

And that happened about 10 years in.

[TSR]

I check way too frequently (pretty much daily), but I don't take any action. For me -- with only a little more saved than you -- the relevant transition was where a bad day or good day in the market easily changed the fourth digit (the "thousand" digit), going from, say, $200,000 to $202,000 overnight. I have a hard time keeping track of the smaller digits, but these days there's a lot more action around the thousand mark. To me this just shows that the market is working about as hard as my contributions. One day I hope to get to the point where I don't bat an eye at an overnight change in the fifth digit, which will show that the market is working much harder than my contributions.

[wander]

Didn't you see it before last year?

[john94549]

I see compound growth every month in my retail IRA CDs. While not spectacular, it does go in but one direction.

Generally speaking, folks dismiss IRA CDs as somewhat lame. While true when markets are on a tear, those lame CDs are ever so friendly in a market swoon.

[tibbitts]

I have about 180k in our retirement accounts. I haven't seen much growth at all in these accounts over the last year or two apart from my contributions. At what point or dollar range do you start to actually see the magic of compounding work?

Assume I have a basic three fund portfolio.

Thanks

You're assuming there is such a thing as the "magic of compounding", but it's very period-depended. You can go through a lifetime with no "magic of compounding"; whether you see the effect or not depends on circumstances.

[roflwaffle]

It takes a bit of time, especially since there's a good chance we may not see the same real post tax growth rate (~10.5+% for the S&P500) over the next ~100 years as we have over the past ~100 years.

[staythecourse]

I would say Mr. Clement describes this as "critical mass" in his excellent books. This is the point where one makes MORE money from portfolio growth then they do with the summation of annual contributions.

Looking at different graphs it really seems like for most it is the last 10 yrs. of their working life where you really see the explosive growth of a portfolio. I would generalize it by saying 20 yrs. of slow, steady growth (some years more and some years less based on market conditions) and then 10 yrs. of HUGE growth then retirement over a 30 yr. working life.

Good luck.

[tibbitts]

I would say Mr. Clement describes this as "critical mass" in his excellent books. This is the point where one makes MORE money from portfolio growth then they do with the summation of annual contributions.

Looking at different graphs it really seems like for most it is the last 10 yrs. of their working life where you really see the explosive growth of a portfolio. I would generalize it by saying 20 yrs. of slow, steady growth (some years more and some years less based on market conditions) and then 10 yrs. of HUGE growth then retirement over a 30 yr. working life.

Good luck.

I completely disagree. I felt a huge effect from compounding in my 20s and 30s: salary at work; fixed income; rapid equity appreciation, etc. Now nearing retirement, I don't feel any compounding except compounding of expenses. It's period-dependent, not dependent on life-stage. Remember that, at least taking a traditional age-in-bonds approach, soon-to-be retirees are looking at having over half their investments being capped at, approximately, 0% real in the current environment.

[joe8d]

Compounding is a factor in the FI area.The near zero interest rates of the past 5 year have rendered that concept dead.

[arcticpineapplecorp.]

Only over break times and at lunch. Other than that, I'm prohibited from checking the compounding at work.

[Dandy]

For me it was when the growth of the portfolio excluding my current year contributions, exceeded my yearly contributions. In effect, my portfolio was contributing more than my savings. That is when I felt the compounding effect was wind at my back.

[Garco]

There's an old expression, "A watched pot never boils." Seems to take forever.

If you watch your investments every day, some days you will see a jump up, and some you'll see a sharp decline. But you won't have any context.

If you've made good decisions on allocation, and if you continue to dollar cost average in (from salary, for example), you trust the market.

I'm retired and I have lots of money. I'd like to have more. But for the first 20 years of investing (retirement saving) I didn't do a damn thing about my asset allocation. (I had a simple 2-fund portfolio with TIAA-CREF.) Doing nothing was a bit extreme, but it was far better than what I did **to myself** when I realized I could change my allocation easily to take advantage of the great run up in the market in the 1990's. Keee-rash.

