Misuse of percentages

[odds-on]

This means you have the probability of frequency and the probability of compounding on your side by betting on smaller moves.

Hi Sinner,

You have not taken into account the probability of winning all the bets

Cheers

 

[Ves]

Burglar

I agree – A stocks ability to drop 20% or rise 25% is exactly the same.

The math though has implications for different approaches – Lone Wolf summed up the price perspective and the implications for risk of ruin.

The value perspective is the exact opposite ie. it is less risky to buy $1 for 50cents and will buy more at lower prices. Implications for risk of ruin lies within the determination of value not within your reaction to price.

A misuse of averages that does occur though is using arithmetical averages of percentages – extrapolating a rough understanding of this is what probably leads some to thinking there is a difference in ‘potential’ for a stock to drop 20% as opposed to rise 25%.

I was thinking the same thing actually - providing that you can exercise skill and judgment there is no reason that one of your best winners may go from $2 to $1 before it ever sees $10.

I think you once explained this to me as the theory of being a "strong hand" vs a "weak hand."

 

[waimate01]

A $1 share can gain 99c or lose 99c just as easily.

If your point is correct, then assuming you start with a hard-earned stake of $1000, on one outcome you've now got $1990 and might celebrate by going out for a nice pub dinner (but not order the lear jet just yet), and on the other outcome you've got $10 and wiped yourself out. These are not symmetrical.

But I disagree with your premise. A share goes down when management gets something wrong, and it goes up when management gets something right. So if I understand correctly, you're saying it's just as easy to get something right as wrong. So therefore I can go through my next multiple choice quiz, choose answer 'A' for everything, and expect to get a borderline pass, right? I disagree - I think it's a lot harder to get things right than it is to get things wrong. It takes no particular skill to mess something up. Therefore it's harder to pick winners than losers.

Anyway, as various other people have indicated, the correct way to think about this is to also consider the probabilities, and multiply the outcome by the probability. Otherwise you'd just buy yourself a lottery ticket and go jet shopping.

 

[galumay]

....... Otherwise you'd just buy yourself a lottery ticket and go jet shopping.

Mostly irrelevant and debatable!

To come back to the initial point though, its not helpful or transparent for people to make statements such as,
"If you lose 20% of your capital, you need a 25% increase to get back to where you started."

Its comparing apples with oranges and a misuse of %'s because they are calculated on different bases.

 

[burglar]

If your point is correct, ...

What you say makes a lot of sense, but it is not all that simplistic.

What the OP is saying is this:
When the base number changes,
(from that which you start out with, to that which you are left with),
the two percentages are no longer comparable.

Just like apples and oranges!

 

[waimate01]

Oh boy, good luck to you guys !

 

[FlyingFox]

Oh boy, good luck to you guys !

Seconded !

 

[burglar]

If it is harder to pick winners than to pick losers,
would the market be rising for centuries?

 

[Leiothrix]

Another quirk of percentages that no one talks about is the fact that the maximum you can lose is 100% however the maximum you can make is limitless 100,000,000,000%

Not true -- you can lose a fair bit more than 100% -- the power of leverage

 

[prawn_86]

If it is harder to pick winners than to pick losers,
would the market be rising for centuries?

Confirmation/survivor bias.

How many of the companies at the start of that graph are still included in the index?

 

[burglar]

Confirmation/survivor bias.

How many of the companies at the start of that graph are still included in the index?

Well, ... let me see!
There is that one company that made the world's best buggy whips.
I believe they survived by manufacturing air bags for the modern horseless carriage! :

 

[sinner]

Confirmation/survivor bias.

How many of the companies at the start of that graph are still included in the index?

Not to mention a large portion of returns are attributable to inflation, which is always going to be a bottom left => top right kind of graph.

 

[prawn_86]

Not to mention a large portion of returns are attributable to inflation, which is always going to be a bottom left => top right kind of graph.

Yeh i wasnt sure if it is a real or nominal chart. It says it is log scale, but that doesnt mean it includes inflation

 

[craft]

Take a sound wave



No matter what scale you put on it, the % change from peak to trough is going to be less than the % from trough to peak – yet the amplitude does not change. In this sense I agree with the OP that percentages are misused. Trend, skewness, money management and other things discussed so far are related yet separate issues.

 

[FlyingFox]

Take a sound wave

View attachment 51959

No matter what scale you put on it, the % change from peak to trough is going to be less than the % from trough to peak – yet the amplitude does not change. In this sense I agree with the OP that percentages are misused. Trend, skewness, money management and other things discussed so far are related yet separate issues.

They are not misused. A percentage is a relative measure! Therefore it is always relative to something.

% = AA/BB x 100 . If if you hold AA constant and change BB, your percentage changes and vice versa.

the beginning of this discussion was about the AA part. Well 2K is 20% of 10K and 25% of 8k. It is not being misused whatsoever. you are comparing two different base amounts.

Similarly your profit amount is relative to you capital base. We could have the same portfolio in terms of percentages but I have 10K invested and you have 30k invested. The portfolio goes up by 10%, I make 1K and you make 3K.

The probability of making a dollar amount profit or loss for both of us is different but the probability of making a percentage profit or loss is the same......

 

[galumay]

It is not being misused whatsoever. you are comparing two different base amounts.

Thats exactly why its being misused, by comparing %'s of different base amounts and then suggesting that it can therefore be inferred that one change is more difficult than the other. In the quoted case, if you lose $2000 on a trade you have to make $2000 on a trade to get back to square. Suggesting that its harder to make $2000 because its a bigger % of a smaller amount is clearly misleading.

 

[prawn_86]

Suggesting that its harder to make $2000 because its a bigger % of a smaller amount is clearly misleading.

So you are saying it is just as easy to make a 25% return as it is a 20% one? What if you lost 9k (90%) of this example? Is it as easy to make 1000% off the new base to get back to square?

Pecentages are used universally to measure return for a reason, because the higher the % required, the harder it is to get.

 

[FlyingFox]

Thats exactly why its being misused, by comparing %'s of different base amounts and then suggesting that it can therefore be inferred that one change is more difficult than the other. In the quoted case, if you lose $2000 on a trade you have to make $2000 on a trade to get back to square. Suggesting that its harder to make $2000 because its a bigger % of a smaller amount is clearly misleading.

for any given portfolio, would you agree that it is easier to make a smaller return (in percentages) than a larger one?

disregard invested capital amount for now..

 

[chops_a_must]

Talk about not being able to fight your way out of a wet paper bag...

 

[sinner]

Thats exactly why its being misused, by comparing %'s of different base amounts and then suggesting that it can therefore be inferred that one change is more difficult than the other. In the quoted case, if you lose $2000 on a trade you have to make $2000 on a trade to get back to square. Suggesting that its harder to make $2000 because its a bigger % of a smaller amount is clearly misleading.

It's obviously harder, because you have a lower starting capital to make back the same amount of money that you lost.