A defaulted textile company's bonds trade at 42. Recovery in 18 months is 30, 55 or 80 with probabilities of 30%, 50% and 20%. What is the expected recovery, and what annual return does buying at 42 imply?

Expected recovery is 52.5, 25% above the price of 42, about 16% a year over 18 months. That return comes with a 30% chance of losing about 29% of the money. Time matters as much as the recovery: if resolution takes 30 months instead of 18, the same 52.5 earns only about 9% a year. A fund wanting 20% a year over 18 months would pay no more than about 40.

Weight each outcome by its probability and add. 0.3 times 30 plus 0.5 times 55 plus 0.2 times 80 is 52.5: the expected recovery, not the most likely one. A lottery ticket with a small chance of a large prize is priced on the average payout, not on the prize. Against a price of 42, 52.5 is a 25% gain if the probabilities are right.

The fund earns no coupon while it waits, so the whole return comes from the gap between 42 and the recovery, spread over however long it takes. Over 18 months, a 25% gain is about 16.0% a year; over 30 months it is about 9.3%. Insolvency processes often run longer than planned, and each extra month dilutes the return without changing the recovery at all.

Three things, in order. The probabilities: shifting just 10 points from the 55 outcome to the 30 outcome cuts the expected recovery to 50.0 and the return to about 12% a year. The timing, as above. And the price at which the risk is worth it: a fund needing 20% a year over 18 months should pay no more than about 39.9. There is also a 30% chance of recovering 30 and losing 29% of the money, and a fund must be able to carry that loss. Close with the view: at 42 the bonds are attractive only to a buyer confident in an 18-month timetable; at 40 or below the margin for delay is much wider.