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Lessons from academia - Can someone explain that Remark? (FRM part 2)

RajivBoolell

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Hi @David Harper CFA FRM, Hi All, - hope you are doing well.
I'm having a hard time understanding these 2 statements from the Lessons from academia chapter of the FRM (apologies if this is a double but i did not find the answer on the forum)

1. The highlighted blue statement says that counterparty credit risk can be more than double on doubling a position size which violates positive homogeneity(I agree with that). But the same remark , then indicates that this is just misunderstanding and that the risk is a random variable with a wider probability distribution? For me this is ambiguous. How is this not still a violation of homogeneity?
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2. Moreover I'm unable to understand what they mean by a composed mapping from position to numbers below (red arrow)?Are they speaking about all risk measures or just VaR? I'm not sure to understand that statement

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Thank you very much for any help you can provide
Rajiv
 
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