Author Topic: How does an investment portfolio accure compound Interest.  (Read 5681 times)

sbones

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How does an investment portfolio accure compound Interest.
« on: June 13, 2016, 01:22:20 PM »
Hello all!

I hope this isn't too noob of a question to ask. But I think it's an important one to ask and it is my first post! :)

I think there is a lot of confusion about this idea. If you buy an index fund, I believe your gains are simply measured in % of the fund from the time you but until the time you sell.

So, given that this is true, how does a fund or portfolio, with index funds in them, accrue compound interest?

I'm also a where that some stocks and funds pay dividends and those can be re-invested to accumulated some compound interest, but I am talk about just funds and portfolios.

Thanks!!!!

dandarc

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Re: How does an investment portfolio accure compound Interest.
« Reply #1 on: June 13, 2016, 01:33:28 PM »
http://jlcollinsnh.com/stock-series/

Why are you arbitrarily looking at only the day you buy and the day you sell?  Example:

Your way:
I bought X shares of the fund and held for 3 years, then sold.  It went up D%.  Therefore my return was D% and there was no compounding.

Another way:
You buy X shares of the fund.  The price goes up A% this year, B% next year, C% the third year.  This fund doesn't pay dividends.  Then you sell, and you get (1 + A%) * (1 + B%) * (1 + C%) = 1 + D%.  Same total return of D%.  The 3 annual returns compounded to yield the total return over the 3 year period.

mathlete

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Re: How does an investment portfolio accure compound Interest.
« Reply #2 on: June 13, 2016, 01:34:27 PM »
It's not really "interest" as much as it is an appreciation in value of the underlying asset.

If an asset raises in price/value by 8% per year, after two years, it is worth 1.1664 times what it was worth at the start. (1.08 * 1.08)

In the context of investments, compound growth is usually something that is discussed after the fact.

If an investment raises by 50% over 3 years, the compound growth rate is said to be about 14.5% (or the cubed root of 1.5).

That doesn't mean that the investment actually went up by 14.5% every year, but the value of the end result is the same.

mathlete

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Re: How does an investment portfolio accure compound Interest.
« Reply #3 on: June 13, 2016, 01:46:31 PM »
No one really knows how the price of an asset will change over any given time period, so compound annual growth rate (CAGR) is a useful assumption to set when trying to determine how much your investments will be worth in X amount of years.

If you're investing for 5 years, a good place to start when picking your CAGR assumption, is to look at every possible 5 year period over the history of the equities market. This is, in essence, what the FIRE calculator does.

http://www.firecalc.com/

See the slide below for another visual. It shows the best and worst possible CAGRs over many different investment time frames.

http://image.slidesharecdn.com/slideshare-130714133930-phpapp02/95/what-makes-us-bad-investors-25-638.jpg?cb=1373809254

So according to the slide, the best 10 year annualized growth rate in history was 18.3%, while the worst was -4.4%. The chart looks as we'd expect. There is a less volatile range of returns the longer you invest your money.

Finally, a fun tool to look at is Money Chimp's stock market CAGR calculator.

http://www.moneychimp.com/features/market_cagr.htm

This lets you see the compound annualized growth rate of the S&P500 over any time frame.

sbones

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Re: How does an investment portfolio accure compound Interest.
« Reply #4 on: June 13, 2016, 02:59:43 PM »
Thanks guys, I'm getting a real education here.

So basically a fund or portfolio without dividends accumulates an annualized return or CAGR? I can understand that.

But I see that almost all retirement calculators use a compounding interest calculator to estimate returns with a given percentage rate over a period of time. Why do they use this?

I still don't know how a portfolio accumulates compounding interest? Shouldn't portfolios simply use an annualized return calculation?

marty998

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Re: How does an investment portfolio accure compound Interest.
« Reply #5 on: June 13, 2016, 03:29:04 PM »
Assuming the dividend is nice and smooth (which is never the case), and the stock you purchase has zero growth or loss (also never the case)

If you have an investment in company XYZ of 100 shares worth $100 and it generates a dividend of $0.06c per share. You will get paid a dividend of $6, which when reinvested, means you now have 106 shares worth $106 after year 1.

