# Power of compounding



## jumbalaya (Jan 17, 2013)

I don't quite understand it... say I bought ABC at $10 today and it fluctuated up and down until it hit $10 again next year. Then in 2 years, it's worth $15. I only gain $5, regardless of whether I buy it today or a year from now?

Does compounding only work if you re-invest dividends? Not all stocks pay dividends...

Thanks!


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## andrewf (Mar 1, 2010)

It still compounds. It's a 50% gain over two years. It doesn't matter whether it is 0% return one year then 50% the following year. Either way, the compound return is 1.5^0.5-1= 22.47% per year.

You didn't mention any dividends in your example, so it's impossible to answer your question.


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## jumbalaya (Jan 17, 2013)

Yeah but, why buy today if you get the same gain of $5 whether you buy it today or buy it a year from now? 

Person A: Buy ABC at $10 in 2013, Sell for $15 in 2015, gain $5

Person B: Buy ABC at $10 in 2014, Sell for $15 in 2015, gain $5

The dividends was a separate question. I know the longer you keep a stock that pays dividends, the more money you will get... so if that's the power of compounding, I understand. With regards to capital gains, I don't see it.


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## HaroldCrump (Jun 10, 2009)

jumbalaya said:


> Yeah but, why buy today if you get the same gain of $5 whether you buy it today or buy it a year from now?


That requires the ability to predict the future.
In your example, can you predict that ABC will be $10 in 2014 and $15 in 2015?

_Do you feel lucky? Well, do ya?_


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## andrewf (Mar 1, 2010)

I don't understand what your question is. 

If there are no cash flows between now and the end of year 2, there is nothing to compound.


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## brad (May 22, 2009)

I think the confusion arises because many people talk about compounding in equity investments as if it were the same as compounding in a savings account: in a savings account, your interest gets added to your principal and then interest is paid on the principal-plus-interest. Stocks don't really work this way, but as andrewf demonstrated in his first response, there is still compounding going on. Inflation also compounds.


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## jumbalaya (Jan 17, 2013)

HaroldCrump said:


> That requires the ability to predict the future.
> In your example, can you predict that ABC will be $10 in 2014 and $15 in 2015?
> 
> _Do you feel lucky? Well, do ya?_


True. but this scenario just points out that investing earlier doesn't mean it's good. The "power of compounding" didn't help Person A here.

brad: Yeah, I think I was confused by this - comparing it to compounding interest in a savings account. 

I guess the point I'm trying to test is that investing earlier isn't such a big deal... it's all about market timing (which is definitely impossible for me to do).


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## Eclectic12 (Oct 20, 2010)

jumbalaya said:


> ... brad: Yeah, I think I was confused by this - comparing it to compounding interest in a savings account.
> 
> I guess the point I'm trying to test is that investing earlier isn't such a big deal... it's all about market timing (which is definitely impossible for me to do).


Or about the alternatives - As much as person A might be jealous of person B, I'm sure both are much happier than person C who has made $0.26 over the two years in a compounding savings account.


Cheers


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## none (Jan 15, 2013)

Not to be belittling but: '.....investing earlier doesn't mean it's good'...... ummm... isn't that obvious?

Investing early/late or whenever in something that doesn't increase in value isn't good.....

Consider you're example, what if the growth occurred in the first year but not the second? When you calculate the average return over the 2 year period then obviously investing early was a good thing.


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## andrewf (Mar 1, 2010)

Investment returns are unknown. Say you knew that there would be a 50% increase over two years, but you didn't know what the return in each year would be. Say you 'gambled' and decided to wait a year to invest, expecting then 0%, then 50% returns in year 1 and 2 respectively (your original example). Then, what actually happens is 50% return in the first year and 0% in the second. Then waiting one year is a disaster. The expected compound annual return is 22.47%--why not invest now? Unless your crystal ball can reliably predict returns?


