Risk Before Strategy

Week 5 · Drawdowns, stops, position sizing and expected value

Course lens

How can a small retail trading account survive execution friction, drawdowns, leverage, and increasingly complex instruments?

The question this week answers

Why should a small account decide how much it can lose before it decides how it wants to trade?

By the end of this lecture

  1. explain drawdown asymmetry
  2. distinguish a stop from an invalidation
  3. calculate position size from account risk and stop distance
  4. calculate expected value and connect repeated losses to survival

Four pieces of the survival toolkit

Drawdown — a loss measured from a previous account peak. Larger losses require a disproportionately larger recovery.

Invalidation — the reason a trade idea is no longer valid; a stop is simply where you exit once that reason is confirmed.

Position sizing — sets the number of shares from the risk budget and the stop distance, not from conviction.

Expected value — combines win rate with win/loss size; win rate alone is not enough to judge a plan.

The smaller the account, the less room there is for a large drawdown before future opportunities become mechanically harder to size

A 50% drawdown is not repaired by a 50% gain

Risk management isn’t something bolted onto a strategy afterwards — it determines whether the account remains able to take the next trade at all.

Simulated account

Starts at $10,000 → a 50% loss reduces it to $5,000

Returning from $5,000 to $10,000 requires a 100% gain on the remaining capital.

The numbers: position sizing

Risking 1% of a $10,000 account:


10,000 × 0.01 = $100 risk budget



Entry $48, invalidation-based stop $45 → stop distance $3/share


100 ÷ 3 = 33.3 → 33 shares (rounded down)



Actual risk: 33 × $3 = $99, not the full $100

Sizing controls the loss on any single attempt — never a gut feeling.

The numbers: expected value

A simulated plan: wins 40% of the time for $150, loses 60% for $80


EV = (0.40 × 150) − (0.60 × 80) = 60 − 48 = $12



The same 40% win rate, with larger losses relative to wins, can still produce a negative EV.

Sizing controls the loss per attempt; expected value describes the long-run average of the plan.

Drawdown changes the recovery problem

Start

$10,000

After 50% loss

$5,000

Required recovery

+100%

Survival is path-dependent: avoiding a deep drawdown can matter more than finding a slightly better entry.

Try it yourself

Calculate

A simulated $20,000 account risks 0.5% per trade. Entry $72, invalidation-based stop $69.

Calculate the share count and the actual dollar risk once it’s rounded down. Then explain why doubling the position size would change survival even if the setup itself is unchanged.

The takeaway

  1. Large drawdowns are disproportionately hard to recover from.
  2. A stop is where you exit; invalidation is why the idea is wrong.
  3. Position size comes from account risk and stop distance, not conviction.
  4. Expected value and loss size matter more to survival than win rate alone.

Next week

Week 6 — swing trading as a case study in overnight exposure and gap risk, built on this week’s position-sizing toolkit.