# Reading 23 - Question 5 - Equity tranche of CDO

Can someone help me find where they show/explain the logic behind the CDO tranche return calculation? This question felt very rouge when I tried to answer and I can’t find it in this section of the reading.

Consider a collateralized debt obligation (CDO) that has a \$250 million struc- ture. The collateral consists of bonds that mature in seven years, and the coupon rate for these bonds is the seven-year Treasury rate plus 500 bps. The senior tranche comprises 70 percent of the structure and has a floating coupon of LIBOR plus 50 bps. There is only one junior tranche that comprises 20 per- cent of the structure and has a fixed coupon of seven-year Treasury rate plus 300 bps. Compute the rate of return earned by the equity tranche in this CDO if the seven-year Treasury rate is 6 percent and the LIBOR is 7.5 percent. There are no defaults in the underlying collateral pool. Ignore the collateral manager’s fees and any other expenses.

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Bond earns T+5% => 250 * 11% = 27.5 M

Sr Tranche earns L + 0.5% = 250 * 0.7 * 8% = 14 M

Jr Tranche earns T + 3% => 250 * 0.2 * 9% = 4.5M

So the equity tranche gets 27.5 - 14 - 4.5 = 9 M \$

it is worth 10% of 250 = 25 M \$

so rate of return = 9M / 25M * 100 = 36%

Thanks CPK for the math.

What i’m having an issue with is finding where exactly in the reading they cover a CDO equity tranche return? There’s nothing in the LOS that inicates we should be able to calculate the return on this… I don’t want to bother trying to learn this if it’s not going to be covered.

I was having a look for you in volume 5 because it goes through all possible risk management tools but I see nothing on CDOs for now. Will let you know if I see something.

this stuff was covered in level 2 and they don’t have an extended example in the readings for lvl3 other than that question. nontheless, you just have to realize that calculating CDO’s return to equity is conceptually the same process as the examples where they describe the effects of leverage. HENCE, I WOULD ADVISE AGAINST IGNORING IT.

I am confused here. If only 10%, 25m is equity, how can you earn the interest on 250m total structure for 27.5m?

Not sure what is confusing you here.

27.5M is split between all CDO tranches according to formula for each tranche. Equity tranche receives the balance after all other tranches are paid according to their seniority.

9M looks a lot for 25M investment but equity tranche carries the highest risk in case of defaults of the underlying bonds.

Thanks, jpsi. I think I got it now. The confusion is about the CDO structure.

So the total return is earned on total asset. Then it minus the interest of senior tranche and junior tranche.