Jorion (Table 7-4 'Risk Minimizing Position') - Final Position weights

[emilioalzamora1]

Hi David, Hi All,

I am referring to Jorion Chapter 7 (Portfolio Risk), 3rd edition:

Perhaps this one is straightforward, but I can't solve for the changed weights (final positions) for the CAD and EUR (85.21% and 14.79% respectively).

I got the marginal VaR (CAD = 0.0528) and (EUR = 0.1521), but then I got stuck how to get the new 'weights'

David, once more, can you please help with this?

Many thanks!

Updated by Nicole to include table:

 

[emilioalzamora1]

Hi David,

I got a solution to this (but perhaps it is simply a coincidence):

1. I took Jorion's equation 7.35 and divided the total Portfolio VAR ($ 257,738) for each currency (CAD and EUR) by their respective wealth (or call it money invested in each currency) termed 'W' which is (CAD = $ 2M; EUR = $ 1M) and then multiplied this with their respective betas (CAD beta = 0.615; EUR beta 1.770)

Then we get for CAD: { 257,738/2M }* 0.615 = 0.07925

and for EUR { 257,738/1M }* 1.770 = 0.4563

2. As a next step we sum these two up (0.07925 + 0.4563) = 0.5355

3. As the marginal VAR for CAD is much lower (hence, CAD is 'preferred' over EUR from a very simplistic Portfolio VaR standpoint), we would like to have a higher weight (position) for CAD:

3.1 Final position (weight) for CAD: 0.4563/0.5355 = 85.2%

3.2 Final position (weight) for EUR: 0.07925/0.5355 = 14.7%

Does this make sense? Strictly following the formula I would vaguely say yes, but it could be a more advanced minimization problem (like solving for the Minimum Variance) either.

Looking forward to your approach, David.
Thank you!

 

[David Harper CFA FRM]

Hi @emilioalzamora1 Here is the XLS which I had constructed for these exhibits https://www.dropbox.com/s/2d8csogmt9ys03d/1116-jorion-portfolio-var.xlsx?dl=0

Hopefully you can see in the first tab (Jorion 7_v2_basic) my calculation approximately match (I think mine are more precise to be honest) including

• At the initial 66.67% weight to CAD, marginal VaR(CAD) = 0.0527 and marginal VaR(EUR) = 0.1516, which I derive in two ways. Either (Jorion 7.17) Marginal VaR = dollar Covariance / Portfolio Volatility * deviate or (Jorion 7.20) Marginal VaR = Portfolio VaR / W * beta(i,P)
• Then the second tab (Jorion 7_v2_minRisk) was my attempt to follow Jorion's instructions: the key input is (yellow) cell C8 which is the new weight of CAD. He says to iterate by shifting weight into (away) from lower (higher) marginal VaRs until the betas and marginal VaRs are equalized. In this case, the marginal VaRs do appear to converge on 0.076... and betas to ~ 1.0 (these are in green rows 34 and 35) So, I did not solve it analytically, I just tried to replicate his instructions. I hope that's helpful!