## [Wiki] - Percentage Gain and Loss (for new investors)

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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

*3!4!/5! wrote:If yesterday was 11% more than today, then you need today to be 10% less than tomorrow to recover.
If yesterday was 25% more than today, then you need today to be 20% less than tomorrow to recover.
If yesterday was 43% more than today, then you need today to be 30% less than tomorrow to recover.
If yesterday was 67% more than today, then you need today to be 40% less than tomorrow to recover.
If yesterday was 100% more than today, then you need today to be 50% less than tomorrow to recover. (That's right, if you have lost an amount equalling all of the money you now have left, then you'll only need to gain an amount equalling half of the money you'll end up with, to get back to even.)

If yesterday was 9999~~~9900% more than today, then you need today to be 99.99~~~99% less than tomorrow to recover (where 9999~~~99 denotes a string of N 9s for any given number N).

I hope I am succeeding in reinforcing the math and demolishing the myth.

This is the converse of Peter Foley's comment, but I the wording is very confusing to me. Is there a way to phrase it better?

===========================
Repeating the wiki article links from page 1:

Second version is here: User:LadyGeek/Percentage gain and loss

First version is here: Percentage gain and loss
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itstoomuch
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

re: version 2.0:
why is there not a table entry for -100 loss line: no value for "new value", "change of" and "gain or loss" ?
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

Because it's \$ 0.00, which can't be recovered. I put the new value as "\$0.00" in both versions.

New version: User:LadyGeek/Percentage gain and loss

First version: Percentage gain and loss
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itstoomuch
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

re vers 2.0
OK for the 0.00 but I hate "dash" as a place keeper, although in this case as an under-define value YMMV
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*3!4!/5!
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

I'm just trying to give food for thought without making any specific recommendations for the Wiki.

I'll just make a couple more points.

A percentage is just a number, e.g.
X%=X/100=X*0.01
37%=37/100=37*0.01=0.37

A change between two quantities A and B can be quantified in various ways, e.g.
A-B and B-A
A/B and B/A
(A-B)/B and (B-A)/A (and maybe also the negatives of these).
It is the last ones that are used in "percentage change" (or "proportional change") and it is the fact that there is a choice of denominator (breaking the symmetry between A and B) that gives rise to the different answers for "percentage change" between A and B.

Oicuryy
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

Didn't we decide a few years ago to measure gains and losses in nepers?

viewtopic.php?f=10&t=133871&p=1974087#p1974087
viewtopic.php?f=10&t=138661&p=2049746#p2049746

Ron
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

Good point, as natural logarithms are used everywhere in economics. From my previous post (on Page 1):

A useful property of logarithms is that they can flatten curves (turn into a straight line). Here's an interesting article why natural logarithms are used in economics: Use of logarithms in economics . Note what was done with the S&P 500. I don't think this type of explanation would be helpful in the context of the wiki article.
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dbr
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

There are many different mathematical functions that are useful fits to different phenomena. It is often helpful to find those that are the right expression for the mathematical nature of what you are looking at or that happen to portray what you are looking at in a particularly clear and simple manner. Sometimes it is a matter of what feature of something you want to study. There is never anything magic about one mathematical tool over another one.

In the case at hand where compound growth is the mathematical nature of what is going on an exponential model and its inverse, the log model, are natural to the problem, allow one to portray things in a simple manner, and direct the focus to features of greatest interest. That's all.

siamond
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

I think this is a useful article. There are multiple small math quirks like that that many investors get confused about, and this article does a good job of clarifying one of them.

A few suggestions, one post at a time... (I didn't read the entire thread, just reacted to the latest Wiki page)

Percentages can be misleading if not combined correctly. For example, a market loss of 10% followed by a gain of 10% will get you back to the same point. This is simply not true.

It is dangerous to have a false statement as an assertive sentence. It could be quoted out of context. Or a reader skimming though the wiki page might miss the last sentence. I would suggest to use an open question format.

Percentages can be misleading if not combined correctly. For example, will a market loss of 10% followed by a gain of 10% get you back to the same point? This is simply not true.

siamond
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

The article does a good job of explaining an improper use of percentages. But it never seems to explain how to do it right (i.e. doing geometric math instead of arithmetic math). Or well, it hints at it in the "misconception explained" section, but doesn't make it explicit enough.

