Hi, I am reading https://learn.bionicturtle.com/topic/study-notes-jorion-chapters-6-11/ on var mapping of linear derivatives. How do I get the marginal var of EUR spot: 0.0453?
Thanks!
Thanks!
Generic Mapping process
- Thread starter Kavita.bhangdia
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Hi @FieryJam Great question! And I'd like to let you know that we will be updating the Jorion Chapters Study Notes (plural), including the mapping chapter, this semester (before the Nov exam). They really do need it. Including refreshed learning spreadsheets, which could be much clearer. With respect to marginal VaR mapping of the forward contract (this is Jorion Table 11-6) please see my screenshot below; and here is the same XLS that I used to replicate Jorion's Table (to my knowledge he has never shared them) https://www.dropbox.com/s/8t0q0m9h5zar0aj/0601-marginal-var-mapping.xlsx?dl=0
Marginal VaR is elegant, it's scaled marginal volatility; i.e., ΔVaR = α*Δσ, where α is the deviate, in this case 1.645 for 95% VaR, and i am letting Δσ refer to marginal volatility (the partial derivative with respect to the position). Probably our most typical expression (see Jorion Ch 7) for marginal VaR is given by ΔVaR = β(i,P)*$VaR(P)/$W, where $W = $ size of portfolio. But given that $VaR(P) = α*σ(P)*$W, ΔVaR = β(i,P)*[α*σ(P)*$W]/$W = β(i,P)*α*σ(P) = [cov(i,P)/σ^2(P)]*α*σ(P) = [cov(i,P)/σ(P)]*α.
So that's also an elegant expression for marginal VaR: (dollar covariance)/(portfolio volatility)*(deviate) = cov(i,P)*α/σ(P). And that's how I got to the marginal VaRs in purple below (inferring volatilities form the given VaRs, then using those to to multiply by the correlation matrix, to get the portfolio variance and standard deviation). I realize this is difficult to follow in the current format, but I think when Deepa and I team to update the notes with well-labeled spreadsheets, the next iteration will be much clearer. I hope that helps!
Marginal VaR is elegant, it's scaled marginal volatility; i.e., ΔVaR = α*Δσ, where α is the deviate, in this case 1.645 for 95% VaR, and i am letting Δσ refer to marginal volatility (the partial derivative with respect to the position). Probably our most typical expression (see Jorion Ch 7) for marginal VaR is given by ΔVaR = β(i,P)*$VaR(P)/$W, where $W = $ size of portfolio. But given that $VaR(P) = α*σ(P)*$W, ΔVaR = β(i,P)*[α*σ(P)*$W]/$W = β(i,P)*α*σ(P) = [cov(i,P)/σ^2(P)]*α*σ(P) = [cov(i,P)/σ(P)]*α.
So that's also an elegant expression for marginal VaR: (dollar covariance)/(portfolio volatility)*(deviate) = cov(i,P)*α/σ(P). And that's how I got to the marginal VaRs in purple below (inferring volatilities form the given VaRs, then using those to to multiply by the correlation matrix, to get the portfolio variance and standard deviation). I realize this is difficult to follow in the current format, but I think when Deepa and I team to update the notes with well-labeled spreadsheets, the next iteration will be much clearer. I hope that helps!
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