Just focus on steadily putting money into your account and on your asset allocation, not on growth. The latter will happen. 15% invested from salary over 40 years, while avoiding excessive debt, will give you a lovely pile of money for retirement.

[nisiprius]

Even in a bank account, even in the days of 3%+ interest rates, you didn't see a lot of growth in just one year. In fact it always looked rather piffling. In an asset with serious fluctuations, like stocks, it is even harder to see.

I think the first time I really noticed the power of compounding was when hit age 59-1/2, decided to consolidate and move as much as possible of my TIAA-CREF holdings to Vanguard, was going through their statements more carefully than usual. I'd mostly paid attention to the (pleasing) total. What I hadn't noticed was that the total was actually over five times the number of dollars I'd contributed.

(Sure, this was around 2006 and the contributions were made mostly around 1975-1990 and the gain wasn't as big if you took inflation into account. It also represented what to some Bogleheads would be a shockingly conservative allocation--I could have made much more with a heavier stock allocation).

Still, five times.

Where "compounding" comes into play is that turning $10,000 into $50,000 over 25 years represents a 6.64% compound rate. Without compounding, $10,000 would earn a total of $10,000 x 6.64% x 25 = about $17,000 over 25 years. With compounding, $40,000.

[nisiprius]

I have about 180k in our retirement accounts. I haven't seen much growth at all in these accounts over the last year or two apart from my contributions.

Using the figures from my out-of-date SBBI handbook, from 1926 through 2009:

--There were 11 five-year periods during which a 100% stocks lost money (and that's total return, including reinvested dividends).
--There were 5 five-year periods during which a 50% stocks/50% bonds portfolio lost money.

A favorite and endless topic of debate in the forum is whether there is some period of time, relevant to an individual investor, over which stock investments can be trusted to settle down to their "historic" averages and no longer become risky. I don't want to open that can of worms except to say that if there is a holding period at which stocks become trustworthy, it is at least 20 years.

The point on which I think everyone agrees is that in any typically-recommend portfolio--one with reasonable allocations to stocks and bonds--there will not only be 5-year periods of no progress, there will be 5-year periods of actual loss. 5 years of bad returns is a period of time that looks easily manageable when you are gazing at two-century-long charts, but feels endless and almost intolerably disheartening when you are experiencing one.

For me, personally, if the number of dollars in the account including my contributions was bigger at the end of the year than the beginning, I could take it philosophically because I was at least making progress. When it was lower--when my ship was leaking faster than I could bail--it did give me a panicky feeling.

[staythecourse]

I have about 180k in our retirement accounts. I haven't seen much growth at all in these accounts over the last year or two apart from my contributions.

Using the figures from my out-of-date SBBI handbook, from 1926 through 2009:

--There were 11 five-year periods during which a 100% stocks lost money (and that's total return, including reinvested dividends).
--There were 5 five-year periods during which a 50% stocks/50% bonds portfolio lost money.

A favorite and endless topic of debate in the forum is whether there is some period of time, relevant to an individual investor, over which stock investments can be trusted to settle down to their "historic" averages and no longer become risky. I don't want to open that can of worms except to say that if there is a holding period at which stocks become trustworthy, it is at least 20 years.

The point on which I think everyone agrees is that in any typically-recommend portfolio--one with reasonable allocations to stocks and bonds--there will not only be 5-year periods of no progress, there will be 5-year periods of actual loss. 5 years of bad returns is a period of time that looks easily manageable when you are gazing at two-century-long charts, but feels endless and almost intolerably disheartening when you are experiencing one.

For me, personally, if the number of dollars in the account including my contributions was bigger at the end of the year than the beginning, I could take it philosophically because I was at least making progress. When it was lower--when my ship was leaking faster than I could bail--it did give me a panicky feeling.

Not to further sidetrack this thread, I just wanted to add the issue with MOST investors is they get confused on what "accumulation phase" really means for the equity investor. The phrase is NOT meant that you are accumulating dollars, but accumulating shares. It is each share that represents a future stream of cash flow. If folks thought this way they would not be upset at flat or down markets, but would actually look forward to buying MORE shares with the same $/ month they regularly invest.