Adding (geometrically) 10% to a given amount X is relatively intuitive: X * (1+10%). Subtracting (geometrically) isn't complicated, but needs to be spelled out: X / (1+10%). And then we have the expected property that X * (1+10%) / (1+10%) = X, which is trivial to understand, and helps grasp why one needs to use the X / (1+10%) to exactly reverse a gain of 10%.

I would suggest to remove the detailed example section (which in its current form is just too much belaboring of the previous explanations, which are already very clear, notably thanks to the graph). And replace it by a short section showing how to do the math in the right way...

PS. I would agree to stay clear of logarithmic math. We'd lose too many readers... More precisely, many people would read the words, but not understand the point well enough to be able to reproduce it by themselves.

livesoft
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

siamond wrote:I would suggest to remove the detailed example section (which in its current form is just too much belaboring of the previous explanations, which are already very clear, notably thanks to the graph). And replace it by a short section showing how to do the math in the right way...

Yes!
From an internet source:

From Algebra I. The following equation has three unknowns (called P for percentage). If you know two of the three, you can find the third.

(1 + P1) (1 + P2) = (1 + P3)

Example:
P1 = 0.1
P2 = -0.2

(1.1)(0.8) = .88, so (1 + P3) = .88 means P3 = -0.12, not 0.10 - 0.20 = -0.10 (you don’t add percentages)

For another example,
One can even set P1 to 0.1 and P3 to 0.0 and solve for P2.
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siamond
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

LadyGeek wrote:I agree, and have created a second draft page: User:LadyGeek/Percentage gain and loss

Oh sorry, I didn't see this alternate proposal when making my previous comments. Yes, I like this new proposal much better, this is much more compact and easy to read, and provides all necessary information in tabular and graphical format, nice job.

My previous point remains though, we need one short section explaining how to do the math right, instead of just explaining how wrong we often are... And I would restore the "I" box at the top that I was reacting to two posts ago, while rephrasing it as I suggested. This seems useful as a concise attention grabber.

dbr
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

siamond wrote:The article does a good job of explaining an improper use of percentages. But it never seems to explain how to do it right (i.e. doing geometric math instead of arithmetic math). Or well, it hints at it in the "misconception explained" section, but doesn't make it explicit enough.

Adding (geometrically) 10% to a given amount X is relatively intuitive: X * (1+10%). Subtracting (geometrically) isn't complicated, but needs to be spelled out: X / (1+10%). And then we have the expected property that X * (1+10%) / (1+10%) = X, which is trivial to understand, and helps grasp why one needs to use the X / (1+10%) to exactly reverse a gain of 10%.

I would suggest to remove the detailed example section (which in its current form is just too much belaboring of the previous explanations, which are already very clear, notably thanks to the graph). And replace it by a short section showing how to do the math in the right way...

Right on. The whole issue here is addressing the misconception regarding the right formulation to apply to the problem rather than to debate how to calculate percentages.

It might be better to label the inverse of multiplication as division rather than subtraction (geometrically), but your point and math are correct and important. But there is more to the context than that. The context is the dependence of portfolio value on time where the model is compounding of successive returns in a formula involving the composition of successive functions (namely multiplication by 1+return for each successive period). The result would be X * 1.1 * .9090 . . . (infinitely repeated decimal) = X. The first year return is 10% and the second year return is -9.0909 . . . %. A source of confusion is that a negative number for return does not indicate that an operation of subtraction is being performed in the compound growth model. You interpret this as subtraction only if you forget what you are doing in the first place. The right picture is to multiply by greater than 1 or by less than one and never enter the conundrum that the offsetting returns should have somehow been numerically equal and opposite but aren't.

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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

dbr wrote:It might be better to label the inverse of multiplication as division rather than subtraction (geometrically), but your point and math are correct and important. [...]

Yes, agreed, I wasn't trying to suggest an exact wording for the wiki, just a possible direction to follow in order to improve the page. I agree that speaking of multiplication and division would be more intuitive for the reader instead of trying to explain terms like geometric vs. arithmetic.

Oicuryy
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

Consider adding a sentence to the first paragraph.

When an investment changes value, the dollar amount needed to return to its initial (starting) value is the same as the dollar amount of the change - but opposite in sign. Expressed as a Percentage gain and loss, the percentage gained will be different than the percentage lost. This is because the same dollar amount is being expressed as a percentage of two different starting amounts.

Ron
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GAAP
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

Minor note: The title uses percentage, the equation in the overview uses percent, and sentence immediately following the equation uses percentage again. The usage is actually correct, but I wonder if that difference should be explained in a footnote.

