Correlation
Measure how two return streams move together · 7 min
- Market A
- Market B
Mostly independent wiggles, then they fall together.
Two markets have a correlation of 0.2 in normal times. In these simulated markets, as in many real crises, what happens to their correlation during a shared selloff?
Correlation measures how two return streams move together, from −1 (always opposite) through 0 (unrelated) to +1 (always together). It is about direction and timing, not size: two markets can be correlated 0.9 while one moves three times as much.
A correlation from a short sample is noisy (roughly ±1 ÷ √n), and it changes with the regime. The generator behind these charts shares one common factor across markets and raises everyone's exposure to it in a crisis, so calm-period correlations understate crisis risk. Measure strategies, not just markets: two different rules on two different markets can still lose on the same days.
- Calm days (every third shown)
- Crisis days
Horizontal axis: market A's daily return. Vertical: market B's on the same day. A cloud tilted up and to the right means they move together.
Generated markets, not real data. They show how a rule depends on the market it meets; they do not predict how real markets behave.
Correlation from four days of returns (in %)
- x, y
- x: +1, −1, +2, 0 · y: +2, −1, +1, −2
- Means
- x̄ = 0.5, ȳ = 0
- Σ (x − x̄)(y − ȳ)
- 0.5·2 + (−1.5)(−1) + 1.5·1 + (−0.5)(−2) = 5
- Σ (x − x̄)², Σ (y − ȳ)²
- 5, 10
- ρ
- 5 ÷ √(5 × 10) = 5 ÷ 7.07 = 0.71
What usually happens to the correlation between risky markets in a market-wide crash?
Three days of returns: x = +1, 0, −1 and y = +2, 0, −2 (in %). What is their correlation?
Which pair diversifies best? Correlations: A–B 0.7, A–C 0.1, B–C 0.4.
Missed questions come back for review after one day, then three, then a week.
Strategy 1 has 20% volatility, strategy 2 has 20%, and their returns have a correlation of 1. You put 50% of capital in the first and 50% in the second. What is the blend's volatility (in %)?
Hint: σ² = w₁²σ₁² + w₂²σ₂² + 2·w₁·w₂·ρ·σ₁·σ₂, then take the square root.
Three years of a fresh generated world are on screen; the next two years do not exist yet. Tune the rule on what you can see, commit to two predictions, then generate the future.
- Your rule so far
Over the next two years, after costs, this rule will…
Will the deepest drawdown after the split be worse than before it?
Generated markets, not real data. They show how a rule depends on the market it meets; they do not predict how real markets behave.
Want to feel it candle by candle? Watch a shock unfold in the flash-crash market →