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10 · Risk parity

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Portfolio and Risk, lesson 10

Risk parity

Giving each part of the portfolio the same risk.

Portfolio variance and the covariance matrix from Diversification, and sizing with borrowed money from Sizing bets.

Part 1. Money isn't risk

Three simulated assets with the same Sharpe ratio and very different swings. The top bar shows where the money goes; the bottom bar shows where the risk comes from.

Spread the riskLive

In 60/40, stocks carry nearly all the risk, and even equal money leaves bonds with a sliver. To give each asset an equal share of the risk, the calmest asset needs the most money. Then the whole mix is calm, too calm for most people unless they borrow to scale it up.

Risk contribution and risk parity

An asset's risk contribution is how much of the portfolio's variance it brings, counting how it moves with everything else. The contributions add up to the whole. Weighting assets so their contributions are equal is risk parity.

Your turn

Stocks swing 16% a year and bonds 5%, uncorrelated. In a 50/50 mix of the two, roughly what share of the risk comes from stocks?

Each asset's share goes with the square of its weight times its volatility: 0.5 × 16% = 8 against 0.5 × 5% = 2.5. Squared, that's 64 against 6.25, so stocks bring 64 / 70.25 = 91%.

Part 2. Measuring each share

Keep going with Pro

You've done the first part. Pro opens the rest of this lesson, and every other one.

Still to come
  1. Measuring each share
  2. A worked problem
  3. What it assumes
  4. The same thing, for real
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Next lessonStress testsWhat happens on the worst days, and planning for them. Start lesson 11

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