So in that case, the equity tranche will actually be as risky as the senior

tranche, because either all of the names default or none of them default.

The probability of all of them defaulting will therefore just be

q = 1% in the 1% case, or 2 in the 2% case, and so on.

So in other words, let's considered this example here.

So the q=1% case, for numerical reasons we didn't take the value of rho all the way

equal to 1, but we can look at the value rho = 0.99 to see what's going on.

In these case, either all the names default together or none of them default.

In that case, the three tranches are all equally risky, and

so the probability of any one defaulting is 1%.

So the expected losses in the tranche is going to be 1% times 3, which is 0.03.

So this value here is roughly 0.03.

On the other hand, if rho equals zero, well because there's no correlation

among default events, we'll always expect there to be maybe just one default or

one or two defaults or zero defaults.

But what it means is that most of the time we're actually going to see a default,

maybe one, maybe zero, but sometimes two or three.

And so with such a low correlation,

we'll always expect to see some credit event happening.

And because it's the equity tranche that is on the hook for that first credit

event, we expect the equity tranche to incur losses most of the time.

And that's why we see this number being much higher for a low value of rho.

And in fact we'll see this behavior for all values of q.

Down here for example, we see q = 4%.

And we see the expected tranche loss is now almost 3,

and that's because we expect with q = 4%,

we expect there to be 4% of 125, which is 5.

So we expect to see on average five losses in the portfolio.

Because correlation is very low down here,

we're always going to expect to see almost five losses in the portfolio,

which means that most of the time the equity tranche will be wiped out.

We're going to see more than three losses.

Most of them we're going to see four or five losses maybe.