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Formula of Unexpected Loss

Thread starter #1
Dear Mr David

Sir, while going through the earlier posts, I came across the following formula for calculating the portfolio Unexpected Loss as benig sent by you to 'ravi80' on 23 June 2008.

UL(p) = SQRT [sum(i) sum(j) correlation (i,j)UL(i) * UL(j)] ...........................(A)

Sir, I have a data of 900 borrowers with the respective EADs, LGDs and Prob of Defaults. I have calculated the Portfolio Expected Loss as

sum {over i = 1 to 900} [(EAD(i) * LGD(i) * PD(i)]


TO CALCULATE UNEXPECTED LOSS

(a) First I have calculated the unexpected loss for each of these borrowers as

say for ith borrower

UL(i) = sqrt[(EAD(i)*LGD(i))^2 * pd(i) - EL(i)^2]

e.g. suppose EAD is 100000, LGD is 0.45 and pd is 0.10,

then EL is 100000*0.45*0.10 = 4500

and UL for this borrower is sqrt[ (100000*0.45)^2 * 0.10 - (4500)^2 ] = 13500

(b)

To calculate the correlation matrix, I have generated 10000 random nos 0 (representating non-default) and 1 (DEFAULT) for each of these 900 borrowers using the respective PDs. Then using these generated random nos., I have arrived at the correlation matrix.

(c) The PORTFOLIO EXPECTED LOSS

sum {over i = 1 to 900} [(EAD(i) * LGD(i) * PD(i)] = 40,940,339

However when I use the formula given above for the Unexpected Loss mentioned at (A), I get the PORTFOLIO Unexpected Loss as 28,720,110

Sir, as per my understanding the Unexpected Loss should be greater than the Expected Loss.

Sir, I plead you to guide me. I sincerely apologize for taking liberty of writing to you and consuming your valuable time. I have just joined this group today.

With regards and thanking you in advance

Maithreyi, India
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#2
hi did u get the solution for the UL (i)th borrower formula.. is it correct? I know its tooo long after your post but...

regards,
Himaanshu



Dear Mr David

Sir, while going through the earlier posts, I came across the following formula for calculating the portfolio Unexpected Loss as benig sent by you to 'ravi80' on 23 June 2008.

UL(p) = SQRT [sum(i) sum(j) correlation (i,j)UL(i) * UL(j)] ...........................(A)

Sir, I have a data of 900 borrowers with the respective EADs, LGDs and Prob of Defaults. I have calculated the Portfolio Expected Loss as

sum {over i = 1 to 900} [(EAD(i) * LGD(i) * PD(i)]


TO CALCULATE UNEXPECTED LOSS

(a) First I have calculated the unexpected loss for each of these borrowers as

say for ith borrower

UL(i) = sqrt[(EAD(i)*LGD(i))^2 * pd(i) - EL(i)^2]

e.g. suppose EAD is 100000, LGD is 0.45 and pd is 0.10,

then EL is 100000*0.45*0.10 = 4500

and UL for this borrower is sqrt[ (100000*0.45)^2 * 0.10 - (4500)^2 ] = 13500

(b)

To calculate the correlation matrix, I have generated 10000 random nos 0 (representating non-default) and 1 (DEFAULT) for each of these 900 borrowers using the respective PDs. Then using these generated random nos., I have arrived at the correlation matrix.

(c) The PORTFOLIO EXPECTED LOSS

sum {over i = 1 to 900} [(EAD(i) * LGD(i) * PD(i)] = 40,940,339

However when I use the formula given above for the Unexpected Loss mentioned at (A), I get the PORTFOLIO Unexpected Loss as 28,720,110

Sir, as per my understanding the Unexpected Loss should be greater than the Expected Loss.

Sir, I plead you to guide me. I sincerely apologize for taking liberty of writing to you and consuming your valuable time. I have just joined this group today.

With regards and thanking you in advance

Maithreyi, India
.(JavaScript must be enabled to view this email address)[/size]
 
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