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## none (Jan 15, 2013)

b/c

1.5^(-.2+.7)-1 = 0.2247449


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## jcgd (Oct 30, 2011)

Op, you answered your own question. Since you can't time time market, yet the market typically goes up over a long period, the earlier you get in the more likely you are to make money. 

Stock prices are dynamic, but if you want to see the volatile compounding consider this:

You buy a stock for $10 today. 
Tomorrow it increases by 1% and is then worth $10.10. 
The following day it increases 1% and now the stock is worth $10.201. 

You made $0.101 the second day due to compounding.


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## Sherlock (Apr 18, 2010)

That's why there's no point in investing in stocks (or ETFs/MFs) taht don't pay dividends unless you're actively trading. Thoguh I'm sure someone who bought AAPL in 2003 would disagree...


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## none (Jan 15, 2013)

How do you arrive at that conclusion?


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## andrewf (Mar 1, 2010)

Sherlock said:


> That's why there's no point in investing in stocks (or ETFs/MFs) taht don't pay dividends unless you're actively trading. Though I'm sure someone who bought AAPL in 2003 would disagree...


That is totally incorrect. Non sequitur.


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## Sherlock (Apr 18, 2010)

Well if you disagree with me, then you're wrong, so there.


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## w0nger (Mar 15, 2010)

compounding in equity markets shouldn't neccessarily be associated with the buy and hold strategy. The idea is to make a profit each transaction and re-invest those profits, hence the effects of compounding...


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## none (Jan 15, 2013)

w0nger said:


> compounding in equity markets shouldn't neccessarily be associated with the buy and hold strategy. The idea is to make a profit each transaction and re-invest those profits, hence the effects of compounding...


yesh, it's just dependant upon the arbitrary time point you decide to calculate gains. I feel like I've been transported back to grade 6.


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## jcgd (Oct 30, 2011)

You buy a share of a company, the company grows/compounds their earnings and the stock price of the company reflects that. There's your compounding. I would say compounding in the equity markets would most strongly represent a buy and hold strategy, letting the compounding do it's thing. You can by and sell with any old things, you don't need the equities market to do that. But yes, I agree with Andrew, None, Wonger, etc.


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## andrewf (Mar 1, 2010)

Sorry Sherlock, but your conclusion didn't follow from the premise. There are many examples that contradict your reasoning. Not sure what more explanation you wanted.


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## lonewolf (Jun 12, 2012)

Investors have to be carefull & make sure thier method is suitable for compounding if thier going to use compounding. When the math is done a method can make money if compounding of gains & losses is not done but bet size is kept the same & or based on a percentage of account size. That same method will lose money if compounding is done.

In my opinion only the very best methods will allow for compounding.

If your playing the market you should know how well your method does using compounding, keeping bet size the same size & or bet size as a percentage of your account. Do your portfolio a favour & do the math


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## andrewf (Mar 1, 2010)

All this makes math sound like magic. Compounding or not is just a way to think about it, it doesn't change the outcome...


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## lonewolf (Jun 12, 2012)

Math like a picture is mans most exact language.

Beta slipage, when using inverse ETFs & or leveraged etfs can cause an investor to lose money even if the market moves in thier direction if the market does like it normaly does have closes both up or down from the previous close on its path up or down in the direction the investor is playing.

Not all methods of the playing the market are powerfull enough to make money when beta slipage enters into the picture.


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## Eclectic12 (Oct 20, 2010)

Sherlock said:


> That's why there's no point in investing in stocks (or ETFs/MFs) taht don't pay dividends unless you're actively trading. Thoguh I'm sure someone who bought AAPL in 2003 would disagree...


Odd ... I can see where an active trader would claim there's a bigger profit compared to buying once and holding.

