Charta is on Google Play: practise on the go. Get the app
Charta

Distinguish six kinds of risk and compare them: sponsor, funding, active management, policy-mix, relative and absolute risk.

FRM® Part II · Risk Management and Investment Management · VaR and Risk Budgeting in Investment Management · FRM2.IM.6.e

The idea

Six risks are distinguished for a defined-benefit plan. Absolute risk is the total volatility or VaR of the assets with no reference to a benchmark. Relative risk is the volatility of returns relative to a benchmark, the tracking error. Funding risk is the risk that assets fall short of liabilities, the volatility of the surplus. Policy-mix risk is the surplus risk generated by the strategic allocation, the policy benchmark against liabilities. Active management risk is the tracking error of the actual portfolio against the policy benchmark. Sponsor risk is the risk that the sponsor's own business weakens just when the plan needs contributions. It depends on how the sponsor's earnings correlate with the surplus. If active and policy risks are uncorrelated, funding variance is the sum of the two: Variance = policy-mix variance + active variance. Exam point: variances add, standard deviations do not.

Formulas

Funding risk from policy-mix and active risk

funding risk² = policy-mix risk² + active risk²

policy-mix risk
the surplus volatility of the policy benchmark against the liabilities
active risk
the tracking error of the actual portfolio against the policy benchmark

Only when active returns are uncorrelated with the policy surplus. Work in variances: subtracting volatilities linearly is the trap.

A practice question

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

Active management risk is best described as the:

  1. risk that the policy benchmark itself lags the growth in the liabilities.Why not: That is policy-mix risk, the benchmark measured against liabilities.
  2. risk that the sponsor cannot meet its contribution obligations.Why not: That is sponsor risk, which concerns the sponsor's ability to fund the plan.
  3. total volatility of the portfolio, measured without a reference.Why not: That is absolute risk, which uses no benchmark or liability reference.
  4. risk from deviations of the actual portfolio from the policy benchmark, measured by tracking error against that benchmark. - correct

Active management risk is the tracking error of the actual portfolio against the policy benchmark, the risk taken through manager selection and active bets.

A harder one

A mandate requires that the manager's annual tracking error against its benchmark must not exceed 3 percent. Separately, the chief investment officer limits the whole fund's one-month 95 percent VaR to USD 60 million with no reference to any benchmark. Which risk types do the two limits control?

  1. Absolute risk and relative risk respectively.Why not: Swaps the two: a tracking-error limit is relative to a benchmark; a plain VaR limit is absolute.
  2. Relative risk and absolute risk respectively. - correct
  3. Funding risk and sponsor risk respectively.Why not: Neither limit refers to liabilities or to the sponsor's business.
  4. Policy-mix risk and funding risk respectively.Why not: Neither limit concerns the strategic allocation or the surplus.

Tracking error against a benchmark is relative risk; a VaR limit that uses no benchmark or liability is absolute risk.

The hardest tier

A plan's funding risk (volatility of the surplus) is 10 percent a year and its active management risk is 4 percent a year. Assume active returns are uncorrelated with the policy benchmark's surplus. The policy-mix risk, the surplus volatility of the policy benchmark relative to the liabilities, is closest to:

  1. 6.0 percentWhy not: Subtracts the volatilities linearly: 10 - 4.
  2. 10.8 percentWhy not: Adds the variances instead of subtracting the active variance from the funding variance.
  3. 14.0 percentWhy not: Sums the two risks, which treats them as perfectly correlated and adds in the wrong direction.
  4. 9.2 percent - correct

Funding variance = policy-mix variance + active variance, so policy-mix = sqrt(100 - 16) = sqrt(84) = 9.2 percent. Variances add; standard deviations do not.

In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.

Start free →

More in VaR and Risk Budgeting in Investment Management