FWIW, a lot of people get this gain/loss concept wrong -- I've had to explain it to people with graduate level engineering degrees...

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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

GAAP wrote:FWIW, a lot of people get this gain/loss concept wrong -- I've had to explain it to people with graduate level engineering degrees...

FYI - I'm an engineer. This is a classic case of what I call a "deceptively simple" problem. The equation is so easy, how could you possibly get it wrong? Yet, you do. Or, make the wrong conclusion. Been there, done that.

For example, livesoft's "Algebra 1" example above. How hard could it be? Try understanding his perspective and how it applies to the problem at hand. It honestly took me a while to get to the "So that's what you meant by..." part.

The wiki article has been revised: Percentage gain and loss, the draft page has been deleted - it's no longer needed.

The latest update incorporates comments from:

siamond - The "i" info box statement
Oicuryy - added sentence to introduction.
livesoft - math example of how to do this right
GAAP - fixed the math formula to show as "percentage"

The wiki uses the same software as Wikipedia, nothing is ever lost. To see prior versions (and which editor did the change), click on the View history tab (top-right corner of the article). Then, click on the link of the time for each version.

Here's what the page looked like before this round of updates: Revision as of 16:54, 16 June 2017

How's it look? Do we have a consensus?
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

LadyGeek wrote:For example, livesoft's "Algebra 1" example above. How hard could it be? Try understanding his perspective and how it applies to the problem at hand. It honestly took me a while to get to the "So that's what you meant by..." part.

Typically starting with "story" problems in fourth grade and extending to college students in math, science, and engineering the hardest part is expressing what we want to talk about in the correct mathematical formulation. A lot of students never master this. The one's that struggle the most are the one's that want to start making colloquial statements in English rather than taking out a pencil and starting to write algebraic expressions. At least in the second case one can ask them why they are writing one expression rather than another.

PS livesoft's example is very astute and compact relative to the problem. The one drawback is that if you don't already understand what he is doing, it might not help very much. The question would be how did we arrive at multiplying two terms of the form (1+Pi), and that is the heart of the whole thing.

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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

Oicuryy wrote:Didn't we decide a few years ago to measure gains and losses in nepers?

viewtopic.php?f=10&t=133871&p=1974087#p1974087
viewtopic.php?f=10&t=138661&p=2049746#p2049746

Ron
LadyGeek wrote:Good point, as natural logarithms are used everywhere in economics. From my previous post (on Page 1):

A useful property of logarithms is that they can flatten curves (turn into a straight line). Here's an interesting article why natural logarithms are used in economics: Use of logarithms in economics . Note what was done with the S&P 500. I don't think this type of explanation would be helpful in the context of the wiki article.

We should be using centinepers (cNp), see this Wikipedia article: Relative change and difference - Wikipedia (Other change units)
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

dbr wrote:...PS livesoft's example is very astute and compact relative to the problem. The one drawback is that if you don't already understand what he is doing, it might not help very much. The question would be how did we arrive at multiplying two terms of the form (1+Pi), and that is the heart of the whole thing.

I was also unable to find the source of his equations, yet they make sense.

livesoft- Please provide a link to your internet source. Alternatively, can you derive them from basic math?
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

It was sent to me in an e-mail from sscritic.

It is basically a restatement of "compounding." I might say something like,

If a portfolio grows by 5% in year one and 10% in year two, how much bigger is the portfolio? I hope it is clear that in this case P1 is 0.05, P2 is 0.10, and one can solve for P3.

-or-

If a portfolio grows by 5% in year one and drops by 11% in year two, how much bigger is the portfolio?
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

dbr wrote:...PS livesoft's example is very astute and compact relative to the problem. The one drawback is that if you don't already understand what he is doing, it might not help very much. The question would be how did we arrive at multiplying two terms of the form (1+Pi), and that is the heart of the whole thing.

I was also unable to find the source of his equations, yet they make sense.

livesoft- Please provide a link to your internet source. Alternatively, can you derive them from basic math?

Good grief. It makes sense because it is an algebraic formulation of compound growth, which is the topic under discussion, isn't it?

The mathematical fundamentals might be the following:

1. What do we mean by compound growth and how is that what we are talking about when we talk about investments. It has to do with how can we write formulas for what happens to a quantity that varies in time over successive intervals.