I'm not sure why there would be no point in investing in a stock that's split 2:1 twice and is trading 60% higher today than when purchased. I'd have to check the 2% - 3% interest being offered over the same time frame compounding works out to but I suspect the value difference makes a point. :biggrin:


Cheers


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## jumbalaya (Jan 17, 2013)

none said:


> Not to be belittling but: '.....investing earlier doesn't mean it's good'...... ummm... isn't that obvious?
> 
> Investing early/late or whenever in something that doesn't increase in value isn't good.....
> 
> Consider you're example, what if the growth occurred in the first year but not the second? When you calculate the average return over the 2 year period then obviously investing early was a good thing.


i've seen the advice to get in on the market asap everywhere on the web, just couldn't understand the reasoning behind it. They also mention missing the greatest ups and downs of the market and how that affects you, but if you hold past that period, it shouldn't affect you...

so what I'm getting from this thread is that there is no compounding/it's not relevant to buy and hold.


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## none (Jan 15, 2013)

This thread deserves a face palm.


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## brad (May 22, 2009)

No, there is compounding, it's just compounding returns, not compounding "interest." 

Here's an excerpt from a New York Times article critiquing Dave Ramsey's investment advice that explains some of this:

"Say you invest $10,000, and you double your money in the first year. You now have $20,000, or a 100 percent return. But in year two, you lose 50 percent. Your balance is back at $10,000. The “average annual return” on your investment is 25 percent (100 percent minus 50 percent divided by two years = 25 percent), but you have earned nothing.

That’s why knowledgeable investment advisers use 'annualized' returns, also called the compound annual growth rate, to measure investments. That formula smooths out the swings in the market and shows what you’ve actually earned on your investment."

See http://financialawakenings.com/investment-updates/pessimistic-math-and-12-returns. 

Also see this story, although this writer fails to make a clear distinction between compound interest and compound returns:

http://www.wisebread.com/the-false-allure-of-compound-interest


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## Four Pillars (Apr 5, 2009)

none said:


> This thread deserves a face palm.


Lol. Yeah.


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## andrewf (Mar 1, 2010)

none said:


> This thread deserves a face palm.


That's what I thought, but I was being polite.


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## none (Jan 15, 2013)

You're a better man than me.


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## Toronto.gal (Jan 8, 2010)

jumbalaya said:


> I guess the point I'm trying to test is that investing earlier isn't such a big deal....


The 'power of compounding' takes time! After all, it's not about a simple interest, but about accumulated returns/long-term investing. However, what you are talking about here, has more to do with short-term, rather than 'early' investing.

Investing in 2013 vs 2014/2015 as per your example, is not exactly what is meant by investing early & not suitable at all for the compounding definition. The magic of the latter, does not happen in 2 years, but in 5/10/20, etc., and after periodic contributions over all those years, hence the point in starting early. Try to find a chart that explains/illustrates compound returns for a short period of time. The 't' in the CI formula = number of year*S* invested.

Do you believe that the average investor that would have started investing at 45, will be better off than the one who started at 25, when both wish to sell at 55? 

Investing early no doubt is important! And with respect to non-guaranteed investments, there is a very good reason why the basic rule is not to invest money that you'll need in the next 5/10 years [as opposed to a year or two], so when you buy a stock in 2013, you should not realistically be expecting a compounding return by 2014/2015.


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## Argonaut (Dec 7, 2010)

I love compounding, and was doing some calculations the other day. I found that in my case, making a measly extra 1% return per year was more than three times as effective as saving an extra $1000 per year.


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## none (Jan 15, 2013)

Says the guy with $300,000 invested.


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## Argonaut (Dec 7, 2010)

Not at all; says the guy with a little money and a lot of time. The time is the important factor in the calculation.


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## none (Jan 15, 2013)

Argonaut said:


> Not at all; says the guy with a little money and a lot of time. The time is the important factor in the calculation.


I think you missed the math - by definition, if you were going to make three times more than 1000 per year ($3000) from an extra 1% you would need to have 300K invested.

See what I did there?


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## Argonaut (Dec 7, 2010)

I don't think you understand the power of compounding. Try this link and play around with some numbers.

http://www.moneychimp.com/calculator/compound_interest_calculator.htm


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## none (Jan 15, 2013)

I do but it depends on how much you start with.

