# How does tranching cause leverage?

I've read that leverage is created with the tranches of a CDS index because the more junior tranches have more risk than the index. I get that the more junior the tranche the more the risk, but I don't see how leverage is created (controlling more with less).

• I am wondering what exactly do you mean by leverage in this situation. I can recall one is pure ratio of tranche size to pool size and the other is ratio of tranche delta to the delta of the underlying pool. I suppose that the CDO structure significantly affects both of them. If you treat equity tranche as the more junior one, stating that it is only 10% of the total pool then obviously it contains biggest risk. – Ascorpio Sep 22 '15 at 21:00
• Can you explain further how those two circumstances could lead to leverage? – AfterWorkGuinness Sep 22 '15 at 21:28
• Let's say that if the pool is 100 mil and equity is 10% = 10 min. Now if we assume that the expected loss on the pool is 5mil, loss on the pool level with be 5%, however, loss on the equity tranche level will be 50% because as most junior tranche it will be the first to absorb losses. This is at least my understanding of the leverage with regards to tranches in any synthetic instrument. You can also check following pdf from fed site as some background link – Ascorpio Sep 22 '15 at 21:43
• Sry couldn't save final edit. This is correct link: Understanding the Risk of Synthetic CDOs . Althoght it's about CDOs, it should help with understanding leverage in general for synthetics. – Ascorpio Sep 22 '15 at 21:51
• Where did you read this? – BAR Sep 23 '15 at 5:09

The leverage is conceptual (as you're not borrowing something to buy more of something in the standard form of leverage). I think it'll become clear when you compare an equity tranche position to a position in the underlying index. An equity tranche on CDX IG, 0-3%, would incur a 26.6% loss if one of the constituents in the underlying index defaults. There are 125 names in the index, each representing 0.8% of the basket. 0.8% / 3% = 26.6%. The underlying index would only suffer a 0.8% loss. This risk asymmetry is why spreads of equity tranches move multiples of moves in the underlying index, and this is called tranche delta. Let's say that multiple is 5x, and we want 100mm of short IG exposure. I can buy 20mm of protection on the IG equity tranche instead of 100mm of the IG index to receive similar economic exposure (obviously with a lot of basis risk). That's where the leverage is.

• I'm a bit lost. I followed your example that 1 default is only 0.8% loss to the total index but a 26.6% loss to the equity tranche, but I lose you after that. – AfterWorkGuinness Sep 23 '15 at 16:11
• Ok, I'll elaborate. When people trade these indices to hedge, they are often looking for mark-to-market gains, not necessarily hold to maturity default payouts. As default probabilities and spreads widen, equity tranches become more expensive because the probability of that 26.6% payout increases vs. only an increased prob. of 0.8% payout on the index. The difference in PnL from those sensitivities to spread is called tranche delta and is the leverage factor. Just like a call option on a stock might move 0.5x of the stock, the mark-to-market of an equity tranche might move ~5x of the index. – realizedvariance Sep 23 '15 at 18:21
• Thanks for the detailed response. I think I get it now. Leverage exists because by investing \$x in the tranche, I have a position that is equivalent to$\Delta_{tranche}\$ * a position in the underlying index. Right? – AfterWorkGuinness Sep 23 '15 at 18:39
• Yup that's correct. There is some basis risk in that position relative to the index because the tranche is also affected by other things (base correlation, etc.), but you're right on where the concept of leverage comes in with tranches. – realizedvariance Sep 23 '15 at 19:30

Without seeing the source I cannot say for sure this is what they were thinking, but this is a way.

You can sell the CDS index and buy the junior tranche, where the proceeds from selling the index can be used to pay for the junior. (note this is only possible with special accounts)

Say you have 100k. If you sell 50k worth of the index you now have 50k to play with (courtesy of the buyer who gave it to you) minus your margin*. Your account value is now 150k minus margin. You take that 50k and use it to buy the junior which is included in the index. And use the other 100k to do the same.

150k position from 100k start.

Leverage.

Of course one must have margin available to run a naked short on practically anything.

*For the big fish, like market makers, well... they play by different rules ;)