2. What are some of the definitions we use in that formulation, including for starters gain and return.

3. What specific nuances appear in those definitions, such as that return is expressed in units of percent.

4. Etc.

The proposition did begin with first, in one period of time, an investment had a certain gain or loss, or return, and then in a subsequent, immediately following period of time, it had a different gain or loss, or return. I think the missing context is stating the thing as a conundrum out of the blue rather than first introducing the conventional and helpful model for how we talk about investment results over time. The actual algebra is no more than I see taught in some fourth grade classrooms. Everything about it being some kind of problem in understanding "percents" is a red herring.

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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

Here's another good question:

My fund tripled in value in one year, what was its performance?

Hint: It was not 300%.
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

LadyGeek wrote:How's it look? Do we have a consensus?

livesoft wrote:My fund tripled in value in one year, what was its performance?

A gain of 109.86 cNp.

Ron
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

I wonder if the wiki could better use an article on compound returns vs. arithmetic returns which would include this compound growth of percentage gains/losses?
Compound return is for 'buy and holders', generally.
Arithmetic returns are for those who 'spend their returns', generally.

And then there's those who have to dollar cost average over the accumulation and decumulation phases. Or they don't want to spend all their gains, or they want to spend less than their gains. sheesh!

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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

For buy and hold, it's compounded Pf = Pin(1+r1)(1+r2) ... (1+rn)
For arithmetic you set up a separate cash account that pays nothing. Every time you have a gain you put it in the cash account. Every time you have a loss you take it from the cash account and re-invest it.
Pf + cash = Pin[(1+r1 + r2 + ... + rn)]

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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

livesoft wrote:

It was sent to me in an e-mail from sscritic.

It is basically a restatement of "compounding." I might say something like,

If a portfolio grows by 5% in year one and 10% in year two, how much bigger is the portfolio? I hope it is clear that in this case P1 is 0.05, P2 is 0.10, and one can solve for P3.

-or-

If a portfolio grows by 5% in year one and drops by 11% in year two, how much bigger is the portfolio?

I knew the equation was familiar, but the concept of "compound interest" and how it applies to percentage change totally escaped me. "Deceptively simple" has gotten me again.

The wiki has been revised to explain the concepts in terms of compounding: Percentage gain and loss

I stopped short of calling the formula derivation "compound interest", as I wanted to focus on the percentages. If the equation is followed to its popular conclusion, the result is the time value of money equation for Future Value. I added a link to Comparing investments which deep-dives into that area.

Hopefully, this introduction will provide a good foundation for exploring further concepts, such as arithmetic vs. geometric mean and CAGR (Compound Annual Growth Rate).

Do we have a consensus, i.e. is the article "good enough" to show to new investors?
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

I would use two different numbers than 10% for P1 and P2, such as 7% and 11% because then they could not be mixed up. And the new numbers are prime numbers.
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

LadyGeeK wrote:Do we have a consensus, i.e. is the article "good enough" to show to new investors?

it's good enough to be better than "YMMV".
IOW, it's Good.
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

^^^ Thanks!
livesoft wrote:I would use two different numbers than 10% for P1 and P2, such as 7% and 11% because then they could not be mixed up. And the new numbers are prime numbers.

I would agree, but I'm trying to accommodate those who don't work with math on a daily basis. Take easy first steps, but learn the concepts.

I intentionally changed your example to match the question at the top of the article, which promised that the question would be answered. Keeping the numbers consistent is important. If the article's question was rephrased as a 7% loss then 11% gain, readers will have to think harder. To new investors, this may be intimidating.
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

livesoft wrote:I would use two different numbers than 10% for P1 and P2, such as 7% and 11% because then they could not be mixed up. And the new numbers are prime numbers.

I would agree, but I'm trying to accommodate those who don't work with math on a daily basis. Take easy first steps, but learn the concepts.

I intentionally changed your example to match the question at the top of the article, which promised that the question would be answered. Keeping the numbers consistent is important. If the article's question was rephrased as a 7% loss then 11% gain, readers will have to think harder. To new investors, this may be intimidating.

LadyGeek. I actually like my contribution. The way I went through the steps, and realizations of geo inverse ops. to get to what is happening. (the inverse of a certain percentage.)
Only, except for the subsection title, "common misconceptions.." and those examples.
No, my mind was really there at the time, and I think I went succinctly through the thinking process aimed at beginners.
Maybe subsection: 'Why the inverse."
Last edited by MIpreRetirey on Sat Jun 17, 2017 9:24 pm, edited 2 times in total.

