Hi @Marco.Musci Component VaR can be calculated three ways ( although, importantly, this are internally consistent: they always give the same answer as demonstrated by my worksheet in https://learn.bionicturtle.com/topic/learning-spreadsheet-jorion-chapter-17/ ), where CVaR = component VaR:
If you look at the last calculation above, the upper limit on the correlation between the position and the portfolio is 1.0; therefore the position's CVaR must be less than (or equal to) the position's individual VaR. It's possible that my statement is imprecise and should be "component VaRs must be LESS than (or equal to) individual VaR" but I'm not sure about that: as I experiment with the numbers, as long as I have another position, the correlation is less than 1.0. Even if (eg) my positions are $5,000 and $10 (99.80% and 0.20%), the correlation is 0.9999970, and the statement is strictly true! I hope that's helpful,
- CVaR = VaR_marginal * $Position
- CVaR = $VaR_portfolio* %position_weight * β(position, portfolio)
- CVaR = $VaR_individual * ρ(position, portfolio)