Risk Parity

Also seen as: equal risk contribution, ERC, risk budgeting

What does "equal risk contribution" mean?

An instrument's risk contribution is its weight multiplied by how much the portfolio's overall volatility changes when that weight changes. The standard definition splits total portfolio volatility into one slice per instrument, and those slices add back up to the whole.

where: $RC_i$ is instrument i's risk contribution, $w_i$ is its weight, $\sigma_p$ is the portfolio's volatility, and $\partial \sigma_p / \partial w_i$ is instrument i's marginal effect on that volatility. Risk Parity is the weighting that makes every $RC_i$ equal.

Because $\partial \sigma_p / \partial w_i$ depends on how instrument i moves against the rest of the portfolio, not only on its own volatility, correlations feed into a risk-parity weighting even though correlation is never something you set.

Which settings does Risk Parity have?

None — the method's card carries no settings, because equalising risk contribution leaves nothing to choose. The only input Risk Parity reads is the calculation window — the field labelled In-sample in the strategy editor — which sets how many months of history the risk estimates cover. Why the statistic a method treats as "risk" changes its answer at all is covered in risk measure selection.

Where can you use Risk Parity?

Risk Parity is available at both levels. Inside a single strategy it sizes the instruments the strategy holds; inside a Combined it splits capital across the strategies the Combined contains, so each strategy contributes an equal share of the Combined's risk.

Defaults in Fincanva

• Risk Parity exposes no settings of its own — selecting the method is the whole configuration.
• The calculation window (In-sample) defaults to 12 months and accepts any whole number of months from 1 upward.
• Weights are recomputed at every rebalance from the risk figures measured over the window ending at that date, so a risk-parity weighting drifts over the life of a backtest rather than staying fixed.
• Risk Parity never assigns a zero weight to an instrument you have selected: every instrument must carry a slice of the risk, so every instrument gets some weight.

Worked example

A strategy holds two instruments with no tendency to move together. Instrument A has 10% volatility, instrument B has 30%.

• At equal weights (50% / 50%) the risk slices are proportional to (weight × volatility)², so A supplies 0.05² = 0.0025 and B supplies 0.15² = 0.0225 — a split of 10% / 90%. A "balanced" 50-50 portfolio is in fact nine-tenths driven by one instrument.
• Risk Parity instead sets the weights to 75% / 25%, because 0.75 × 10% = 0.25 × 30% = 7.5%. Now each instrument supplies exactly half the risk.

The 50-50 portfolio looks balanced by weight and is heavily lopsided by risk; the 75-25 portfolio looks lopsided by weight and is balanced by risk. Which of those two is "balanced" is exactly the question Risk Parity answers differently from Equal Weights.

How is Risk Parity different from Inverse Volatility?

Inverse Volatility reads each instrument's risk in isolation and weights by one divided by that figure. Risk Parity targets the finished portfolio's risk split, which also depends on how the instruments move together. In the worked example above the two methods happen to agree on 75-25, because the instruments were uncorrelated — that equivalence is a special case, and it breaks as soon as the instruments move together.

Fincanva describes how these methods work; it does not recommend one. See Is this financial advice?.