MIpreRetirey
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

Re-submission.

Percentages are actually a multiplication operation.

1st, the percentages must be converted to a decimal or fractional representation.

+10% is equivalent to a decimal multiplication of 1.1
-10% is equivalent to a decimal multiplication of 0.9

And then you can see how a gain of 10% followed by a loss of 10% does not get you back to even. Because the two returns compounded after one another is equivalent to writing P * 1.1 * .9 = P * .99, which is not back to even.

If you do it in fractions, then a 10% gain can be written 11/10 , or any multiple such as 110/100, and
a 10% loss can be written as 9/10, or 90/100.
Now the equation can be written P * 110/100 * 90/100 = P * 9900/10000, and you see what's happening (like in the graph and chart)?, multiplying by
90/100 is not the inverse operation of multiplying by 110/100. The inverse operation of multiplying by 90/100 is multiplying by 100/90 (which is +11.11...% These would be called geometrically inverse operations (as in multiplication and division.)
And the inverse to * 110/100, is * 100/110. (which is +9.09...%) As in the chart/graph. They are never exactly equal, no matter how small the number.
So, a 10% loss requires an 11.1% gain to recover, and a 10% gain would take a 9.09% loss to be even.

In dollar terms, you did nothing but either gained, or lost, 10 coins on a hundred and then they were reversed back to 100.

siamond
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

LadyGeek wrote:Do we have a consensus, i.e. is the article "good enough" to show to new investors?

Hm, not sure. Let me start by small quibbles before making a more important point in the next post...

Small quibble #1:

\$1,100 = \$1,000 + (\$1,000 * 10%) = Starting value + (investment return)
\$1,100 = (\$1,000 * 1) + (\$1,000 * 0.10)
[...]
\$1,000 * (1 + 0.21) = \$1,000 * (1 + 0.10) * (1 + 0.10)
To say this another way, your investment returned +21% over 2 years.

Why do we switch from a percentage notation (10%) to an absolute number (0.10) and back to a percentage (21%)? If the point is to make it as simple as possible, I'd keep it consistent, e.g.
\$1,100 = \$1,000 + (\$1,000 * 10%) = Starting value + (investment return)
\$1,100 = (\$1,000 * 100%) + (\$1,000 * 10%)
[...]
\$1,000 * (1 + 21%) = \$1,000 * (1 + 10%) * (1 + 10%)

Small quibble #2:

We can now answer the question at the top of the article:

Well, no, the relevant question was asked at the beginning of the section, not at the beginning of the article (i.e. the entire page).

siamond
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

Now let me get to my main point (quibble #2 was a hint!). The introduction and the overview address this precise problem:

When an investment changes value, the dollar amount needed to return to its initial (starting) value is the same as the dollar amount of the change - but opposite in sign. Expressed as a Percentage gain and loss, the percentage gained will be different than the percentage lost. This is because the same dollar amount is being expressed as a percentage of two different starting amounts.

The 'different perspective' section addresses the following problem:

Here is another way to express the same idea. You have an initial investment of \$1,000. At the end of the first year, your investment grows by 10%. Your investment also grows by 10% at the end of the second year.

Well, this isn't the same problem, isn't it? The first problem is about applying gain and/or a loss. The second problem is about compounding two gains. I would strongly suggest to keep the Wiki page simple, and solely focus on the first problem.

Here is one possible way to salvage this. Keep the structure exactly the same, but discuss the following in the 'different perspective' section:

Here is another way to express the same idea. You have an initial investment of \$1,000. At the end of the first year, your investment grows by 10%. Then your investment shrinks by 10% at the end of the second year.

And then go through the very exact same type of equations while addressing this problem. Which is a specific case of the broader problem discussed in the overview & first section. Makes sense?

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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

Oicuryy wrote:Didn't we decide a few years ago to measure gains and losses in nepers?
viewtopic.php?f=10&t=133871&p=1974087#p1974087
viewtopic.php?f=10&t=138661&p=2049746#p2049746

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Where'd ya get those nepers?

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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

The wiki has been revised: Percentage gain and loss

MIpreRetirey wrote:Re-submission.

Sure. As noted in an earlier post, nothing is ever lost is in the wiki. Using View history, I pulled the text from the last version to contain your original text: Revision as of 16:54, 16 June 2017 and modified it for your above post.

