A 50% Loss Needs a 100% Gain | Volatility Drag and the Arithmetic of Recovery

Описание: CLAIM: "A 50% loss needs a 50% gain to break even."

Lose half your money and you need a fifty percent gain to get back to even.
It is one of the most repeated pieces of arithmetic there is, and it is
wrong — not by a rounding error, but by a factor that grows the worse the
loss gets. The reason is a denominator: a loss is measured against the money
you had, and a recovery is measured against the money you kept, and those
stop being the same number the moment anything goes wrong.

We took that asymmetry and followed it out to the end. First across every
loss from nothing to ninety-five percent. Then into a portfolio doing the
mildest thing it possibly could — up ten percent, down ten percent, over
and over, averaging exactly zero. Then across two hundred thousand simulated
portfolios over thirty years, every one of them carrying the same average
annual return, to find out what an average return is actually telling you.

This is a descriptive simulation of arithmetic. It is not investment advice,
and it does not suggest what anyone should do with any money.

WHAT WE TESTED
1. The gain required to undo a loss, computed across every loss from zero
to ninety-five percent, to find where the familiar rule of thumb stops
being a reasonable approximation and starts being badly wrong.
2. A portfolio alternating a ten percent gain with a ten percent loss for
fifty round trips — one hundred moves whose arithmetic mean is exactly
zero — plus the same moves reordered, to test whether sequence matters.
3. Two hundred thousand portfolios simulated over thirty years, all pinned
to the same seven percent average annual return, with only the
year-to-year variability changing between them.

THE MODEL
Compounding arithmetic plus a volatility-drag simulation. Test 1 = recovery required vs loss taken. Test 2 = a portfolio that gains and loses the same percentage repeatedly. Test 3 = why the average return lies.

CHAPTERS
0:00 The Claim
1:30 Test 1 The Recovery Curve
2:57 Test 2 The Flat Portfolio
5:02 Test 3 Why The Average Lies
7:23 The Honest Bit
8:13 Verdict
8:45 What It Means

Every figure quoted in this video was measured from the simulation described above, not taken from a secondary source. Where a number is uncertain, the video says so.