For example, starting with 200K adding an extra 3K per year is equivalent to an additional percentage per year (after 20 years).


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## Argonaut (Dec 7, 2010)

Well yes, but your $300k comment only made sense with looking at one year. In which compound interest is largely irrelevant.

In my case: TFSA balance of roughly $33,333. Retirement in 40 years for a nice round number.

- $5000 annual contribution, and 10% return gives me a balance of $3.9 million
- Bump that up to $6000 annual contribution, and the balance is $4.4 million
- Keep the $5000 contribution, but manage 11% return and the balance is $5.4 million
- So adding an extra $1000 gives me $500k down the road, whereas an extra percent gives me $1.5 million

This doesn't factor in possible DRIPs either, which makes compounding more pronounced. It just assumes a repurchase with leftover dividends during the contribution phase. I'm already ahead of the game at 18% annual return in the TFSA, which I know will be hard to maintain. But the calculations I looked at will make me claw for every percentage point.


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## My Own Advisor (Sep 24, 2012)

@Argo,

Can you imagine though it you could keep up that pace (18%), even for another 5 years? 

Wouldn't it be nice....

TFSA balance of $33 K is nicely done. I'm just under $30 K. Need some more high-yielding CDN stocks in there.


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## lonewolf (Jun 12, 2012)

The link argonaut provided for the compound interest calculator is the one I have been using for back testing compound gains & losses. The problem is the gains & losses are differnt each trade which results in a lot of work calculating each one. 

Does anyone know of a compound calculator on the net where each percentage increase or decrease does not have to be calculated seperately & added to the previos number to get the end result.

I was looking for a compound interest calculator where principal is typed in & a high number of percentage gains or losses for each trade is typed in. Then the calculator does the rest with out having to type number of times the interest is compounded because it is almost always 1 because the rate usually changes. I was looking for a calculator that does this to 2 decimals.

Thanks in advance


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## Jungle (Feb 17, 2010)

You can also use total return, but I like CAGR (compounded annual growth rate) for measuring just about anything. 

And like ARGO said, an extra 1-2% on that CAGR can make a BIG difference over the years.


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## HaroldCrump (Jun 10, 2009)

Jungle said:


> And like ARGO said, an extra 1-2% on that CAGR can make a BIG difference over the years.


That is why mutual funds with 2.5% MERs will never make anyone rich.


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## Four Pillars (Apr 5, 2009)

HaroldCrump said:


> That is why mutual funds with 2.5% MERs will never make anyone rich.


That's just wrong Harold - there are lots of mutual fund company shareholders and executives/salespersons who have gotten rich from these products. Please double check your facts before posting.


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## Toronto.gal (Jan 8, 2010)

The early morning bike-rides really make you think clearly FP. :encouragement:


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## Four Pillars (Apr 5, 2009)

Toronto.gal said:


> The early morning bike-rides really make you think clearly FP. :encouragement:


Haha thanks.

As sad as I am at the demise of our backyard rink, it's nice to be able to ride to work without freezing my brain and other body parts.


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## Sampson (Apr 3, 2009)

I think the 'power of compounding' has been wrongly engrained into our heads. Its a quick metric to demonstrate the benefits of saving early in life, but in my view, there are 2 more important 'rules' people should concern themselves with.

1. Equity outperformance over other asset classes requires great lengths of time 15-20+ years.
2. Sequence of returns risk can wipe out all the benefits of compounding. Argo's $4M portfolio could become $2M in a year if risk is not adequately controlled for. Additionally, 10% annually for 5 years is very different from 30% in year 1, 2% in year 2, 2% in year 3, -5% in year 4, and X% in year 5.


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## Argonaut (Dec 7, 2010)

This is where I think that a dividend strategy has its merits, as much as it has become cool to bash dividends on this forum. A handful of companies that provide a nice aggregate yield - I aim for 4% but at the current levels of dividend stocks it may be closer to 3.5%. Suddenly that extra 6% per year doesn't seem so hard to achieve in the long run to get to 10%. Growing dividends tend to grow with share prices, providing a return that is more stable and predictable than the general market. Cue the dividend bashers.


