What is the expected number of losses in the portfolio -

Question

Download the spreadsheet Credit_PSet.xlsx

The first worksheet, "LossDstributionCalculations.." displays the default probabilities for N = 20 credits that are numbered 1 to 20_ Over the course of this quiz you will use the Gaussian copula model with p = 0 to compute the expected tranche losses in various tranches.

Before beginning the specific questions below you should use the default probabilities to compute the loss distribution, p^N(F) = Prob(I losses out of N).

You should also assume that each credit has a notional of A = 1 unit and that the recovery is R = D for all credits.

Note

When you have completed this quiz it will actually be quite straightforward to extend your work to non-zero values of p as described in the video modules. In particular, you could use the 1-factor Gaussian copula model and then compute the distribution of the number of losses conditional on the value of the common factor, M. One could do this for n representative values DIM, say ml, and then approximate

P(l)  = _-∞∫^∞P^N(l/M)Φ(M) dM

with

p(1) ≈ ∑_{i =1}ⁿ p^N(l|M = m_i) Prob(M ∈ Δ_i)

where Δ_i, is an interval centered at mi with Δ_i∩Δ_j, for i ≠ j and UΔ_i = (-∞, ∞). Note that this can be done very quickly using your work from Question 1 and an Excel Data Table. You could then compute the expected tranche losses easily for different values of ρ and reproduce similar figures to those in the video "A Simple Example: Part IL" (In practice, of course, one would not do this in Excel but would instead use a more suitable programming language.)

1 . Quiz Instructions
What is p^N(3)?

You should round your answer to three decimal places. For example. if you calculate the probability to be .4567 then you should submit an answer of .457.

2. Quiz Instructions

What is the expected number of losses in the portfolio? (There is a simple way to calculate this that we discussed in one of the video modules. Moreover, you can use this simple way to check that you computed the distribution of the number of losses correctly)

You should round your answer to two decimal places. For example, if you calculate an answer of 2.456 then you should submit an answer of 2.46.

3. Quiz Instructions

Compute the variance of the number of losses in the portfolio.

You should round your answer to two decimal places. For example, if you calculate an answer of 2.456 then you should submit an answer of 2.46.

4. Quiz Instructions

What is the expected tranche loss in the tranche with lower and upper attachment points of 0 and 2, respectively?

You should round your answer to two decimal places. For example_ if you calculate an answer of 2.456 then you should submit an answer of 2.46.

5. Quiz Instructions
What is the expected tranche loss in the tranche with lower and upper attachment points of 2 and 4, respectively?

You should round your answer to two decimal places. For example, if you calculate an answer of 1456 then you should submit an answer of 2.46

Enter answer here

6. Quiz Instructions

What is the expected tranche loss in the tranche with lower and upper attachment points of 4 and 20, respectively? (Your answer to this question and the previous two questions should be consistent with your answer to the second question.)

You should round your answer to two decimal places. For example, if you calculate an answer of 2.456 then you should submit an answer of 2.46.

Attachment:- Credit_PSet.xlsx