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Describe how a firm's risk appetite relates to the risk management decisions it makes.

FRM® Part I · Foundations of Risk Management · How Do Firms Manage Financial Risk? · FRM1.FR.2.b

The idea

Risk appetite is the amount and type of risk a firm is willing to take in pursuit of its objectives, and the board sets it. It must sit below risk capacity, so that a buffer remains. Risk capacity is the most risk the firm could bear before breaching a constraint such as minimum capital or a covenant. Appetite is expressed in a statement, for example a target credit rating or a maximum loss at a given confidence level. It is then turned into risk limits for business lines and desks. Risk tolerance is the acceptable variation around objectives. If measured risk exceeds appetite, the firm must reduce exposure or hedge. If it is well below appetite, it may be forgoing return. A common mistake is to confuse appetite with capacity or with the limits that implement it. Exam questions often ask which of the three a statement describes, or how much to cut to fit appetite.

Formulas

Parametric VaR of a normal portfolio

VaR = z × σ × V

z
the standard normal quantile for the confidence level, 2.326 at 99%
σ
the standard deviation of returns over the horizon
V
the portfolio value

Assumes normal returns with zero mean. With the risk profile unchanged VaR scales with V, so a portfolio is cut in proportion to appetite ÷ current VaR.

A practice question

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

Which statement best defines a firm's risk appetite?

  1. The largest loss the firm could absorb before it becomes insolventWhy not: This describes risk capacity, which is the ceiling, not the amount the firm chooses to take.
  2. The set of position limits allocated to individual trading desksWhy not: These are risk limits, which implement appetite at the desk level rather than define it.
  3. The risk the board is willing to take to pursue the firm's objectives - correct
  4. The forecast of the firm's average annual loss from its activitiesWhy not: This describes expected loss, a measured quantity, not a preference or choice about risk.

Appetite is a choice about how much and what kind of risk to run, approved by the board. Capacity is the maximum, limits are the operational controls, and expected loss is a statistic.

A harder one

A trading firm's board sets an appetite that the 99% one-day VaR of its portfolio must not exceed USD 10 million. The portfolio is worth USD 600 million and has a daily return standard deviation of 0.9%. Assuming normally distributed returns and a z value of 2.326 for 99%, by how much must the portfolio be cut, with its risk profile unchanged, to comply?

  1. About USD 2.6 millionWhy not: Treats the excess VaR as the amount of exposure to cut instead of scaling the position.
  2. About USD 154 millionWhy not: Divides the excess VaR by the limit instead of by the current VaR when scaling the position.
  3. No reduction is neededWhy not: Uses the 95% value of 1.645, which gives a VaR of about USD 8.9 million, but the appetite is set at 99%.
  4. About USD 122 million - correct

VaR = 2.326 x 0.009 x 600 = USD 12.56 million. Exposure must shrink by the ratio 10 / 12.56, so the new size is 477.6 and the cut is 600 x (1 - 0.796), about 122 million.

The hardest tier

A firm's annual earnings have a standard deviation of USD 12 million from a commodity exposure. The board's risk appetite caps earnings standard deviation at USD 8 million. A hedge instrument is perfectly correlated with the exposure, so hedging a fraction h of it leaves a standard deviation of (1 - h) x 12. What is the minimum hedge fraction consistent with appetite?

  1. 67%Why not: Sets h equal to 8 / 12, which is the fraction of risk that may remain rather than the fraction to hedge.
  2. 56%Why not: Applies the target to variance, using 1 - (8/12)², although the appetite is stated for standard deviation.
  3. 33% - correct
  4. 50%Why not: Applies a rule-of-thumb half hedge instead of solving (1 - h) x 12 = 8.

Require (1 - h) x 12 <= 8, so h >= 1 - 8/12 = 33.3%. The residual standard deviation is linear in the unhedged fraction, so the answer is not 8/12 and variance is not the right scale.

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