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# GARP.FRM.PQ.P1Unexpected loss formula decipher

#### aimjo

##### New Member
For a portfolio of loans, how to calculate unexpected loss?

There seems to be a complicated formula but could not understand it.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @aimjo If you are referring to formula 5.8 in Schroeck, then I agree with you: not only is it too complicated, but we had to explain to GARP why it's actually wrong (see https://www.bionicturtle.com/forum/...-part-1-exam-feedback.12896/page-5#post-56335, it actually appeared as a mistake on the Nov 2017 exam)

The correct portfolio UL is given in our notes by the following (and was presented in the previously assigned Ong (https://www.bionicturtle.com/forum/resources/internal-credit-risk-models-by-michael-ong.131/): This is correct and hopefully familiar: portfolio UL is a essentially similar to portfolio standard deviation (e.g., https://en.wikipedia.org/wiki/Modern_portfolio_theory). It's actually the same formula.
• In the standard mean-variance 2-asset portfolio variance, we have σ$(1)^2 + σ$(2)^2 + 2*σ$(1)*σ$(2)*ρ(1,2),
• but 2-asset portfolio UL^2 = UL$(1)^2 + UL$(2)^2 + 2*UL$(1)*UL$(2)*ρ(1,2), which is the same. This is just a reduction of the above formula under the square root: portfolio UL^2 = UL$(1)*UL$(1)*ρ(1,1) + UL$(2)*UL$(2)*ρ(2,2) + 2*UL$(1)*UL$(2)*ρ(1,2). I hope that's helpful,

#### aimjo

##### New Member
Hi David,

Thanks a lot for explaining this. It is really helpful.