“The storm starts, when the drops start dropping
When the drops stop dropping then the storm starts stopping.”
― Dr. Seuss, Oh Say Can You Say?
“Pray don’t talk to me about the weather, Mr. Worthing. Whenever people talk to me about the weather, I always feel quite certain that they mean something else. And that makes me so nervous.”
– Oscar Wilde, The Importance of Being Earnest, Act 1
We will talk about weathermen and the predictions they make. And we will mean something entirely different. By weathermen, we will mean the models in a bank and the predictions they make or the hypotheses they form. And for the realism of Dr. Seuss’ drops dropping, we will substitute the realism of P&L.. More specifically, we will talk about P&L attribution (PLA) and the role it plays in helping us use the realism of P&L to test the hypotheses posed by our various risk models – which actually is its primary purpose in life.
We will focus specifically on 3 hypotheses formulated by a bank’s risk models, its VAR model and its CVA/EPE model respectively. Namely, for a given bank:
I. Change in the mark-to-market value of its positions are materially determined by changes to a specified set of variables and parameters (i.e. risk factors) and the expected change is quantified by the sensitivities obtained to these risk factors from its models;
II. There is a specified % probability that the value of its positions will lose more than its VAR number over any given interval equal to the VAR holding period;
III. The cost of insuring its aggregate positions against the risk of counterparty Z defaulting is not expected to exceed the cumulative sum of the CVA fees charged to its trading desks for originating exposure to counterparty Z.