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State what is meant by a risk budget and by risk budgeting.

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

The idea

A risk budget is the total amount of risk an investor is willing to bear, stated in risk units such as VaR or tracking error, and then divided among asset classes, managers or strategies. Risk budgeting is the process around it. Decide how much risk to run, allocate it where expected reward per unit of risk is greatest, and monitor actual use against the allocation. The unit matters. A capital split of 70 percent equities and 30 percent bonds is not a risk budget, because equities may supply over 90 percent of the risk. Stand-alone VaRs do not add up when correlations are below one, so budgets are built from component VaRs, which do sum to the total. Efficient budgets tend to equalise expected excess return per unit of marginal risk. Exam point: budgets are shares of risk, not shares of capital.

A practice question

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

Which statement best defines a risk budget for an investment fund?

  1. A top-down allocation of the total risk the investor will bear, in units such as VaR or tracking error, among asset classes and managers. - correct
  2. A cash reserve set aside from fund assets to meet margin calls and redemption requests.Why not: Confuses a risk budget with a liquidity reserve; a budget limits the risk taken, it does not hold cash.
  3. The maximum notional amount that the investment guidelines allow the fund to hold in each asset class or with each manager.Why not: Describes a capital limit; a risk budget is stated in risk units that reflect volatility and correlation.
  4. The annual fee allowance the sponsor pays external managers for taking risk.Why not: Confuses risk with the fee budget; a risk budget caps risk exposure, not cost.

A risk budget is the total acceptable risk (VaR or tracking error) divided among components. It is a risk allocation, not a cash reserve, a notional cap or a fee allowance.

A harder one

A plan holds 70 percent equities and 30 percent bonds. Equity volatility is 18 percent, bond volatility 6 percent and the correlation is 0.1. Component VaR shows equities contribute about 97 percent of total fund VaR. Which conclusion is consistent with risk budgeting?

  1. The fund is well diversified in risk terms because capital is split 70/30.Why not: Reads capital weights as risk shares; with much higher volatility, equities dominate risk despite a 70 percent weight.
  2. The risk budget is met provided the notional weights add up to 100 percent.Why not: Weights always sum to 100 percent; that says nothing about how risk is allocated.
  3. Moving bonds to 50 percent of capital would equalise the risk contributions of the two classes.Why not: Equal capital still leaves equities far more volatile; equal risk shares need far more bond capital or leverage.
  4. The risk budget is concentrated in equities, so risk should be judged by each asset class's share of VaR rather than by its share of capital. - correct

Component VaR, not capital weight, measures risk usage. With volatility three times higher, the equity share of risk (97 percent) far exceeds its 70 percent capital share.

The hardest tier

A fund's total tracking-error budget is 3.0 percent. Its active returns across mandates are uncorrelated. Manager A is allocated 1.2 percent and manager B 1.6 percent of tracking error at fund level. The largest tracking error that manager C can be allocated is closest to:

  1. 0.20 percentWhy not: Subtracts tracking errors linearly: 3.0 - 1.2 - 1.6; tracking errors combine in quadrature.
  2. 2.49 percentWhy not: Subtracts the standard deviations from the variance budget of 9, mixing units.
  3. 2.24 percent - correct
  4. 1.00 percentWhy not: Combines A and B in quadrature, but then subtracts the result linearly from 3.0.

Variance budget 3.0² = 9.0; used 1.2² + 1.6² = 1.44 + 2.56 = 4.0; remaining 5.0; sqrt(5.0) = 2.24. Risk budgets are allocated in variance when risks are uncorrelated.

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