Query about ES calculation in Dowd Study Guide Page 15

[SaiJyotsna92]

Hi,
I am new to asking in the forum and presently didn't understand the calculation of 95% ES for a single bond?
In the calculation here: [2% * 1 + (5%-2%) * 0] /5%
1. What are 1 and 0 in the above calculation: I thought it to be payoffs, Is it correct?
2. I assumed 2% is the default probability but the payoff is 0, why is it multiplied by 1?

Can you please help me with this? Thanks in advance.

Best Regards,
Sai Jyotsna.

 

[Eltanariel]

@SaiJyotsna92 , when calculating VaR or ES, you don't look at the payoff but at the amount you'll lose.
In case of a default, you'll lose 100% (ie the 1) of the value of the bond and in case of no default you'll lose nothing (ie the 0)

 

[David Harper CFA FRM]

Hi @SaiJyotsna92 Expected shortfall is a conditional average: it is the average loss given we assume the outcome is in the (1-C%) tail. So, in the above calculation, the 95.0% ES is looking for the average loss in the 5.0% tail. This 5.0% loss tail includes 2.0% (i.e., the extreme edge of the distribution) where (assuming zero recovery) the full par value is lost (Dowd uses 1.0 to keep it really simple, but this could be $100.0 or $1,000.00). But as the PD is 2.0%, the 5.0% loss tail also includes 3.0% probability (the difference between 98 and 95%) where nothing is lost). So the formula is just the weighted average loss of the 5.0% tail, which is 0.40 because 2/5 of the 5.0% tail is a full loss (1.0) and 3/5 of the 5.0% tail is zero loss. I hope that's helpful!

 

[SaiJyotsna92]

Thank You, it's really helpful.