Marginal VAR / without using beta

[dthigale]

Hi David,

I found the menthod used in Schweser notes much easir to calculate Marginal VAR / component VAR.

I tried solving the same example of currencies and the answer matches perfectly.

A B C
σp^2 V^2 = 2 1 0.0025 0 2
0 .0144 1

Solve: A and B
2 * 0.0025 + 1 * 0 .005
2* 0 + 1 * 0.0144 .0144

Portfolio Variance: (Solved A B * C)
.005 * 2 + .0144 * 1 = .0244 σp = 0.1562

MVAR1 = .005 / .1562 * 1.645 = 0.052657 ~ 0.0527
MVAR2 = .0144 / .1562 * 1.645 = 0.151652 ~ 0.1517

Comp VAR1 = MVAR1 * Weight w1 * Portfolio Value = .0527 * 2000 = $ 105.40
Comp VAR2 = MVAR2 * Weight w2 * Portfolio Value = .1517 * 1000 = $ 151.70

From the Portfolio VAR we can also calculate the Portfolio VAR = 1.645 * .1562 * 3000 = $ 770.85 << Will be reduced in optimal portfolio

For optimizing the Portfolio we could check the ration of Excess Return / MVAR
You assumed 8 % for the first asset and 5 % for the second asset
Hence the ratio A : 0.08 / .0527 = 1.5180
B : 0.05 / 0.1517 = 0.3296
In optimal portfolio, both ratios need to be near-by equal and that is shown in Schweser by changing the allocation. You have used 'go seek' function however both approaches would be difficult in exam. One could only suggest how the portfolio could be rebalanced.

The point is we donot have to use Beta. The calculations become complex using beta but that my feeling.

Thanks.

-D.

Ref: Schweser notes / Vol 1 /Portfolio VAR.

 

[David Harper CFA FRM]

Hi Dinesh,

I don't see the point, sorry. The first issue is simply the calculation of marginal VaR.
http://www.bionicturtle.com/premium/spreadsheet/8.b.2_jorions_analytical_var/

I show two ways to do that:

Jorion 7.17: Marginal VaR = dollar Covariance / Portfolio Volatility * deviate
Jorion 7.20: Marginal VaR = Portfolio VaR / W * beta(i,P)

I think yours above is basically Jorion 7.17 ... either way, I don't see how without beta is better/worse than with beta for the calculation of marginal VaR ... beta = Cov()/Var() so i personally don't find it easier/harder but that's just me ...

But the second issue is optimizing the portfolio, which is achived by rebalancing to a constant value for either excess return/beta or excess return/marginal VaR
...how have you achieved that solution analytically? Jorion says it must be iterated...
...sorry i don't see any improvements here

Thanks, David

 

[dthigale]

Hi David,

I thought the Schweser mechanics was easier especially when solving problem in the exam for MVAR / CVAR. Optimization is possible only thru increasing the weight in the portfolio having higher excess / marginal VAR ratio that is a trial and error method.

Thanks for your review and attention.

I am sorry for taking your time on this.

-D.

 

[David Harper CFA FRM]

...no worries... i just thought you were suggesting there was an alternative to "go seek" but trial/error sounds like the same idea. thanks, David