Value at Risk (Varcovar methodology) – FX Forwards

[Ashok_Kothavle]

Dear Mr David,

I was referring to following paper by Mr Thomas J Linsmeirer and Mr Neil D Pearson.

http://www.exinfm.com/training/pdfiles/valueatrisk.pdf

On page 10, FX Forward VaR computation using Varcovar method is illustrated.

Assuming a FX Forwards of BUY 10 million GBP and Sell 15 million USD, with deal maturing in three months.

As mentioned in the paper,

3 month GBP rate = 6.063%,

3 month USD rate = 5.469%,

GBP/USD rate = 1.5355


MTM’s w.r.t. the risk factors are –

(1) GBP 3month rate = GBP 10 million/(1+6.063%*91/360)*1.5355 = 15,123,223


(2) USD 3 month rate = - USD 15million/(1+5.469%*91/360) = - 14,795,461 (Short Position)


(3) GBP / USD exchange rate = 15,123,223


Using the available rates of GBP 3month rate, USD 3month rate and GBP/USD spot rates for last one year, I arrive at correlation matrix and define portfolio standard deviation =

SQRT(w1^2*Sigma(GBP)^2 +

w2^2*Sigma(USD)^2 +

w3^2*Sigma(GBP/USD)^2 +

2*w1*w2*Sigma(GBP) * Sigma(USD) +

2*w1*w3*Sigma(GBP) * Sigma(GBP/USD) +

2*w2*w3*Sigma(USD) * Sigma(GBP/USD))

VaR = (15,123,223 + (- 14,795,461) + 15,123,223) * Portfolio Stdev * 2.326

But this value apparently results in a very high value. Much larger than the net MTM value of the transaction (=327,762).

Not able to figure out what is wrong.

Mr David, will appreciate if you can guide me or share any excel on FX Forwards VaR using Varcovar?


Regards

Ashok Kothavle

 

[ami44]

When you look at the formula at page 13 for sigma(portfolio), be aware that the sigma(1), sigma(2) and sigma(3) in it are not the standard deviation of the risk factors r(USD), r(GBP) and S(USD/GBP). Instead they are the standard deviation of the standardized positions X1, X2 and X3. Your formula for sigma(portfolio) seems to indicate, that you got that wrong.

Also your formula for the VaR is incorrect. Look at the top of page 14
VaR = sigma(portfolio) * 2.326
No need for your factor X1+X2+X3.

In my opinion the math part of this paper is weak and confusing (probably due to it's age), I would try to find another source for this stuff.

I hope that helped.

 

[Ashok_Kothavle]

When you look at the formula at page 13 for sigma(portfolio), be aware that the sigma(1), sigma(2) and sigma(3) in it are not the standard deviation of the risk factors r(USD), r(GBP) and S(USD/GBP). Instead they are the standard deviation of the standardized positions X1, X2 and X3. Your formula for sigma(portfolio) seems to indicate, that you got that wrong.

Also your formula for the VaR is incorrect. Look at the top of page 14
VaR = sigma(portfolio) * 2.326
No need for your factor X1+X2+X3.

In my opinion the math part of this paper is weak and confusing (probably due to it's age), I would try to find another source for this stuff.

I hope that helped.

Dear Ami44,

Thanks a lot for your valuable input. It will be a great help if you can find some other source for this.

With best regards

Ashok