# Structural Models - PV of Expected Loss vs Expected Loss

In one of the Schweser Mocks, there was a question about the PV of expected loss under the Strucutral model which was:

PV of Expected Loss = 23.51

Expected Loss = 22.86

How is this possible? I know under Structural models, PV of expected loss is comprised of: Time value of Money and Risk Premium for Risk of Credit Loss. Is the “Expected Loss” calculated differently which causes this difference?

The premium overpowers the discounting in the TVM calculation

I guess this is a case where the risk premium dominates time value. If not, the PV of expected loss should have been lower than expected loss (which considers the bond specific factors in terms of default probablity and interest rate)

Remember for calculating expected loss, the probablity used is (e1, e2) and the interest rate is the actual coupon rate. These are specific to the bond

For PV of expected loss, the interest rate is “risk free rate” and the probablity is (d1, d2). These parameters are ‘risk -neutral’.

Hm… what do you mean by the interest rate is the “risk free rate” and these parameters are “risk-neutral”

When you calculate the PV of expected loss the rate which you apply to discount is the ‘risk free’ rate and “d1/d2” to calculate the probablity is the ‘risk-neutral’ probablity, meaning (the way I understood) is that the generic default probablity in the market (and not specific to the debt you are analysing). So this calculation would give you the expected loss (for the given K (face value of debt) and A (asset value)) under normal conditions.

Now, when you calculate Expected loss, the parameters are specific to the debt you are analysing. Refer to CFA material, Reading 45, page 203, Example 4. It describes the same scenario which you have specified above. In that example just substitute the values of “-d1” and “-d2” instead of “-e1” and “-e2”, and the rate of interest as 1% (and not 3%), in the equation for expected loss. The value you will arrive at will be \$13.41, which is greater than PV of expected loss, which is what you would expect under normal conditions.

I’m also struggling with this concept.

The expected loss = undiscounted loss based on the credit risk of the bond?

PV of expected loss = PV of loss based on Risk Free and risk-neutral (or “market”) probability of default?

If the PV of expected loss > expected loss, does this imply that the bond is less risky than a risk free bond?

If the bond is as good as a risk free bond, you would expect the PV of expected loss to be lower (simple time value of money concept) than expected loss, if not, it means that the risk in the bond ‘over powers’ the time value. So you end up where PV of expected loss is greater than expected loss, means the bond is that much more risky.

Caution- this is how I drilled this concept into my head, and it seems to work!!

When you say the risk of the bond ‘overpowers’ the time value, can you clarify.

An example would helpful: If I have a risky corporate bond, under what situation is PV of the expected loss > expected loss?

I wrote a post some time ago : http://www.analystforum.com/forums/cfa-forums/cfa-level-ii-forum/91340734

For the purpose of the exam:

If PV of expected loss > expected loss, risk over powers time value of money (which is probably true for lot of corporate bonds)

If PV of expected loss < expected loss, then time value of money over powers risk premium (if this was true, means the credit is generally ‘very good’ and the bond of the firm which we are analysing also has got great credit quality)