You then get a dividend of $6.36 in year 2 which means you now have 112.36 shares worth $112.36 after year 2 (growth of $6.36)

Each year the growth is a little more than the year before.

Portfolios don't accumulate compound interest. Portfolio growth, however, can be described in terms akin to compound interest.

MDM

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Re: How does an investment portfolio accure compound Interest.
« Reply #6 on: June 13, 2016, 04:00:26 PM »
I still don't know how a portfolio accumulates compounding interest? Shouldn't portfolios simply use an annualized return calculation?

How would you express the difference between "accumulates compounding interest" vs. "an annualized return calculation" in equation form?

BDWW

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Re: How does an investment portfolio accure compound Interest.
« Reply #7 on: June 13, 2016, 04:16:21 PM »
I'll throw my hat in the ring.  The compounding effect happens because each annual percentage gain is applied to the total(principal + gain) of the previous year.

A hopefully simple example. Say you have $100 in an account that returns 10% per year. For this first example let's assume you spend the 10% gain each year. So for 3 years you would have

Year 1: $100 + (10%) = $110 , and you spend the gain -$10
Year 2: $100 + (10%) = $110 , and you spend the gain -$10
Year 3: $100 + (10%) = $110 , and you spend the gain -$10

Your account is still at $100 dollars, and you were able to spend $30 dollars. Now we'll let it compound.

Year 1: $100 + 10% = $110.
Year 2: $110 + 10% = $121.   Note the starting balance is the ending balance of the previous year
Year 3: $121 + 10% = $133.1

Because you left your gains in the fund, that becomes the basis for the next years returns.
By letting them compound, you gained $3.10 over the original $30 dollars if you'd spent it each year.
$33.1 vs $30.  Voila compound interest.

MilesTeg

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Re: How does an investment portfolio accure compound Interest.
« Reply #8 on: June 13, 2016, 04:58:31 PM »
Growth only investments (e.g. 100 shares of a company without a dividend) do NOT compound. Only investments that regularly generate new income (that is re-invested) can compound. This means things like dividend stocks (assuming you re-invest the dividends) and things like CDs and savings accounts. (like a CD or savings account) enjoy compounding. The only way to get compounding is if you are using income from the investment to increase your holdings.

You can force some "compounding" in a growth asset if you ride the highs and lows. Say, for example Microsoft which bounces up and down quite regularly. If you buy low, sell high and wait for another low to buy more shares that you had originally, you can get "compounding". This is a really dumb idea for most folks though (far, far too risky and there are tax implications).

MDM

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Re: How does an investment portfolio accure compound Interest.
« Reply #9 on: June 13, 2016, 05:14:40 PM »
Growth only investments (e.g. 100 shares of a company without a dividend) do NOT compound.

Let's say you buy 100 shares of a company without a dividend for $50 each.  After one year the price per share has increased by 10%.  In the second year the price per share increases by another 10%.  What is the price per share at the end of two years, and how does that compare with the "compound interest" formula of $50 * (1.1)^2?

MilesTeg

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Re: How does an investment portfolio accure compound Interest.
« Reply #10 on: June 13, 2016, 07:09:46 PM »
Growth only investments (e.g. 100 shares of a company without a dividend) do NOT compound.

Let's say you buy 100 shares of a company without a dividend for $50 each.  After one year the price per share has increased by 10%.  In the second year the price per share increases by another 10%.  What is the price per share at the end of two years, and how does that compare with the "compound interest" formula of $50 * (1.1)^2?

Saying that an investment increased in value 10% per year is specifying it's annualized return. It's a measure of performance typically expressed as an average due to the volatile nature of the market. It is not compounding. Compounding is something that affects your capital (which could be expressed in dollars, shares, or any other valuation unit); it should not be confused with changes in valuation.

