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Characterise financial correlation risk and name the areas of finance where it shows up.

FRM® Part II · Market Risk Measurement and Management · Correlation Basics: Definitions, Applications, and Terminology · FRM2.MR.8.a

The idea

Financial correlation risk is the risk of loss from adverse changes in the correlation between two or more financial variables, such as asset returns, exchange rates or the defaults of different borrowers. Correlation is covariance divided by the product of the two standard deviations. In symbols, ρ = Cov(X, Y) ÷ (σX × σY). The Pearson measure captures only linear dependence, so a correlation of zero does not mean independence. The risk appears wherever a position or a hedge relies on co-movement. That includes investments and diversification, trading of multi-asset and credit derivatives, risk management through portfolio VaR and hedge ratios, regulation, and the stability of the financial system as a whole. A hedge removes a fraction ρ² of variance, so it weakens when correlation falls. Exam point: correlation is the measure, correlation risk is the exposure to its change, and estimates made in calm markets are unreliable in stress.

Formulas

Share of variance removed by a minimum-variance hedge

hedge effectiveness = ρ²

ρ
the correlation between changes in the spot exposure and the hedge instrument

It uses the square of the correlation, not the correlation itself, so a modest fall in ρ cuts effectiveness sharply. The residual share of variance is 1 − ρ².

A practice question

From the question bank, with the reason each wrong option is wrong.

Which statement best defines financial correlation risk?

  1. Loss from adverse changes in the correlation between two or more financial variables. - correct
  2. The risk that the volatility of a single asset rises unexpectedly.Why not: Describes volatility risk of one asset; correlation risk needs at least two variables moving together.
  3. The risk that a counterparty fails to meet its contractual obligations.Why not: That is credit risk in general; it connects to correlation only when several defaults are linked.
  4. The risk that two assets move in opposite directions, which always produces a loss.Why not: Treats negative co-movement as the loss event; the risk is a change in correlation against the position, and negative correlation usually helps diversification.

Correlation risk is the exposure of a position, hedge or portfolio to changes in the co-movement of two or more variables. It is not volatility risk of one asset and not default risk of one borrower.

A harder one

An airline hedges jet fuel purchases with a futures contract. With the minimum-variance hedge, the proportion of the unhedged variance that is removed equals the squared correlation between spot and futures changes. If that correlation falls from 0.90 to 0.60, by how many percentage points does the proportion of variance removed fall?

  1. 30 percentage points, from 90% to 60%.Why not: Uses the correlation itself instead of its square as the share of variance removed.
  2. 56%, a relative fall from 81% to 36%.Why not: Reports the relative decline rather than the percentage-point change that was asked for.
  3. 45 percentage points, from 81% to 36%. - correct
  4. A rise of 45 points, from 19% to 64%.Why not: Uses 1 minus rho², the residual variance, rather than the variance removed, and so gets the direction wrong.

Hedge effectiveness = rho²: 0.90² = 0.81 and 0.60² = 0.36, so the share of variance removed falls by 0.45, or 45 percentage points. This is correlation risk in a hedge.

The hardest tier

A portfolio holds two assets in equal weights, with volatilities of 20% and 30% a year. A risk manager is concerned that the correlation between them, estimated at 0.2, will rise to 0.7 in a stressed market. Portfolio volatility moves from approximately:

  1. 19.6% to 23.1%. - correct
  2. 19.6% to 25.0%.Why not: Takes 25%, the weighted average of the volatilities (the case of perfect correlation), as the stressed value instead of using a correlation of 0.7.
  3. 18.0% to 23.1%.Why not: Starts from zero correlation (square root of the weighted variances) rather than from the estimated 0.2.
  4. 3.9% to 5.4%.Why not: Reports portfolio variances rather than volatilities.

sigma_p = sqrt(0.25 x 0.04 + 0.25 x 0.09 + 2 x 0.25 x rho x 0.06). At rho = 0.2 this is 19.6%; at 0.7 it is 23.1%. A long-only portfolio is exposed to a rise in correlation.

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