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).
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.
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.
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 ;)