Inconsistencies in marginal var formula - Jorion Ch7

[kchristo]

In the formula sheet for Marginal Var, it states that
marginal var = deviate * Covariance(asset, portfolio)/(std. dev. of portfolio)
It also states that marginal var = deviate * Beta(asset, portfolio) * (std. dev. of portfolio).

Given that Beta(asset, portfolio) = Covariance(asset, portfolio)/(std. dev. of portfolio):
marginal var = deviate * Beta(asset, portfolio) * (std. dev. of portfolio) = deviate * Covariance(asset, portfolio)/(std. dev. of portfolio)*(std. dev. of portfolio)
Therefore marginal var = deviate * Covariance(asset, portfolio) - However, this doesn't jive with the original definition above as it's lacking the 1/(std. dev. of portfolio) term

 

[kchristo]

Think I may have answered my own question by forgetting that beta has variance of the portfolio in the denominator, rather than std dev

 

[David Harper CFA FRM]

Hi @kchristo You got it:

Marginal VaR, signified with delta (confusing) as given by ΔVaR = α*β(i,p)*σ(p) where β(i,p) = COV(i,p)/σ^2(p) such that
ΔVaR = α*[COV(i,p)/σ^2(p)]*σ(p) = α * COV(i,p)/σ(p). Thanks,

 

[kchristo]

Thanks, David!