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## Sampson (Apr 3, 2009)

Argonaut said:


> Growing dividends tend to grow with share prices, providing a return that is more stable and predictable than the general market.


Realistically, I wonder how much of an effect the dividend have compared to consistent contributions. Even at the height of yield in my portfolio, the amount of new money entering my portfolio from dividends was quite minimal (20%) compared to new savings. I am clearly in the accumulation phase, but when one considers a real 'hypothetical' portfolio where the majority of its makeup for the first 10+ years are from contributions, then the effect of the dividends is appreciably small.

I don't know that there are any 'dividend bashers' - but some folks that either don't believe the hype, or believe that it is far too easy to chase yield and have poorer overall returns.


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## andrewf (Mar 1, 2010)

It's a total mischaracterization to say that dividends are being 'bashed' on the forum.

There's nothing wrong with dividends. But dividends are no better than other ways to earn after tax total return. We're bashing dividend fetishization.


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## Toronto.gal (Jan 8, 2010)

Sampson said:


> 1. Realistically, I wonder how much of an effect the dividend have compared to consistent contributions.
> 2. I don't know that there are any 'dividend bashers'


*1.* Leaving contribution comparison aside, the div. effect is not small at all. If you DRIP, it adds up considerably! Today, a stock you bought a decade ago for $20, might only be a mere $25, so while your capital gains of your original investment would be low, by the time you added the dividends you received in those 10 years x the number of additional shares you purchased with said dividends, then the return suddenly does not look that bad at all thanks to those dividends! In fact, those dividends, at a reasonable yield of 4%/5%, would easily pay 1/2 of your original investment [not counting any contributions]. 

*2.* I'm critical of those chasing ridiculous dividend yields, but that's not bashing. I also disagree with single strategies, but that's also not bashing, merely an opinion.


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## My Own Advisor (Sep 24, 2012)

Totally agree with you T.gal regarding your point # 1. I find the DRIPs are definitely accelerating my portfolio growth.


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## Sampson (Apr 3, 2009)

I don't downplay the value of dividends at all TGal, but let me use the TFSAs as an example.

Everyone in the accumulation phase should ask themselves how large their TFSA is. Did it get there because of the dividends? or because of the contributions? Over time, I have no doubt that the returns from the initial investments (whether due to dividends or other forms of returns) will be a major factor, but not early in an investors career.

I have about $35.5k in my TFSA, only about 5% came from dividends, 20% from capital gains, and 75% from the contributions. I liken this to someone early in the accumulation phase, most of the monies are from contributions.


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## Argonaut (Dec 7, 2010)

It's hard to get the full effect of dividends and compounding when we're only talking about a four year window. It's like breeding rabbits. Eventually you'll be getting more rabbits by internal bunny portfolio growth than you can contribute by bringing in fresh new rabbits. Granted, bunnies probably yield a bit higher than 4%.


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## Jungle (Feb 17, 2010)

Dare I say that certain dividend stocks can grow cash flow faster to support a financial goal than doing a couch potato total return method? Also eliminating the sequence of portfolio withdraw risk (like cashing in your portfolio during 2008 to live of the money..) 

hmmm great debate. Total return will probably win over the years but if growing dividend cash flow can support the goal, there is a winner.


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## My Own Advisor (Sep 24, 2012)

I like your thinking jungle but you're going down a dangerous road /debate .

Here is a calculator I enjoy using when looking to see what just one of my dividend paying stocks might be paying in another 20 years since I've owned them.

http://www.dividend-calculator.com/quarterly.php

Using starting yield 3%, dividend growth rate 3%, 100 shares, cost per share $50, 30 years to hold....

You started with $5000.00 and ended up with $21147.51 for a total gain of 322.95%. This was over 30 years so that makes your average annual gain 10.77%.


