Skip to content
EN

Elements · Risk

The Four Laws of Risk.

What every strategy eventually meets, written as four laws — each with the arithmetic behind it.

I

Losses are real.

Every strategy loses, and losses compound against you: the deeper the fall, the steeper the climb back. Risk is not a footnote to return — it is the first thing we measure.

∎Proof

grec=L1−Lg_{\mathrm{rec}} = \frac{L}{1 - L}
Proof · losses are asymmetricIllustrative
0%100%200%300%400%symmetric intuition−10% → +11%−25% → +33%−50% → +100%−75% → +300%0−20%−40%−60%−80%loss L → gain needed to recover
The gain needed to recover from a loss L is L / (1 − L). A 10% loss needs 11% back; a 50% loss needs 100%; a 75% loss needs 300%. The arithmetic is not symmetric, which is why the first law of risk is that losses are real — and why limits come before returns. Exact arithmetic, not data.

Q.E.D.

II

Losses have causes.

Large losses rarely come from nowhere. They come from three places we can name in advance.

  • Leverage — size that assumes tomorrow looks like the best of yesterday.
  • Overfitting — models that memorised noise and call it structure.
  • Correlation — assets that fall together exactly when diversification is needed.

∎Proof

σp2=∑i∑jwiwjρijσiσj  ⟶  (∑iwiσi)2(ρij→1)\sigma_p^2 = \sum_i \sum_j w_i w_j \rho_{ij} \sigma_i \sigma_j \;\longrightarrow\; \Big(\sum_i w_i \sigma_i\Big)^{2} \quad (\rho_{ij} \to 1)

Q.E.D.

III

Losses can be stopped.

A loss that has a limit is a cost; a loss without one is a catastrophe. Every position, strategy and book carries a maximum loss ℓ set before it trades, and the system — not hope — enforces it.

∎Proof

DDt≥ℓ  ⟹  wt+1=0DD_t \ge \ell \;\Longrightarrow\; w_{t+1} = 0

Q.E.D.

IV

Risk control is a loop.

Not a department — a sequence we run every day:

  • Measure — exposure, volatility, correlation and liquidity, from clean data.
  • Limit — size and loss budgets per position, strategy and book.
  • Monitor — live versus expected behaviour, continuously.
  • Act — cut, hedge or retire automatically when a limit is touched.
  • Review — every breach is logged, explained and fed back into research.