I really wish there was an option of eliminating the graphics of the amount of dollars they have in their portfolio and just have it represented as the amount of shares. If it did it would be MUCH easier to see the benefit of investing in sideways or down markets. Knowing x dollars is buying 50 shares that month vs. 40 shares would be better at building confidence that a portfolio was still growing even if the numbers in dollars are not.

Good luck.

[Garco]

I agree with the previous comment. But as Nisiprius' comment implies, when the market crashes we are likely to feel that most of our "shares" are tickets on the Titanic.

[itstoomuch]

Ans. When you stop looking at the trees and view the entire forest.

[ofcmetz]

I'm 35 and started investing seriously in 2005. I really noticed compounding in 2013 when the increase of my portfolio beat my contributions for that year. I guess everything I've invested in equity funds since early 2009 has compounded pretty nicely. I agree with the other posters not to look too often and to wait until the expected increase is more than your yearly contributions. Probably a $400,000 portfolio of you are contributing about $20,000 a year. I track the yearly ending values of my portfolio and how much was contributed that year. It gives me a little history to look back on.

[john94549]

Compounding in equities is illusory, at best. On the other hand, compounding in a retail CD is just math. You can actually go to readily-available on-line calculators (moneychimp comes to mind) and plug in your initial buy, the rate, the term, and "voila", the amount at maturity (with compounding) just pops up, like magic.

Back in January of 2008 (when one could still actually get long-term IRA CDs at 5.75%), I bought a 10-year IRA CD from KeyBank. I plugged in all the data on Moneychimp, and calculated what the CD would be worth at maturity.

The irony of the calculation, right before the stock-market melt-down and the Great Recession, was not lost on me. I suspect I was one of the last to purchase the aforementioned IRA CD. Rates began to tumble shortly thereafter.

[dbr]

Compounding in equities is illusory, at best. On the other hand, compounding in a retail CD is just math. You can actually go to readily-available on-line calculators (moneychimp comes to mind) and plug in your initial buy, the rate, the term, and "voila", the amount at maturity (with compounding) just pops up, like magic.

Back in January of 2008 (when one could still actually get long-term IRA CDs at 5.75%), I bought a 10-year IRA CD from KeyBank. I plugged in all the data on Moneychimp, and calculated what the CD would be worth at maturity.

The irony of the calculation, right before the stock-market melt-down and the Great Recession, was not lost on me. I suspect I was one of the last to purchase the aforementioned IRA CD. Rates began to tumble shortly thereafter.

Compounding merely means that the return at any time period applies to what was accumulated at the beginning of that period. What was accumulated at the beginning of a time period is the result of the compounded application of previous returns to the beginnings of their time periods. So that is what compounding means. When the return applied is constant in every time period, the result is easy to see and understand. When the return is variable, negative as often as positive, the result is complicated enough to appear illusory. Not compounding would be adding return at each time period based only on the size of the original investment. That could still look strange if the added return were variable, including negative. It is also possible for constant return compounding to be at a negative return. Radioactive decay is an example of that.

In this thread the issue has been confused by most of the replies noting that the investor is also observing the effects of continual contributions. Those too can be variable or even negative (withdrawals). Also the thread has emphasized observing the amount of gain, aka return applied to present attainment of value. That observes compounding only to the extent the present value is as large as it is because the return has been applied to previously obtained results rather than only to original investment, aka simple return. The application of return to the accumulation of successive contributions may be the larger part of the result as well. In a sufficiently generalized model we could call that compounding also, but in finance compounding would usually mean applying return to initial investment and previous returns on that investment. There would, however, be a sequence of "initial" investments to account for year by year.

I think the OP got his actual answer, which is that having invested starts to have visible consequences when the return in a year equals or exceed the contributions in a year. How one sees this with variable returns is not so clear, however.

[Random Walker]

One can really see the benefits of compounding when a bear market ends and a new bull starts. If the investor has been reinvesting dividends throughout the bear, he is buying more shares at lower cost. When the share value then rises, he will see the additional benefit of all the reinvested dividends.