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## eulogy (Oct 29, 2011)

Jungle said:


> Dare I say that certain dividend stocks can grow cash flow faster to support a financial goal than doing a couch potato total return method? Also eliminating the sequence of portfolio withdraw risk (like cashing in your portfolio during 2008 to live of the money..)
> 
> hmmm great debate. Total return will probably win over the years but if growing dividend cash flow can support the goal, there is a winner.


I agree with you, if the goal is to produce income. Most people are pretty good at producing an income (job) while they're growing their investments. 

When you mention "portfolio withdraw risk" I do find that to be mental accounting (I usually call it mental masturbation ). It's just some accounting in your head that makes you feel better. A stock is worth what a stock is worth *or* A stock minus dividend is worth what a stock plus a dividend in your bank account. It remind me of excitement for a big fat tax refund, when at the end of the day my after tax income was always what it was.


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## Sampson (Apr 3, 2009)

Argonaut said:


> It's hard to get the full effect of dividends and compounding when we're only talking about a four year window.


That was my point all along, post 48. I also guess many people don't max out their TFSA, so the nominal value of the dividends would be even smaller.


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## namelessone (Sep 28, 2012)

It compounds exponentially if you keep invested and the investment keeps on growing. 
As a simple example, I started investing 6 years ago. In just 3 months in 2013, my $ gains almost equals to the accumulative $ gain from the past 5 years.


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## Toronto.gal (Jan 8, 2010)

Sampson said:


> That was my point all along.....


As was mine when trying to explain to the OP the meaning of his thread title in post #31.

*My-Own-Advisor:* I'm a synthetic & traditional DRIPPER, and with the latter, as you know, every penny is reinvested every Q. I was aggressive contributing to some of the severely punished stocks over the last couple of years, ie: MFC/RY, and as a result, now the dividends are doing the hard work, ie: the contribution.


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## andrewf (Mar 1, 2010)

Jungle said:


> Dare I say that certain dividend stocks can grow cash flow faster to support a financial goal than doing a couch potato total return method? Also eliminating the sequence of portfolio withdraw risk (like cashing in your portfolio during 2008 to live of the money..)
> 
> hmmm great debate. Total return will probably win over the years but if growing dividend cash flow can support the goal, there is a winner.


This is the stock picker argument. 'I can beat the market'. The empirical evidence does not support that assertion.

Sequence of returns risk is the same for dividends vs. capital gains portfolios of equivalent volatility.


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## andrewf (Mar 1, 2010)

My Own Advisor said:


> Using starting yield 3%, dividend growth rate 3%, 100 shares, cost per share $50, 30 years to hold....
> 
> You started with $5000.00 and ended up with $21147.51 for a total gain of 322.95%. This was over 30 years so that makes your average annual gain 10.77%.


Math faux pas. Average % gain is meaningless. This is a thread about compounding, isn't it?


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## Sampson (Apr 3, 2009)

andrewf said:


> Sequence of returns risk is the same for dividends vs. capital gains portfolios of equivalent volatility.


Agreed. I meant only to say that the exponential power can be mitigated or removed quickly depending on how consistently positive returns are over a period of time.

@ TGal, I saw the post, but have to admit I sorta forgot about it half way through this conversation, so many different points in this thread.


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## My Own Advisor (Sep 24, 2012)

Hey andrewf, yes it is, so my post should probably belong to another thread 

And yes, average gain is meaningless vs. real-returns.


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## andrewf (Mar 1, 2010)

No, not that. The longer the time frame, the higher the average return %.

Say 10% compound annual growth rate. 1 year average % return is 10%. 10 year is 15.9%. 20 year is 28.6%. 30 year is 54.8%. 40 year is 111%. All with the same CAGR of 10% per year. Average (arithmetic) % return is meaningless... you have to use the geometric mean annual return aka CAGR.


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## My Own Advisor (Sep 24, 2012)

I see! Thanks.


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