Explain what risk tolerance and risk budgeting mean
The idea
Risk tolerance is the senior decision about how much risk the organisation is willing and able to bear in pursuit of its objectives, taken with reference to what it could survive as well as what it would prefer. Risk budgeting allocates that total to specific activities, so a limit exists before an exposure is taken rather than after it is questioned. The budget can be expressed in standard deviation, value at risk or contribution to total risk, and the last is the most informative because it accounts for how positions interact rather than treating each in isolation.
Formulas
Contribution to total risk
contribution = w × Cov(position, portfolio) ÷ σp
- w
- the position's weight
- Cov(position, portfolio)
- the covariance of the position's return with the portfolio's
- σp
- the standard deviation of the portfolio
The contributions of all positions add up to the portfolio's standard deviation. A position can contribute far more of the risk than its share of capital.
Risk capacity
capacity = assets − minimum needed
- capacity
- how much loss the investor can afford
- assets
- what the investor has
- minimum needed
- the amount required to meet essential goals
Capacity is the ability to take risk, a matter of numbers. Willingness is the feeling, and the two can disagree.
Risk tolerance
risk tolerance = min(willingness, capacity)
- risk tolerance
- the level of risk the portfolio should carry
- willingness
- how much risk the investor feels able to take
- capacity
- how much loss the investor can afford
The smaller of the two governs. A bold investor with little capacity is held back, and a cautious one with plenty of capacity is still treated as cautious.
A practice question
What does risk budgeting do?
- Allocates the organisation's total risk tolerance across specific activities - correct
- Sets the annual operating expense limit for each business unitWhy not: A cost control exercise, unrelated to how much risk each activity may run.
- Determines the cost of hedging each activity in the marketWhy not: A market price, set by what the hedge trades at rather than by an internal allocation.
Risk budgeting works like a spending budget, but for risk. First the organisation decides the total risk it is willing and able to bear. Then it splits that total among its activities, such as trading desks or asset classes, before any positions are taken. Sum of risk allocations <= Total risk tolerance. Example: a fund with a total tolerance of 120 million of annual loss might give 50 million to equities, 40 million to credit and 30 million to interest rate positions. Each manager then knows the limit. It is not a cost budget.
A harder one
Why is allocating risk by contribution to total risk more informative than by standalone volatility?
- Because standalone volatility is too hard to estimateWhy not: It is measured easily; the objection is that it ignores how an activity combines with the others.
- Because it reflects correlations with the rest of the portfolio - correct
- Because contribution measures are required by regulationWhy not: Some regimes encourage them, which is a consequence of their usefulness rather than the reason for it.
Standalone volatility is how much an asset swings on its own. Contribution to total risk is how much it adds to the whole portfolio's swings, and that depends on correlation, meaning how closely it moves with the other holdings. Portfolio variance = Sum of weight x weight x covariance, over every pair. Two units with the same standalone volatility can have very different effects. A diversifying unit adds little, while a unit moving with the rest adds a lot. Standalone figures would wrongly discourage the diversifiers.
The hardest tier
A board is comfortable with a loss that would leave the firm unable to meet its obligations. What has been overlooked?
- Capacity to bear the loss - correct
- The ease of measuring the exposureWhy not: Measurement is a separate question, and the exposure here has evidently been quantified.
- The regulator's reporting requirementsWhy not: Reporting is a disclosure duty. What is missing is the recognition that this loss ends the firm.
Risk tolerance has two parts. Willingness is how much loss the board is comfortable with. Capacity is how much loss the firm can actually survive. The lower of the two is the real limit. Here the board is willing to accept a loss that would leave the firm unable to pay what it owes, so it has ignored capacity. For example, a firm with 100 million of capital cannot sensibly accept a possible loss of 150 million, however relaxed the board feels.
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