I then modified the sequence (and noted doing so) to be consistent with the article's sequence of a 10% loss followed by a 10% gain. Please review. The section title could probably be clarified.

siamond wrote:Let me start by small quibbles before making a more important point in the next post...

Small quibble #1:
...Why do we switch from a percentage notation (10%) to an absolute number (0.10) and back to a percentage (21%)? If the point is to make it as simple as possible, I'd keep it consistent..

Percentage is a unit, e.g. 100 percents = 1.00, so it should be converted to the actual number. The text has been revised per your second quibble which fixes the inconsistency.

siamond wrote:Now let me get to my main point (quibble #2 was a hint!). The introduction and the overview address this precise problem:

I have salvaged the section as you suggested. livesoft's formula has been reworked so everything flows as a single example.
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

I don't think you will like this suggestion: The page needs a nice quiz to check one's mastery of the material.
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

You are right, I don't like quizzes. I also don't think we should challenge a reader's mastery of the material in the wiki (which follows Wikipedia guidelines). Showing a single example completely worked through is sufficient.

===============
I have revised MIpreRetirey's section title, as the intent is to show "why not", not "why".

Additionally, I forgot to mention that MIpreRetirey has introduced the term "compounding". I have added a note to explain what this means.

See: Percentage gain and loss

Pop quiz: If you add or withdraw money from your investment, can you use "percentage gain or loss" to calculate your return?
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

Yea. Afterwards, per siamond's comment, and others'. This reeks of compound growth and anticipation of compound growth.

If it were about the title, it would just be about converting percentage notation into equivalent decimal and fractional notation as a multiplication or division factor (or operation.) Also, it might show how to change back from a ratio of (final value)/(initial value) to a percentage change representation.
And this is almost absurdly simple like 4th or 3rd grade math. How many would not already grasp these?

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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

It's not the math per se, but the application of the math which causes the confusion. The point is to let new investors know the math does exist and how it works. Or, an investor may not have thought about this in enough detail to make the connection.

This is not just about compound growth, but also about hearing the daily news how much the market has gained or dropped. Or, an investor is reviewing portfolio performance. Putting things in perspective is important, especially when emotions are involved.

We could not reach a consensus to include any of this aspect in the wiki article. Keep the article as a basic "tool", then use it in the proper context when someone needs guidance during a forum discussion.
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

Ladygeek, first off, thank you for your infinite patience. Although I agree that this is extremely basic algebra, it is amazing to see how intelligent people can mess it up. I made a test with my wife last night... Ok, no further comment without my lawyer doing the talking!

More seriously, I think we're almost there. I have one last (possibly disruptive!) comment though. It seems to me that the "percentage change" section and the "different perspective" section now say nearly exactly the same thing. I realize this is partly a consequence of my feedback, but... well, read it while forgetting the history of how the page was assembled and you should see it.

It is a little hard to choose, as both sections do a good job, but I'd suggest to simply remove the "percentage change" section, for the sake of a more straightforward Wiki page. Belaboring too much is often counter-productive. Apologies to MIpreRetirey!

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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

I would really suggest LadyGeek to close this thread down before we get anymore YMMV
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

I think the way this wiki page will primarily be read is after someone is pointed to it by a link in a forum thread and not by a search nor by happenstance.
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

Lots of links to this article in other articles (such as articles on risk tolerance, variance drain, risk and return, etc) may improve its visibility if that is a goal. It's definitely something that people should know about.

Surprising that it's something people don't realize. I like the 10% math since you can do it in your head.

\$100 + 10% = \$110.
\$110 - 10% = \$99
\$99 does not equal \$100.

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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

TD2626 wrote:Lots of links to this article in other articles (such as articles on risk tolerance, variance drain, risk and return, etc) may improve its visibility if that is a goal. It's definitely something that people should know about.

Surprising that it's something people don't realize. I like the 10% math since you can do it in your head.

\$100 + 10% = \$110.
\$110 - 10% = \$99
\$99 does not equal \$100.

^Now that should go at the top of the page.

As in:

Surprising that it's something people don't realize. I like the 10% math since you can do it in your head.

\$100 + 10% = \$110.
\$110 - 10% = \$99
\$99 does not equal \$100.