Dave

[dbr]

One can really see the benefits of compounding when a bear market ends and a new bull starts. If the investor has been reinvesting dividends throughout the bear, he is buying more shares at lower cost. When the share value then rises, he will see the additional benefit of all the reinvested dividends.

Dave

When returns are large and positive, positive compounding becomes very evident. When the returns were small one see little effect. If the returns are large and negative one sees the effects of compounding in the negative direction. This has nothing to do with dividends. If one had not reinvested the dividends, that would have constituted withdrawals. Taking withdrawals increases the negative effect on wealth. Taking withdrawals also reduces the effect of large positive returns, but the investor may not notice the effect unless the withdrawals are large.

Obviously if you don't withdraw money from your investments the eventual growth of those investments is greater than if you do take withdrawals. There is nothing more to how dividends affect this than that.

[staythecourse]

Compounding in equities is illusory, at best.

Sorry, but that is just so wrong. Compounding is just math. I think you are trying to say CD compounding is predictable and equities is not. I am actually happy that is it unpredictable. If it wasn't there would be no risk premium over CD. It is the most basic of theory. Not understanding that basically means you just think equity investors sometimes (most of the time) just get "lucky" when they get returns better then CD's.

Good luck.

[john94549]

I think you are trying to say CD compounding is predictable and equities is not.

Correct. To assume equities will compound requires myriad assumptions, some of which might be true, while others might not. In my humble opinion, compound interest is just math.

Last I checked, just about every site "selling" equities noted "equities may lose value*."

Within FDIC/NCUA insurance limits, CDs don't lose value. If purchased at retail, interest compounds at the stated rate.

Which is not to say one should avoid equities. Just don't assume equities will "compound". From time-to-time, they "implode".

*As an example, just check out VEMAX from April 20 to date. Yup, "equities may lose value." Ironically enough, VEMAX was atop my personal leaderboard until April 20, when it started to go south.

[dbr]

I think you are trying to say CD compounding is predictable and equities is not.

Correct. To assume equities will compound requires myriad assumptions, some of which might be true, while others might not. In my humble opinion, compound interest is just math.

This question is about definitions. If compounding is taken to include the definition that return is constant in successive periods, then equities don't compound because equity returns vary over time. A bank account or CD could compound by this defintion until they change the interest rate. Radioactive decay compounds because all atoms have the same probability of decay in a time period.

If the definition of compounding allows the return to vary from time period to time period then equities do compound. The only assumption is that the return in a period is applied to the principle accrued at the beginning of the period. This includes all the additions made in previous periods, which is what is meant by compounding. Simple growth would mean that the addition in a time period is computed only from the original amount invested and not applied to further increments from periodic return. Simple compounding could still be with variable returns.

I can't think of any assumptions that apply other than these definitions. Naturally the compound growth of equities can be very noisy, either increasing or decreasing in each period, having both growth and decline trends, and not necessarily ending up any extended period with a positive gain.

[gator15]

I've been investing for nearly 13 years now. At this point my contributions still outweigh the interest I've earn each year by a great distance. I expected to earn more in interest than I have over the last two or three years considering how aggressive my portfolio is. This may be the issue. I track my balance monthly and sometimes I will look back a year or two to see where I stood at the time just to see how I'm progressing. I realize I've earned some interest. I just thought it would be more. I want let it deter me. I will just keep saving and hopefully the Yearly interest will reach a point that's satisfying.

[john94549]

Naturally the compound growth of equities can be very noisy, either increasing or decreasing in each period, having both growth and decline trends, and not necessarily ending up any extended period with a positive gain.

Exactly. Equities might, or might not, grow in value. That said, whatever they might, or might not, do, is hardly akin to compound interest. To liken equities to something which actually compounds and increases in value, year-in, year-out, is a stretch. Stocks can go down, and stay down, for a very long time*. The same cannot be said for a retail CD, FDIC/NCUA-insured.

*Had the average Japanese investor/saver been transported in a time machine back to 1990, then given the option of a 2% CD, interest compounded, principal and interest government-guaranteed, well, you get my drift.

