Why I am no fun at parties (reason #136 of 733).

20th Aug '19 by Gromley

13 comments 1586 reads

The sun is out and I’m just back from my holiday,s so feeling a little playful (my definition of ‘playful’ is reason number 28) so I thought to bring some joy (#79) to your lives by addressing a bugbear of mine.

Downside protection is so vitally important, because if a stock falls by one third 33.333 … % it needs to rise by 50% to recover your loses and if it falls by 50% it needs to double.

Don’t get me wrong, downside protection **IS** very important , I spend a lot of time on the subject (#44), but the above statements are a trick, a mathematical gimmick.

It is a matter of convention that we measure the percentage change in something by taking the difference between the new value and the old value and dividing by the old value – it is so ingrained in our minds that we don’t even think about it.

But, just suppose that convention had taken another path and we routinely described percentage change with reference to the new value not the old one.

Instead of a movement of 100 to 50 being described as -50% [ (50-100) /100 ] it would be -100% [ (50-100)/50 ] and the change needed to reverse such a move would be +50% [ (100-50) /100 ] and not +100% [ (100-50)/50 ].

Anyway if you are still with me and have not yet gouged your eyes out; the point I am addressing is that the quotes above are usually used to infer that a large fall is very difficult to recover. I would argue that nothing is further from the truth – “the market” zig-zags upwards over time (although past performance is no guarantee of the future) and it doubles far more frequently than it halves.

Now I do not want to mislead; if a single stock falls by a substantial amount then you do need to consider very seriously whether it is fatally wounded and how strong the case for recovery is. “Catching falling knives” is not a great hobby and what goes down, often goes down more.

Also we all KNOW that the modern economy is so disrupted that reversion to mean no longer works.

DO WE? Is the internet really more disruptive than the Spinning Jenny? (This is reason number 2 and you really, really,…

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pka

20th Aug '19

"Instead of a movement of 100 to 50 being described as -50% [ (50-100) /100 ] it would be -100% [ (50-100)/50 ]"

However, that would mean a movement of 100 to 0 would be described as - infinity [= (100 - 0) / 0], which doesn't make a lot of sense.

Gromley

Thanks pka,

There always has to be one who is "too smart for their shoes".

The best counter I can offer is my initial thought process on reading your reply :

1. "Spoilsport"

2. You may actually be less fun at parties than even me! ;-)

3. Some vague recollection of the escalation of childhood arguments, which went : mine is 10, well mine is 100, one thousand, one million, infinity, infinity plus one - at which point I would become apoplectic with rage because infinity is the "biggest number there is" so '+1' can't happen (I'm now less convinced on this point!)

4. Creeping back to regain my tedious crown; once the share price gets to zero - what percentage change do you need to regain your initial investment?

5. You should not be afraid of infinity, we might be living in it. (Again reverting to childhood arguments - this time "how big is space")

Nick Ray

Yes - this is a commonly stated issue which is often misunderstood. Because stocks are geometric (i.e we talk about returns as a ratio of new/old) the opposite of a fall of -25% (3/4) is +33% (4/3). You take the reciprocal of the ratio and each is as "easy" to achieve as the other.

I have some plots in an old comment of mine which show that median drawdown of stocks over a year is -29% (0.71) and the median 52w-high is +54% (a bit better than 1/0.71 in fact). So that is a practical demonstration that it is not more difficult to recover than to fall (assuming that the stock is not in fact in terminal decline as you mention.)

By the way this is the basis for volatility harvesting. If we take the arithmetic average of values which are symmetrically geometrically distributed about 1 (so for example 1/4, 1/3, 1/2, 1, 2/1, 3/1, 4/1) the average is greater than 1. If we choose a set of stocks at random from a given index and rebalance every year there will be a slight performance improvement compared with the index which comes about for the same reason. In fact it is equal to 0.5*s^2 where s is the volatility of the portfolio. Although usually that is not a very big payoff. For example if volatility is 20% (a bit more than NAPS typically) then gain is 0.5*0.2^2 = 0.02 or 2%.

21st Aug '19

Hi Gromley,

"2. You may actually be less fun at parties than even me! ;-)"

I have no doubt that's true!

"3. Some vague recollection of the escalation of childhood arguments, which went : mine is 10, well mine is 100, one thousand, one million, infinity, infinity plus one - at which point I would become apoplectic with rage because infinity is the "biggest number there is" so '+1' can't happen (I'm now less convinced on this point!)."

