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I'm very confused in various formulations of "scenario" in portfolio optimization related articles. Can somebody describe me what exactly is scenario in this case?

I see different approaches when I come across various articles.

As I understand it now: a scenario consists of certain period of time from which we take returns (for example 2 weeks 05.05.2001-19.05.2001) and then we create, say, N such scenarios (taking different periods of time, the next would be 06.05.2001-20.05.2001). After that we apply every such scenario to optimize portfolio given certain technique.

Is it okay? What are the other ways to define scenarios? What lengths of such scenarios are the best?

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  • $\begingroup$ Can you reference the article here? $\endgroup$ Commented Jun 12, 2024 at 22:12
  • $\begingroup$ For example here: ise.ufl.edu/uryasev/files/2011/11/kro_CVaR.pdf Scenario generation chapter. $\endgroup$ Commented Jun 12, 2024 at 22:19

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I took a quick look at your cited paper.

On Your Questions: Is it okay? What are the other ways to define scenarios? What lengths of such scenarios are the best?

Is it okay? - Yes, it refers to a time window of certain market conditions. As you mentioned, taking the return of assets from that historical period and applying it today is a form of scenario modelling.

What are the other ways to define scenarios? - Not sure if you heard of reverse stress testing, but it starts with the desired loss amount and it reverses back to the possible market conditions that could result in said loss.

What lengths of such scenarios are the best? - It depends mostly on what you want to model. For example, if you wanted a VaR across a yearly horizon, obviously it would make sense to take returns from a historical yearly period.

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  • $\begingroup$ What do you mean by "applying it today"? By my sentence I meant that we are taking, say, 20 scenarios {05.05.2001-19.05.2001, 06.05.2001-20.05.2001, ... and so on} and express some equations from certain model and for example use linear programming to solve it with minimizing risk (or maximizing expected return) with constraints. Do I understand "scenarios" in a right way? $\endgroup$ Commented Jun 12, 2024 at 22:49
  • $\begingroup$ Are you taking 20 fortnightly holding returns, using them to compute SD and expected return for mean-variance portfolio optimization? If so, you should have been more specific. In that case, I wouldn't really call it scenarios, it would be just historical returns. $\endgroup$ Commented Jun 12, 2024 at 22:59
  • $\begingroup$ I mean that 05.05.2001-19.05.2001 is first scenario, 06.05.2001-20.05.2001 is second scenario and so on. And I'm taking returns for each scenario, like log(s(06.05)/s(05.05)), log(s(07.05)/s(06.05)) ... etc, s - price of an asset And this is for one asset only portfolio (for simplification) $\endgroup$ Commented Jun 13, 2024 at 0:27
  • $\begingroup$ Maybe also another question: is scenarios the same as looking through certain period of time with windows? And if we fit copula to the data, we fit to the historical logreturns on certain period of time and then we need to also assign some probabilities to each scenario? How do I retrieve or choose these probabilities? Maybe it's a lot of questions, but I really struggle with distinguishing between choosing probabilites of scenarios and probabilites of certain logreturns of assets $\endgroup$ Commented Jun 13, 2024 at 2:56
  • $\begingroup$ If you take those "scenarios" and apply the relative returns today, that is a historical VaR scenario, but if you take those "scenarios" as a input to generate expected returns and perform portfolio optimization, those are just historical returns. It is more about what you do with those "scenarios" that defines them. $\endgroup$ Commented Jun 13, 2024 at 9:37

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