How to calculate total probability of loss from combination of probabilities

**prr** · 12-09-2009, 08:59 AM

I have a list of financial products which have an annual expected loss and dollar size per item. I need to estimate what the expected loss would be for a group of these items if they were put together. So, for example instead of owning just one financial product which has a $100mm value and a 50bps annual expected loss I would own a $100mm notional product with a 50bps annual probability of loss, a $120mm product with a 30bps annual probability of loss and a $50mm product with a 150bps annual expected loss.

How would I calculate my expected loss for the $270mm in products I have in the latter case? Your help would be greatly appreciated. Thank you

**davegugg** · 12-09-2009, 06:48 PM

I think this is more a math problem than excel, isn't it?

Lets say:
a = Dollar Size
z = bps of expected loss
x = Dollar expected loss

a * z = x

Thus if you have 100mm value and 50 bps expected annual loss, your formula is:
100mm * .005 = x, and in this case x = .5mm

To get multiple entries, you'd have to get the total dollar size and total dollar expected loss, and then convert that back to bps.

For example:

a1 * z1 = x1
a2 * z2 = x2
a3 * z3 = x3

a1 + a2 + a3 = Total a
x1 + x2 + x3 = Total x

Total a / Total x = Total z

Does that answer your question?

How to calculate total probability of loss from combination of probabilities

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