Compounding and drawdown

The asymmetry

Here is the most important table in this course, and it contains no opinions. A loss of 10% needs a gain of 11% to recover. A loss of 25% needs 33%. A loss of 50% needs 100% — the account must double just to stand where it stood. The reason is humble arithmetic: the loss is taken on the full amount, the recovery is earned on what is left. Percentages feel symmetric because the numerals match; the bases do not, and the bases are what you eat.

Read the table in the worked example until it is reflex. Every rule in this folder is downstream of it. Risk per trade stays small (Lesson 18) because the recovery column grows teeth so fast. Stops sit at levels (Lesson 20) because an unplanned loss is how a 12% drawdown quietly becomes a 38% one. This table is the ‘why’ underneath the entire folder — underneath, honestly, the entire journal.

Compounding, the engine

Compounding is what happens when gains are allowed to join the base and earn gains of their own. $10,000 growing at 8% a year is $10,800 after one year — unremarkable. After ten years it is $21,589: more than doubled, because years six through ten were earning 8% on the earlier years’ gains too. After twenty, $46,610. After thirty, $100,627 — ten times the stake, and the final decade added more than the first two combined.

Read those figures with their assumptions attached, because they are doing quiet work: exactly 8% every year with no down years, no money added or taken out along the way, no fees, no taxes, and no adjustment for inflation — the $100,627 is a nominal figure, worth less in today’s purchasing power than it sounds. Real accounts violate every one of those assumptions. The example isolates the mechanism; it is not a forecast.

Two inputs drive that snowball, and only two: the rate, and time in the game. Of them, time is the one a working person actually owns — which is why Lesson 4 framed investing as a long game and why the site keeps a compounding calculator: to make the snowball visible before it is needed as motivation. But compounding has a gatekeeper, and it is the next section: the snowball only rolls if it survives.

The drawdown’s second cost

A drawdown — the fall from an account’s peak to its valley — charges twice. The first charge is the table above: the recovery gain now required. The second is billed to the operator. Deep drawdowns are where discipline goes to die: the urge to win it back quickly, to double the size, to take the trade that is merely available instead of the one that is planned. Each of those responses digs the valley deeper, and the recovery column lengthens again.

This is why drawdown limits are chosen in advance, in Lesson 22’s plan, as cold numbers rather than hot feelings: the depth at which risk steps down, the depth at which trading stops and reviewing starts. An investor meets the same law in slower motion — a portfolio down 40% needs the same 67% recovery — with one mercy: no margin clerk forces the exit at the bottom. The defense, for both, is identical and unglamorous: never let a single position, or a single season, dig a hole whose recovery column you cannot honestly climb.

Why smooth beats violent

One more piece of arithmetic, because it corrects a common misreading of averages. Take two accounts over two years, built to share the same arithmetic average return: +5% a year. The first gets there violently — up 20% one year, down 10% the next ((+20 − 10) ÷ 2 = +5%): $100 becomes $120, then $108. The second gets there smoothly — up 5% twice: $100 becomes $105, then $110.25. Same average, different endings: the smooth path finishes $2.25 ahead, because compounding never sees the average at all. It only multiplies — and multiplication punishes the down-leg harder than it rewards the up-leg, because the violent path’s −10% was charged on the enlarged $120 base.

Traders meet this as the reason wild sizing feels profitable in the good months and quietly is not. Investors meet it as the reason a steadier portfolio can finish ahead of a flashier one with the same average return that swung harder both ways. Either way the moral of Folder 5 is the same, and the next lesson turns it into a signed document: protect the base. The gains are the market’s business. The base is yours.

Where this breaks

The compounding picture in this lesson is deliberately smooth: a steady rate, no down years, no money in or out. Real accounts break every part of that. Returns arrive unevenly, and the order matters — a deep loss early shrinks the base every later gain must work on. Fees and taxes take their cut each year whether the account rose or not, and inflation quietly reprices the finish line. None of that undoes the arithmetic above; it means the arithmetic is the floor of the problem, not the whole of it.

Practice

Work these three on paper. (1) An account falls 20%. What gain, exactly, brings it back to even? (2) $10,000 falls 30%. Where does it land, and what gain does recovery require? (3) Two two-year paths share the same arithmetic average return, +5% a year: a violent +25% then −15%, and a smooth +5% then +5%. Run $100 through both. Which finishes higher, and by how much?

Work it through: (1) +25% — the recovery is earned on the 80 that survived, and 20 ÷ 80 = 25%. (2) $10,000 × 0.70 = $7,000; recovery needs $3,000 on a $7,000 base, about +43%. (3) Violent: $100 → $125 → $106.25. Smooth: $100 → $105 → $110.25. Same average, and the smooth path finishes $4.00 ahead — the −15% was charged on the enlarged $125 base.