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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

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  • $\begingroup$ "I am struggling to find anything on how to set a VaR limit" - My experience is this is often imposed by your mandate. You are given a risk limit (in terms of VAR or drawdown) and that maps to your return rather than starting with your return and establishing the amount of risk required to generate that return. $\endgroup$
    – user42108
    Nov 20, 2021 at 17:27

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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.

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  • $\begingroup$ Thank you Dimitri, I used VaR for the example just because it is common. What I mean is, my VaR, X, would be within the set [Xl, Xh]. And my my value for X depends on my risk appetite. But how I would go about defining the set [Xl, Xh], i.e. the acceptable range that VaR could take. $\endgroup$
    – Offtensive
    Nov 14, 2021 at 11:25
  • $\begingroup$ Even if you are not a large institution that has to set aside regulatory capital for risk, it's useful to take this approach to quantify limits, please look at this paper for some concrete examples moodysanalytics.com/-/media/whitepaper/2015/… $\endgroup$ Nov 14, 2021 at 11:30
  • $\begingroup$ Thanks, I have edited my original post to include an example. Say I have a portfolio where my cumulative return needs to be $3m, I have done that as my daily mean return will be $12k. I assume I have made a mistake somewhere, probably as I have assumed I can achieve a constant PnL everyday. This is along my lines of thinking, i.e. how would I work out a distribution of hypothetical PnLs and then set VaR from that. $\endgroup$
    – Offtensive
    Nov 14, 2021 at 15:20
  • $\begingroup$ Really not enough information given, and you're not focusing on what you're comfortable with if things go wrong. If your average daily p&l is 12k, but once in a hundred years you lose a billion, then are you confortable with that? $\endgroup$ Dec 4, 2021 at 15:12

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