[dbr]

Naturally the compound growth of equities can be very noisy, either increasing or decreasing in each period, having both growth and decline trends, and not necessarily ending up any extended period with a positive gain.

Exactly. Equities might, or might not, grow in value. That said, whatever they might, or might not, do, is hardly akin to compound interest. To liken equities to something which actually compounds and increases in value, year-in, year-out, is a stretch. Stocks can go down, and stay down, for a very long time. The same cannot be said for a retail CD, FDIC/NCUA-insured.

My point, which may seem pedantic, in which case it can be ignored, is that just because something is not akin to compound INTEREST does not mean there is no process of COMPOUNDING involved. Compounding of interest is a special case of compounding. The general case of compounding may look very different in results from the case of compound interest, but it is still compounding.

If we are addressing an investor who is using compound fixed interest as a model but looking at stocks, that investor will certainly be misled. The reason for that, however, is not that stock returns don't compound but rather that stock returns are highly variable, including negative. Again, there needs to be a comparison to a case where there is no compounding, but there is no such case in the context of returns by the way return is defined.

[john94549]

dbr, so, you're agreeing with me? Equities might (or might not) "grow", but they most assuredly do not "compound" in the technical sense.

[John3754]

dbr, so, you're agreeing with me? Equities might (or might not) "grow", but they most assuredly do not "compound" in the technical sense.

The technical definition of compounding is generating earnings from previous earnings. That's it, that's all it means. So you're saying that equities do not generate earnings from previous earnings?

I think it should be noted that compound interest, which is what you're talking about, is not the definition of compounding, it's just one specific example.

[dbr]

dbr, so, you're agreeing with me? Equities might (or might not) "grow", but they most assuredly do not "compound" in the technical sense.

The technical definition of compounding is generating earnings from previous earnings. That's it, that's all it means. So you're saying that equities do not generate earnings from previous earnings?

I think it should be noted that compound interest, which is what you're talking about, is not the definition of compounding, it's just one specific example.

You seem to have both an understanding of what I have been saying and some misunderstanding of what I am saying.

Compound interest, which is one thing thing I am talking about (agreed), but NOT the only thing I am talking about (here your statement above does not agree) is not the definition of compounding (agreed), but it is one specific example (agreed). My primary point is that equity returns are also examples of compounding (don't know if you agree with that, but seemingly you would).

The technical definition of compounding includes generation of earnings from previous earnings (agree). I am most definitely saying that equities DO generate earnings from previous earnings. (That was a primary point.)

My primary issues were two:

1. It is certainly the case that equity returns are mathematical examples of compounding though a little more complicated realization of compounding is required than is seen with simple constant interest. This arises from the definition of return and the definition of compounding. It is possible to define compounding so narrowly as to construe that equities don't compound but it would be silly to make such a confining restriction and leave us with no way to talk about how equities evolve over time.

2. Relevant to the original question of this thread, the growth of equity investments is complicated enough that when one "sees" compounding does not have a clear answer. The issue is sidetracked from compounding when there are also contributions and withdrawals.

[john94549]

dbr, at long last, I think I understand. Compounding is a broader concept than what I assumed. Thanks for your patience.

[Kevin M]

Much of this discussion seems to have devolved into what could simply be described as the fact that a geometric mean, or compound annual growth rate (CAGR) can be calculated after the fact for any investment; for certain fixed-income investments the CAGR can be known in advance, but for an investment with any risk it can only be guessed or estimated.

I thought it would be interesting to just Google the phrase actually used by OP, "magic of compounding", and see what a "reliable" site or two said.

First one I looked at is US Department of Labor: The Magic of Compounding.

Compounding investment earnings is what can make even small investments become large investments given enough time.
How It Works - The money you save (either in a savings account, a mutual funds or in individual stocks) earns interest. Then you earn interest on the money you originally save, plus on the interest you've accumulated. As your savings grow, you earn interest on a bigger and bigger pool of money.

So highly simplified, but explicitly talking about interest on interest.

