UL for a Portfolio of two credit assets

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New Member
Subscriber
upload_2015-4-29_10-9-6.png
Can you kindly clarify as to the following terms not included under square root.

like Wi2XUi2

Or is it that the sigma i=1 to 2 & j= 1 to 2 is missing?
 

ShaktiRathore

Well-Known Member
Subscriber
Yes its correct
For 2 asset ULp=sqrt[sigma(i=1 to 2)sigma(j=1 to 2)wiwj*rho(i,j)*Uli*Ulj]
Ulp=sqrt[w1^2*Ul1^2+ w2^2*Ul2^2+2*rho(i,j)* w1w2*Ul1*Ul2]
w1=w2=.5=>Ulp=sqrt[.5^2*Ul1^2+ .5^2*Ul2^2+2* rho(i,j)* .5*.5*Ul1*Ul2]
.taking .5^2 outside the sqrt becomes .5 =>
Ulp=.5*sqrt[Ul1^2+ Ul2^2+2* rho(i,j)* Ul1*Ul2] .
Thanks
 

David Harper CFA FRM

David Harper CFA FRM
Subscriber
Yes, apologies, it's a typo, I am editing the document to fix that but also include some elaboration on the UL calculations, we will republish it Monday. Apologies for the confusion
 
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