And below is more.
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

LadyGeek in this post wrote:We should be using centinepers (cNp), see this Wikipedia article: Relative change and difference - Wikipedia (Other change units)
I fought the urge as long as I could. But in the end I just couldn't resist. So, reluctantly, here is the table from the Wiki article with columns added for centinepers (1/100 of a neper or cNp):

Code: Select all

``                                         -- Then back to \$1,000 --If \$1,000    --- It's a change of ---    --- needs a change of ---  Becomes        \$         %      cNp         \$         %      cNp``

Code: Select all

``    \$0.00  -\$1,000.00   -100%     n/a   +\$1,000.00     n/a     n/a  \$100.00    -\$900.00    -90%    -230     +\$900.00   +900%    +230 [*]  \$200.00    -\$800.00    -80%    -161     +\$800.00   +400%    +161  \$300.00    -\$700.00    -70%    -120     +\$700.00   +233%    +120  \$400.00    -\$600.00    -60%     -92     +\$600.00   +150%     +92  \$500.00    -\$500.00    -50%     -69     +\$500.00   +100%     +69  \$600.00    -\$400.00    -40%     -51     +\$400.00    +67%     +51  \$700.00    -\$300.00    -30%     -36     +\$300.00    +43%     +36  \$800.00    -\$200.00    -20%     -22     +\$200.00    +25%     +22  \$900.00    -\$100.00    -10%     -11     +\$100.00    +11%     +11\$1,000.00      +\$0.00     +0%      +0       +\$0.00     +0%      +0\$1,100.00    +\$100.00    +10%     +10     -\$100.00     -9%     -10\$1,200.00    +\$200.00    +20%     +18     -\$200.00    -17%     -18\$1,300.00    +\$300.00    +30%     +26     -\$300.00    -23%     -26\$1,400.00    +\$400.00    +40%     +34     -\$400.00    -29%     -34\$1,500.00    +\$500.00    +50%     +41     -\$500.00    -33%     -41\$1,600.00    +\$600.00    +60%     +47     -\$600.00    -38%     -47\$1,700.00    +\$700.00    +70%     +53     -\$700.00    -41%     -53\$1,800.00    +\$800.00    +80%     +59     -\$800.00    -44%     -59\$1,900.00    +\$900.00    +90%     +64     -\$900.00    -47%     -64\$2,000.00  +\$1,000.00   +100%     +69   -\$1,000.00    -50%     -69``
* For example using the Excel LN function:

Code: Select all

``-230 = 100 * LN( 100 / 1000)+230 = 100 * LN(1000 /  100)``

And here is the table with regularly spaced centinepers:

Code: Select all

``                                         -- Then back to \$1,000 --If \$1,000    --- It's a change of ---    --- needs a change of ---  Becomes        \$         %      cNp         \$         %      cNp``

Code: Select all

``  \$135.34    -\$864.66    -86%    -200     +\$864.66   +639%    +200 [**]  \$165.30    -\$834.70    -83%    -180     +\$834.70   +505%    +180  \$201.90    -\$798.10    -80%    -160     +\$798.10   +395%    +160  \$246.60    -\$753.40    -75%    -140     +\$753.40   +306%    +140  \$301.19    -\$698.81    -70%    -120     +\$698.81   +232%    +120  \$367.88    -\$632.12    -63%    -100     +\$632.12   +172%    +100  \$449.33    -\$550.67    -55%     -80     +\$550.67   +123%     +80  \$548.81    -\$451.19    -45%     -60     +\$451.19    +82%     +60  \$670.32    -\$329.68    -33%     -40     +\$329.68    +49%     +40  \$818.73    -\$181.27    -18%     -20     +\$181.27    +22%     +20\$1,000.00      +\$0.00     +0%      +0       +\$0.00     +0%      +0\$1,221.40    +\$221.40    +22%     +20     -\$221.40    -18%     -20\$1,491.82    +\$491.82    +49%     +40     -\$491.82    -33%     -40\$1,822.12    +\$822.12    +82%     +60     -\$822.12    -45%     -60\$2,225.54  +\$1,225.54   +123%     +80   -\$1,225.54    -55%     -80\$2,718.28  +\$1,718.28   +172%    +100   -\$1,718.28    -63%    -100\$3,320.12  +\$2,320.12   +232%    +120   -\$2,320.12    -70%    -120\$4,055.20  +\$3,055.20   +306%    +140   -\$3,055.20    -75%    -140\$4,953.03  +\$3,953.03   +395%    +160   -\$3,953.03    -80%    -160\$6,049.65  +\$5,049.65   +505%    +180   -\$5,049.65    -83%    -180\$7,389.06  +\$6,389.06   +639%    +200   -\$6,389.06    -86%    -200 [**]``
This should make everything perfectly clear.