Read More Here:

http://thecollegeinvestor.com/919/average-annual-return-vs-compound-annual-return/
« Last Edit: June 13, 2016, 07:12:14 PM by MilesTeg »

PhysicianOnFIRE

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Re: How does an investment portfolio accure compound Interest.
« Reply #11 on: June 13, 2016, 07:17:07 PM »
Keep in mind that dividends are subtracted from the value of the asset. So if you have a stock worth $100 and it pays a $4 dividend, you now have a $96 asset and $4 in cash - taxes on the dividend (let's say you're taxed 15% qualified dividend + 5% state income tax). So you've actually got a $96 asset and $3.20.

If you reinvest the dividend, you've got $99.20 in assets.

This is why I'm not a fan of dividends, at least not during my peak earning years. In retirement, tax drag should be minimal.

MilesTeg

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Re: How does an investment portfolio accure compound Interest.
« Reply #12 on: June 13, 2016, 07:26:58 PM »
Keep in mind that dividends are subtracted from the value of the asset. So if you have a stock worth $100 and it pays a $4 dividend, you now have a $96 asset and $4 in cash - taxes on the dividend (let's say you're taxed 15% qualified dividend + 5% state income tax). So you've actually got a $96 asset and $3.20.

If you reinvest the dividend, you've got $99.20 in assets.

This is why I'm not a fan of dividends, at least not during my peak earning years. In retirement, tax drag should be minimal.

Uhh, no that's not how it works at all. The value of an asset (share price) is not value locked with dividends. Dividends are paid of out PROFIT, not market valuation (i.e. shares). Those two things are related, but distinct.

It IS true that you must actually re-invest those dividends to get compounding and you do get taxed, but you still end up with more than you had before (barring changes in the market that would affect the share price).

MDM

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Re: How does an investment portfolio accure compound Interest.
« Reply #13 on: June 13, 2016, 07:30:48 PM »
Growth only investments (e.g. 100 shares of a company without a dividend) do NOT compound.
Let's say you buy 100 shares of a company without a dividend for $50 each.  After one year the price per share has increased by 10%.  In the second year the price per share increases by another 10%.  What is the price per share at the end of two years, and how does that compare with the "compound interest" formula of $50 * (1.1)^2?
Saying that an investment increased in value 10% per year is specifying it's annualized return. It's a measure of performance typically expressed as an average due to the volatile nature of the market. It is not compounding. Compounding is something that affects your capital (which could be expressed in dollars, shares, or any other valuation unit); it should not be confused with changes in valuation.
Read More Here:
http://thecollegeinvestor.com/919/average-annual-return-vs-compound-annual-return/

Yes, "average annual" is not the same as "compound annual".  One can read more about that in https://www.bogleheads.org/forum/viewtopic.php?t=143975.  The usual simple example is
- Start with $100.
- Increase 100% in one year and decrease 50% in another (doesn't matter which comes first).
- After the second year you are back to $100, for a 0% change from the starting value.
- The "average annual" growth is (+100% + -50%)/2 = 25%
- The "compound annual" growth is [(1+100%) * (1-50%)]^(1/2) = 0%

"Compound annual" is thus the better measure of growth.

But the growth of an investment portfolio behaves the same (excluding tax effects), regardless of whether the growth comes from dividends or changes in valuation.  The value after year "n" = Original Amount * (1 + year_1_change%) * (1 + year_2_change%) * ... * (1 + year_n-1_change%) * (1 + year_n_change%)

MDM

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Re: How does an investment portfolio accure compound Interest.
« Reply #14 on: June 13, 2016, 07:37:57 PM »
The value of an asset (share price) is not value locked with dividends.
Actually, it is.

See http://www.investopedia.com/articles/stocks/07/dividend_implications.asp:
"On the ex-dividend date, the stock price is adjusted downward by the amount of the dividend by the exchange on which the stock trades."