Most mathematicians nowadays believe that infinity plus one is no bigger than infinity.

"4. Creeping back to regain my tedious crown; once the share price gets to zero - what percentage change do you need to regain your initial investment?"

That's easy - it's an infinite percentage!

"5. You should not be afraid of infinity, we might be living in it. (Again reverting to childhood arguments - this time "how big is space")."

That's possible. The observable universe has a finite but enormous radius (determined by its age since the Big Bang multiplied by the speed of light), but many astrophysicists speculate that the universe beyond the observable portion might be infinitely large.

bryans1311

I think this party needs more beer!

back2value

Gromley,

From the many, long wasted hours at school my favourite faux paradox of this ilk was the argument that when a bullet, or a stone, is fired or thrown at someone it gets to half the distance from the shooter / thrower to the target, then three quarters, then seven-eighths, then an ever-increasingly fractional distance from the target, so assuming there are infinite numbers and infinitely decreasing fractional distances, "how does it ever hit you?" Unsurprisingly, however, no-one was prepared to risk getting shot, or bruised, in order to try and prove this.

None of this is relevant to the point you're making, sorry. But I do agree that I get annoyed with the so-called "de-rampers" at another place glibly reminding me how big a percentage leap in price my shares will need to achieve in order just to get back to where I started.

B2V

GrahamF

Gromley

A well made point. I experienced a similar problem during a period of employment when I was tasked with forecasting sales volumes for production planning. The manufacturing and logistics “experts” running the system produced a number for forecast accuracy. This number was the difference between actual volume and forecast volume divided by the forecast volume. So, if you forecast 80 but the actual was 100 your forecast was out by 25% as far as they were concerned. However, if you forecast 120 but the actual was 100 your forecast was only out by only 16.7% as far as they were concerned and you were a better forecaster. I explained the fallacy to them (both forecasters were out by 20 against the same actual volume so are as accurate as each other so they needed to be using a percentage of the actual as their measurement not a percentage of the forecast).

As you can probably guess, the experts were too set in their ways to be able to admit that their forecast accuracy measurement was nonsense and decided to ignore the ‘troublemaker’.

So, what did I do? Deliberately over forecast and thus improve my accuracy scores of course.

I won’t recall how I tried to explain that the total volumes of sales were relatively easy to predict but the volumes of each individual item within those volumes was not predictable with much accuracy lest I never get invited to a party again!!

WarrantStar

If the calculation was to divide the change in value by the average of the old and new value, then the percentage change would be the the same whether direction of change is up or down (apart from the sign)

Eg down from 100 to 50 would be a percentage change of 100 x -50/75 = -66.7%

or Up from 50 to 100 would be a percentage change of 100 x 50/75 = +66.7%

Compromise can be a good thing!

HumourMe

22nd Aug '19

Most mathematicians nowadays believe that infinity plus one is no bigger than infinity.

Whenever I've compared them I've not been able to discern a difference.

HHR

Thanks for this entertaining and thought provoking article. Here is my two penneth;

It is harder for a stock priced at 50p to move by 50p than it is for a stock priced at 100p to move by 50p.

Therefore whether the loss/gain is called 50% or 100% the investment maxim that losses pack a greater punch than gains still holds true.

Is the pain from a 50% loss of the same magnitude as the pleasure from a 100% gain?

xcity

When you say:
"It is harder for a stock priced at 50p to move by 50p than it is for a stock priced at 100p to move by 50p."
that's a tautology.

Since you say
"losses pack a greater punch than gains"
it seems that you really meant:
"It is harder for a stock priced at 50p to rise by 50p than it is for a stock priced at 100p to fall by 50p."

That's empirical and can be tested. I don't think it's really true in a bull market.

But it also fails to take account of:

A stock priced at 50p can fall by no more than 50p, but can rise by many, many multiples of 50p.

Grateful to Gromley for raising this. It's one of my irritations with a number of fora that such oft quoted sayings are flaunted as self-evident truths when they simply demonstrate an inadequate understanding of numbers. The pervasive use of percentage changes in economics and investment means that our usual heuristics produce a distorted understanding of historic change and the probabilities of future change.

23rd Aug '19

Another way of looking at it.

A fall by 10 requires a greater % change to reverse than a rise by 10.
If a given % change is equally likely up or down, then that would imply that all share prices with some volatility would tend to 0.

Why I am no fun at parties (reason #136 of 733).

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Gromley

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