Setting VaR Limits Within a Broader Risk Appetite Framework
Summary
The document asks how a portfolio’s Value at Risk and Expected Shortfall limits should relate to its annual profit target, including a proposed calculation that turns a daily return target and assumed Sharpe ratio into a daily VaR figure. The response points to a broader risk appetite framework as the basis for setting limits, rather than deriving them mechanically from a profit target. Limits should reflect the firm’s tolerance across market and non-financial risks, including operational, reputational, and model risk.
The response also cautions against relying on VaR or Expected Shortfall alone. These measures may not capture extreme market moves, especially when assumptions about the distribution fail. It recommends supplementing them with stress scenarios focused on far-tail losses and with constraints on sensitivities to market factors. The answer does not provide a formula for converting a desired return into a risk limit, nor does it establish a suitable limit for the example; setting limits remains dependent on the institution’s risk appetite and broader controls.
Key ideas
- Risk limits belong within an organization-wide risk appetite framework that includes non-financial risks.
- A profit target and an assumed Sharpe ratio do not, on their own, establish an appropriate VaR limit.
- VaR and Expected Shortfall may fail to describe losses in extreme market conditions.
- Stress scenarios and limits on market-factor sensitivities can complement statistical risk measures.
Tags
Full text
# How to set VaR and other Risk Limits # How to set VaR and other Risk Limits I have read a lot of literature on how to calculate VaR and it's advantages and disadvantages. But I am struggling to find anything on how to set a VaR limit. For example, say if I am a Risk Manager and management expects the Portfolio to return \$10m over 1 year, how should I set VaR and Expected Shortfall limits for this? I understand this will differ amongst firms, but I have struggled to find any basic literature that can give me a base to build upon this. Second, say if I am a Trader for that Portfolio and I am expected to make $10m profit over the next year with X VaR and Y Expected Shortfall, how should I utilise my VaR and Expected Shortfall limits to achieve my target. Many thanks Offtensive Edit: If I am trying to consider the strategy below: Yearly target: \$3m Trading days: 250 Daily Target: \$12k Therefore I would want a strategy that gives me an average return of $12k per day. If my Sharpe Ratio is 1, therefore Sigma = 12k 99% is 2.32 sigma away from the mean So 12k - 2.32 * 12k = -16k So I would run \$16k VaR That's wrong isn't it? That I can make $3m per annum with a \$16k daily VaR ## Answer by Dimitri Vulis (score 1) https://quant.stackexchange.com/a/68764 Market risk limits are part of a risk appetite framework, which includes appetite for othe risk stripes, like non-financial (operational), reputational, and model risk. A good paper on setting up a risk appetite framework is The Financial Stability Board (FSB) Principles for an Effective Risk Appetite Framework (November 18, 2013). The general principles in $\S3$, Risk limits, will help you (not only with market risk). Also, I'm not quite comfortable with using VaR/ES alone for market risk limits. Perhaps you use it just as an example? The VaR tells you how much money you can lose when things are "normal" (not just normally distributed), but all too often people lose lots of money when things are "not normal", bur rather make "once in a trillion year" moves (assuming normal distribution). At least, you should have a comprehensive set of market risk stress scenarios, far in the tail of your VaR/ES, and set constraints (limits, guidelines, whatever) on how much you can lose under those scenarios. Also constraints on sensitivities to market factors are sometimes insightful.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.