JumpInTheFIRE

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Re: How does an investment portfolio accure compound Interest.
« Reply #15 on: June 13, 2016, 08:06:39 PM »
The value of an asset (share price) is not value locked with dividends.
Actually, it is.

See http://www.investopedia.com/articles/stocks/07/dividend_implications.asp:
"On the ex-dividend date, the stock price is adjusted downward by the amount of the dividend by the exchange on which the stock trades."

And even if the exchange didn't do that, the market quickly would because the company has lost value in exactly the amount of the dividend paid.  If a company is worth $10,000 and they pay out $1,000 in dividends, the company is now only worth $9,000. 

MilesTeg

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Re: How does an investment portfolio accure compound Interest.
« Reply #16 on: June 13, 2016, 08:27:25 PM »
The value of an asset (share price) is not value locked with dividends.
Actually, it is.

See http://www.investopedia.com/articles/stocks/07/dividend_implications.asp:
"On the ex-dividend date, the stock price is adjusted downward by the amount of the dividend by the exchange on which the stock trades."

Nope, still not the case. The price of a stock is not an objective measure of the value of a company. It is a subjective measure of the value of the company from the perspective of the share holders. As your link states, the change in value of the stock is almost always just noise in the daily value fluctuation. That's because market capitalization is subjective and speculative, always. For example. Take two companies, AAPL and Tesla.

Tesla has a market capitalization of $30 billion dollars. It has never turned a profit, yet has grown in price by 700% in the last three years. There is no objective reason for that kind of valuation change. The share holders are speculating (i.e. making a BET) that TSLA will actually start making a profit (and a substantial one at that).

Compare to Apple, which has a market capitalization of ~$600bn and a YEARLY PROFIT of $60 billion dollars, yet its stock has been in decline for nearly 2 years (and only up by about 30% in the last three). The stock is down, more than anything else, because Steve Jobs died.

Neither of these companies (and I could list hundreds more) have a valuation that is an objective measure of its current worth. All companies are valued (by the market/shareholders) based on possibilities and other subjective measures.

In a perfect world, we could objectively value companies. Unfortunately, we don't live in a perfect world.

This is sort of investing 101.

MilesTeg

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Re: How does an investment portfolio accure compound Interest.
« Reply #17 on: June 13, 2016, 08:32:29 PM »
The value of an asset (share price) is not value locked with dividends.
Actually, it is.

See http://www.investopedia.com/articles/stocks/07/dividend_implications.asp:
"On the ex-dividend date, the stock price is adjusted downward by the amount of the dividend by the exchange on which the stock trades."

And even if the exchange didn't do that, the market quickly would because the company has lost value in exactly the amount of the dividend paid.  If a company is worth $10,000 and they pay out $1,000 in dividends, the company is now only worth $9,000.

The value of a company is defined by what the market sees as the value of that company, and little else. Take my example of TSLA in my other post. By no objective measure is TSLA worth _anything_. It has never turned a profit, and has even given away all its IP. By any objective measure, it is currently worth bupkis (well, it has the worth of its real estate, machinery, etc. but that's no where near $30 billion).

However, the market currently values it at $30 billion, mostly due to future earnings potential (and other speculative valuation measures).

MDM

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Re: How does an investment portfolio accure compound Interest.
« Reply #18 on: June 13, 2016, 08:37:14 PM »
The price of a stock is not an objective measure of the value of a company. It is a subjective measure of the value of the company from the perspective of the share holders.

True, but what is your point?

People pay and receive money for stocks based on the actual price, not some "objective measure." 

The value of one's holdings is the same regardless of whether a change is due to a dividend payment or a price change, correct?  Or are you saying that is not the case?  If you are saying that is not the case, please show the math so we can understand your point.

MilesTeg

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Re: How does an investment portfolio accure compound Interest.
« Reply #19 on: June 13, 2016, 08:39:05 PM »
The price of a stock is not an objective measure of the value of a company. It is a subjective measure of the value of the company from the perspective of the share holders.

True, but what is your point?

People pay and receive money for stocks based on the actual price, not some "objective measure." 

