Assignment X2 Question X2.6(iii)

[Alp Can]

The solution gets to 95th percentile of loss by calcing the probs of the events of defaults = 0, 1, 2, etc, and aggregating and subtracting from one.

I don't get this approach. I defined the 95th percentile as the case of 95 out of the 100 bonds defaulting, in view of increasing loss amounts. Could someone help me understand the correctness of the solution's approach?

 

[Alvin Kissoon]

Hi Alp,

We are trying to find the 95th percentile point of the loss. For a discrete distribution, this is defined as the minimum loss such that the probability of getting worse than this loss is less than or equal to 5%. Think of it as there are a distribution of potential losses depending on how many bonds default (0, 1, 2 and so on) and we want to find the 95% point.

This is not the same as the probability of 95 of the 100 bonds defaulting. There is only a 2% chance of any bond defaulting in this question, so that probability would be much much smaller than 5%. You referring to increasing loss amounts makes me think of finding the 95th biggest loss, which is also not valid here as we have not considered the probability of achieving any of the losses.

I hope this helps but please let me know if you have any followups.

Alvin.

 

[Alp Can]

I see. Thank you Alvin.