Adapting VaR to Changing Portfolio Risk

# Adapting VaR model in a dynamic trading environment


# Adapting VaR model in a dynamic trading environment












I study FRM part II (P2.T5.25.5 Conceptual Soundness and Sensitivity Analysis in VaR Models) and encounter this question in Bionic Turtle, please help. Would really appreciate if you can provide with some sources/papers.

*25.5.1: During a regulatory review, a Chief Risk Officer (CRO) is asked to justify how the bank’s VaR model adapts to shifting portfolio risks in a dynamic trading environment. Regulators express concern that some banks still rely on historical P&L-based VaR, which may not capture risk evolution as positions change. One panel member suggests using a standardized volatility model like GARCH, while others debate whether simplifying the model sacrifices predictive accuracy. Which approach best ensures that the VaR model accurately reflects changing portfolio risk?

a. Prioritizing historical P&L stability over dynamic adjustments to avoid excessive model complexity.

b. Applying GARCH-based volatility modeling across all asset classes due to its superior conditional risk measurement.

c. Using pseudo-history to incorporate dynamic portfolio shifts, improving scenario-based VaR estimates.

d. Relying on parametric VaR for better interpretability, as complex risk estimates can reduce decision-making clarity.*

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/82381

Related: Value at risk (portfolio with stocks, bonds, and options)

This problem is not clearly written at all. I hope the real FRM exam is better! I'm bothered by the sentence:

> Regulators express concern that some banks still rely on historical P&L-based VaR, which may not capture risk evolution as positions change

Is the problem's author trying to suggest that some banks actually look at the statistics of their historical P&L? Like, in the last 3 years, 99% of trading days we didn't lose more than \$X, and therefore our value at risk is \$X? I struggle to imagine a situation in which this methodology might be acceptable to regulators in the first place. Maybe if exactly 100% of the portfolio is the same single asset, and the composition cannot change.

Otherwise, the historical P&Ls of your portfolio are irrelevant, and GARCH wouldn't help. Rather, you must consider how the portfolio that you have right now might perform if the market behaves like it did historically.

Take a look, for example, at https://www.bis.org/publ/bcbs128.pdf (Basel II - being replaced by later standards, but I'll use this one), pp 195ff, for a discussion of what VaR methodologies have usually been acceptable to regulators:

> variance-covariance matrices, historical simulations, or Monte Carlo simulations

You need the history of the market factors (rates)

> The choice of historical observation period (sample period) for calculating value-at-risk will be constrained to a minimum length of one year. For banks that use a weighting scheme or other methods for the historical observation period, the “effective” observation period must be at least one year (that is, the weighted average time lag of the individual observations cannot be less than 6 months).

If all the market factor sensitivities are linear then the following methodology, may likely to suffice: get the variance-covariance matrix of the historical market factor returns, perform matrix multiplication of the factor sensitivities, the historical the variance-covariance matrix, and normsinv(confidence interval). About the latter, the spec says:

> In calculating the value-at-risk, a 99th percentile, one-tailed confidence interval is to be used

Matrix multiplication is choice 'd' "Parametric Var".

If the factor sensitivities may be non-linear, then choice 'c' "Using pseudo-history" maps into two different methodologies, both of which may be acceptable:

Calculate the P&Ls of your current portfolio using the historical market factor returns.

Use the variance-covariance matrix and Monte Carlo to generate many P&Ls of your current portfolio.

Under both of these, you sort the P&Ls and look for the 99% percentile.

Choice 'b' "Applying GARCH-based volatility" isn't mutually exclusive.