The value of one's holdings is the same regardless of whether a change is due to a dividend payment or a price change, correct?  Or are you saying that is not the case?  If you are saying that is not the case, please show the math so we can understand your point.

My point is what I already said, dividend and stock price are not intrinsically linked.

sbones

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Re: How does an investment portfolio accure compound Interest.
« Reply #20 on: June 14, 2016, 01:35:15 AM »
I still don't know how a portfolio accumulates compounding interest? Shouldn't portfolios simply use an annualized return calculation?

How would you express the difference between "accumulates compounding interest" vs. "an annualized return calculation" in equation form?
So there is no difference?

marty998

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Re: How does an investment portfolio accure compound Interest.
« Reply #21 on: June 14, 2016, 01:43:25 AM »
I agree with Miles on this.

You guys who argue that the price drops by the value of the dividend are correct in theory. But since when has theory ever been borne out in reality when it comes to financial market gyrations?

:)

MDM

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Re: How does an investment portfolio accure compound Interest.
« Reply #22 on: June 14, 2016, 02:03:30 AM »
I still don't know how a portfolio accumulates compounding interest? Shouldn't portfolios simply use an annualized return calculation?
How would you express the difference between "accumulates compounding interest" vs. "an annualized return calculation" in equation form?
So there is no difference?
If it walks like a duck....

runningthroughFIRE

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Re: How does an investment portfolio accure compound Interest.
« Reply #23 on: June 14, 2016, 02:18:00 PM »
The price of a stock is not an objective measure of the value of a company. It is a subjective measure of the value of the company from the perspective of the share holders.

True, but what is your point?

People pay and receive money for stocks based on the actual price, not some "objective measure." 

The value of one's holdings is the same regardless of whether a change is due to a dividend payment or a price change, correct?  Or are you saying that is not the case?  If you are saying that is not the case, please show the math so we can understand your point.

My point is what I already said, dividend and stock price are not intrinsically linked.
Let's say you want to buy a bag of a dozen apples, but there isn't a way to be 100% sure how tasty the apples in a given bag will be when you buy them.  You find a seller willing to sell you a bag for $5, and since you have had this seller's products before you determine this is a fair price.  Before you can buy the bag, however, someone buys a single apple from that bag, and is kind enough to let you have a small piece to show you how tasty it is.  You have no way of knowing for certain how good the apples in the bag are, but you can make a reasonably informed guess at this point.  You still want to buy the bag, but now that it has fewer apples in it, you won't pay the same $5 for it, and instead pay $4.58, assuming that all the apples in the bag are roughly the same quality.  If you instead thought that the apple removed was of lower than average quality, you'd be willing to pay more than $4.58.  Inversely, if you thought the apple removed was of above average quality, you would have demanded the bag at less than $4.58.  Either way, the price decreased as a direct result of there being fewer apples in the bag.

It's a silly little example, but how is this any different from how stocks and dividends are related?  Unless you think that stock valuations have absolutely no basis in reality at any level, I don't see how you can argue that they aren't intrinsically linked to some extent.

BDWW

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Re: How does an investment portfolio accure compound Interest.
« Reply #24 on: June 14, 2016, 02:57:48 PM »
The price of a stock is not an objective measure of the value of a company. It is a subjective measure of the value of the company from the perspective of the share holders.

True, but what is your point?

People pay and receive money for stocks based on the actual price, not some "objective measure." 

The value of one's holdings is the same regardless of whether a change is due to a dividend payment or a price change, correct?  Or are you saying that is not the case?  If you are saying that is not the case, please show the math so we can understand your point.