How about Morningstar: The Magic of Compounding:

When you were a kid, perhaps one of your friends asked you the following trick question: "Would you rather have $10,000 per day for 30 days or a penny that doubled in value every day for 30 days?" Today, we know to choose the doubling penny, because at the end of 30 days, we'd have about $5 million versus the $300,000 we'd have if we chose $10,000 per day.

Compound interest is often called the eighth wonder of the world, because it seems to possess magical powers, like turning a penny into $5 million.

Again, talking about interest.

Then I got bored.

This did get me thinking though that the typical examples showing how much difference starting early makes, which I've used myself, are kind of flawed. The typical examples, as I showed in an earlier reply simply to demonstrate the interest-on-interest component, assume steady returns. If one gets a lousy sequence of returns, starting early may not help nearly as much. This gets into the distinction between internal rate of return, which Vanguard and others call personal rate of return, and the return on the funds themselves. The former factors in cash flows into and out of the investment in addition to the return of the investments themselves.

EDIT: Our own Bogleheads Wiki article on Bogleheads investment Philosophy uses exactly this simplified type of example to demonstrate the benefit of starting early: Bogleheads® investment philosophy - Bogleheads

Kevin

[dbr]

This did get me thinking though that the typical examples showing how much difference starting early makes, which I've used myself, are kind of flawed. The typical examples, as I showed in an earlier reply simply to demonstrate the interest-on-interest component, assume steady returns. If one gets a lousy sequence of returns, starting early may not help nearly as much.

Generalizing the formulation of compounding to variable returns is a very simple idea. It is inherent in defining return at all. The actual computation of the results may give some complicated behavior. Being able to formulate that behavior is the whole point. You can't even talk about the effect of various sequences of returns if you haven't formulated the problem.

This gets into the distinction between internal rate of return, which Vanguard and others call personal rate of return, and the return on the funds themselves. The former factors in cash flows into and out of the investment in addition to the return of the investments themselves.

When there are contributions and withdrawals the formulation and the results become more complicated, but, as stated, it is a problem that has already been worked in the form of IRR. The idea of return applying to what ever return was already earned is still the starting point for the analysis. One would be gobsmacked as to what other concept one would apply to the situation.

EDIT: Our own Bogleheads Wiki article on Bogleheads investment Philosophy uses exactly this simplified type of example to demonstrate the benefit of starting early: Bogleheads® investment philosophy - Bogleheads

Yes, the formulation still contains the understanding inherent in the compounding idea. It also contains the consequences of variability of returns risk, among other fundamentals of investing. It would not be possible to understand investing whether in savings or in stocks without applying the idea of compounding of returns.

Kevin

[ryman554]

I think the OP got his actual answer, which is that having invested starts to have visible consequences when the return in a year equals or exceed the contributions in a year. How one sees this with variable returns is not so clear, however.

I think the OP got this answer, too, from a reply above:

When the daily (normal) fluctuations hit the <n>th digit, when the regular (bi-weekly, weekly, monthly) contributions are in the same digit.

Ex: I put in 2k a month. Daily fluctuations $20/day, that's 1% of my contribution. Meh. This interest rate is really low. When am I going to see this growth?
Ex: I put in 2k a month. Daily fluctuations $1k/day, that's 50% of my contribution. Neat. I'm growing as fast as I'm putting in.
Ex: I put in 2k a month. Daily fluctuations $10k/day, that's 5x of my contribution. Wow! My money is really working for me! I hope the market goes up!


Right now I'm in stage 2 and have emotionally transitioned to it. So you can say "I've noticed" and it's given me more momentum to keep it up.

[German Expat]

I don't think the OP is really asking about compounding. He is probably more worried about the changes in his already invested balance and their influence vs just saving more.

I felt that the changes in my invested balance (going up or down) started to really make an impression on me when my invested balance reached 10x the newly yearly added money. I would not really call this compounding, this is more a psychological effect. Even in the bad years around 2007 my year end balance was still higher at the end of the year then the previous year because of all the additional money we saved. Now this would be a completely different story today.