How can two risky bonds, each paying only 90% of the time, be carved into a triple-A senior claim and a toxic junior one?
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One risky bond priced by expected value
Price the $1,000 bond that pays with probability 90% at $900, and compute the 11.1% yield that default alone implies when the risk-free rate is zero.
The two-bond pool under independent defaults
Build the table of pool values $2,000, $1,000 and $0, deriving the probabilities 81%, 18% and 1% from independent defaults.
Senior and junior tranches, rated and priced
Split each pool outcome by priority, derive default probabilities of 1% for the senior (Aaa) and 19% for the junior (junk), price them at $990 and $810, and check the total is still $1,800.
Two clienteles for two tranches
Record who buys each slice, pension funds and endowments the senior and hedge funds the junior toxic waste, and the growth in hedge fund capital that made the market explode.