My point is what I already said, dividend and stock price are not intrinsically linked.
Let's say you want to buy a bag of a dozen apples, but there isn't a way to be 100% sure how tasty the apples in a given bag will be when you buy them.  You find a seller willing to sell you a bag for $5, and since you have had this seller's products before you determine this is a fair price.  Before you can buy the bag, however, someone buys a single apple from that bag, and is kind enough to let you have a small piece to show you how tasty it is.  You have no way of knowing for certain how good the apples in the bag are, but you can make a reasonably informed guess at this point.  You still want to buy the bag, but now that it has fewer apples in it, you won't pay the same $5 for it, and instead pay $4.58, assuming that all the apples in the bag are roughly the same quality.  If you instead thought that the apple removed was of lower than average quality, you'd be willing to pay more than $4.58.  Inversely, if you thought the apple removed was of above average quality, you would have demanded the bag at less than $4.58.  Either way, the price decreased as a direct result of there being fewer apples in the bag.

It's a silly little example, but how is this any different from how stocks and dividends are related?  Unless you think that stock valuations have absolutely no basis in reality at any level, I don't see how you can argue that they aren't intrinsically linked to some extent.

Because unless a dividend is paid as "return of capital", it comes from revenue streams. The valuation of a stock based on current worth (book value) and future earnings (P/E). Investors are aware of dividend schedules far ahead of ex-dividend or payment dates. The price has usually been "adjusted" for dividend far before it's ever paid.

And the vast majority of empirical evidence backs this up. You can easily go look at historical price data and see that the dividend payment usually has little to no bearing on the stock price.

It's a great theory you've got there, it's just too bad it doesn't mesh with reality.

MDM

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Re: How does an investment portfolio accure compound Interest.
« Reply #25 on: June 14, 2016, 04:18:51 PM »
It's a great theory you've got there, it's just too bad it doesn't mesh with reality.

See What Really Happens To A Stock Price On The Ex-Dividend Date, from which one can cherry pick from a variety of quotes to "prove" one point or another.  In any case, it's off topic from the OP's question.

PhysicianOnFIRE

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Re: How does an investment portfolio accure compound Interest.
« Reply #26 on: June 14, 2016, 08:31:40 PM »
It's a great theory you've got there, it's just too bad it doesn't mesh with reality.

See What Really Happens To A Stock Price On The Ex-Dividend Date, from which one can cherry pick from a variety of quotes to "prove" one point or another.  In any case, it's off topic from the OP's question.

Yes, the asset drops by the value of the dividend. Then, like every other trading day, the price fluctuates. Denying that the dividend is subtracted from the share price is denying reality. Thank you for the link.

ooeei

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Re: How does an investment portfolio accure compound Interest.
« Reply #27 on: June 15, 2016, 01:15:09 PM »
Dividends don't perfectly reflect a stock price drop, but to say they're unrelated isn't correct either.  It's easy to see if you imagine an extreme example.  Company A has no dividend, Company B pays a 20% dividend every year.  They both have a profit of 20% per year.  Assuming both companies have the exact same amount of sales, cash flow, expenditures, and are exact mirrors of each other, you're telling me their prices should still be about the same on the market.  The thing that will drive them apart is that while Company B is paying out all of its profits to shareholders, Company A is using that money to grow its business in a way Company B can't match.  Eventually, assuming they are both decent companies whose investments make them money, Company A will grow much larger than Company B, and the stock price will reflect that.  The flip side to this is, if you reinvest the dividend from Company B into its own stock, you should see the exact same overall profit (neglecting taxes). 

Obviously there is noise in the real world. The question is, do you trust leaving your money with the company, or would you rather they give it back to you (so you can then give it back to them through reinvestment...).  Dividends can help keep a company accountable to shareholders, as it's a certain amount of money they have to give shareholders instead of using it on a crazy scheme just because they don't know what else to do with it. 

Would you rather have 1 share worth $100 or 2 shares worth $50? 

For an individual stock there is enough noise in the price that a dividend won't affect it as much as everything else.  So it's true that if you pick one stock and look before and after the dividend it could've gone up or down.  I suspect if you looked at 100, 200, 500 stocks to average out the noise, there would be an overall pattern consistent with the theory.  The other complicating factor is that often dividend and non-dividend stocks are in different industries, thus comparisons become even more tricky.