Edited 6/24/2017 to add following showing how "If \$1,000 Becomes" column calculated in 2nd table.
** For example using the Excel EXP function:

Code: Select all

``  135.34 = 1000 * EXP(-200 / 100)7,389.06 = 1000 * EXP(+200 / 100)``
Last edited by #Cruncher on Sat Jun 24, 2017 11:27 am, edited 1 time in total.

dbr
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

TD2626 wrote:Lots of links to this article in other articles (such as articles on risk tolerance, variance drain, risk and return, etc) may improve its visibility if that is a goal. It's definitely something that people should know about.

Surprising that it's something people don't realize. I like the 10% math since you can do it in your head.

\$100 + 10% = \$110.
\$110 - 10% = \$99
\$99 does not equal \$100.

This would better be rewritten as

\$100 + 10% * \$100 = \$100 + .1 * \$100 = \$100 + \$10 = \$110
\$110 - 10% * \$110 = \$100 - .1 * \$110 = \$100 - \$11 = \$99

or

\$100 * (1 + 10%) = 1.1 * \$100 = \$110
\$110 * (1 - 10%) = 0.9 * \$110 = \$99

Writing formulas that don't even mean anything such as \$100 + 10% really, really does not help.
Last edited by dbr on Sun Jun 18, 2017 3:12 pm, edited 1 time in total.

MIpreRetirey
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

No concern. The intent was for the fine edge of who and what this is for.

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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

^^^ Thanks for understanding.

The wiki has been revised: Percentage gain and loss
siamond wrote:Ladygeek, first off, thank you for your infinite patience. Although I agree that this is extremely basic algebra, it is amazing to see how intelligent people can mess it up. I made a test with my wife last night... Ok, no further comment without my lawyer doing the talking!

More seriously, I think we're almost there. I have one last (possibly disruptive!) comment though. It seems to me that the "percentage change" section and the "different perspective" section now say nearly exactly the same thing. I realize this is partly a consequence of my feedback, but... well, read it while forgetting the history of how the page was assembled and you should see it.

It is a little hard to choose, as both sections do a good job, but I'd suggest to simply remove the "percentage change" section, for the sake of a more straightforward Wiki page. Belaboring too much is often counter-productive. Apologies to MIpreRetirey!

siamond, I would agree with you. With apologies to MIpreRetirey, the section has been removed. However, I retained the introduction of compounding as a note in the "A different perspective".

livesoft wrote:I think the way this wiki page will primarily be read is after someone is pointed to it by a link in a forum thread and not by a search nor by happenstance.

I think not. The hardest part of using a wiki is finding information. Link everywhere you think it should go. I have added the "Bogleheads® investing start-up kit" navigation menu to the bottom of the page. All of the pages in that menu will then be linked together. Once the page goes "live" I will add the page to that menu.

TD2626 wrote:Lots of links to this article in other articles (such as articles on risk tolerance, variance drain, risk and return, etc) may improve its visibility if that is a goal. It's definitely something that people should know about.

Surprising that it's something people don't realize. I like the 10% math since you can do it in your head.

\$100 + 10% = \$110.
\$110 - 10% = \$99
\$99 does not equal \$100.

I was adding your description to the top of the page while livesoft was requesting it. I reversed the order to be aligned with the example. Additionally, I added variance drain to the "See also" section. Risk (risk tolerance) is in the "Bogleheads® investing start-up kit" menu.

#Cruncher wrote:
LadyGeek in this post wrote:We should be using centinepers (cNp), see this Wikipedia article: Relative change and difference - Wikipedia (Other change units)
I fought the urge as long as I could. But in the end I just couldn't resist. So, reluctantly, here is the table from the Wiki article with columns added for centinepers (1/100 of a neper or cNp):

As an engineer, I'm comfortable working with 10*log10(), which is known as a Decibel. I like the idea and will update the spreadsheets when I can, along with a brief description.

I don't think this should hold anything up with regards to getting this page completed.

Do we have a consensus to "go live" and show new investors?
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dbr
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### Re: [Wiki] - Percentage Gain and Loss (for new investors)

There is also this: https://en.wikipedia.org/wiki/Percentage see especially the section titled "Compunding percentages."