How Junior CDS Index Tranches Create Economic Leverage
Summary
Junior tranches of a credit default swap index absorb losses before more senior portions, so a small change in the underlying portfolio can produce a much larger proportional change in the tranche’s value or spread exposure. The document illustrates this with an equity tranche: a constituent default causes a loss equal to that name’s basket weight relative to the tranche’s narrow attachment range, while the index itself loses only the constituent’s basket weight. This sensitivity is described as tranche delta.
A trader seeking a given directional exposure may therefore use a smaller notional in the equity tranche than in the index, which is leverage in economic exposure even without borrowing in the usual sense. A second answer describes increasing gross positions through short index exposure, but notes that this requires suitable accounts and margin. The examples are conceptual and carry substantial basis and margin considerations; they do not establish a universal hedge ratio or quantify realized risk.
Key ideas
- Junior CDS index tranches take losses sooner and can be more sensitive than the full index.
- Tranche delta describes how tranche exposure responds relative to moves in the underlying index.
- A smaller tranche notional may provide exposure comparable to a larger index position.
- This is economic leverage and can involve substantial basis risk.
- Short positions and margin can create another form of account-level leverage, subject to trading constraints.
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Full text
# How does tranching cause leverage? # 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). ## Answer by realizedvariance (score 2, accepted) https://quant.stackexchange.com/a/20858 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. ## Answer by BAR (score 0) https://quant.stackexchange.com/a/20859 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 ;)
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