Paravi Chemicals' bonds trade at 40 and you expect a restructuring in 18 months with recoveries of 20, 55 or 80 per 100 of face at 30%, 50% and 20%. What are the expected recovery and the expected IRR, and what would make you pass?

Expected recovery is 49.5 per 100, and at a price of 40 that is an IRR of about 15.3% a year over 18 months; the probability-weighted IRR is lower, about 12.5%. Both sit below a 20% hurdle, which at 18 months needs a price of about 37.7. The trade has a 30% chance of losing half the money, and every six months of delay shaves the return. Pass unless the price is lower, the liquidation branch is less likely than 30%, or the timetable is firmer than 18 months.

Buying a defaulted bond is like buying a disputed plot of land: the price is low because nobody knows which of three rulings the court will give, and the value is the rulings weighted by how likely each is. Expected recovery is the probability-weighted average of the outcomes: 0.30 times 20, plus 0.50 times 55, plus 0.20 times 80, which is 49.5 per 100 of face. Against a price of 40, the expected gain is 9.5 per 100, 23.8% over 18 months. Annualised, 49.5 over 40 to the power of 12 over 18, less one, is 15.3% a year. There is no coupon to add; a defaulted bond earns only its recovery.

Each branch has its own return. Liquidation at 20 is a loss of 20 on 40 paid: -37% a year. The plan at 55 is 24% a year, the sale at 80 is 59%. Weight those by probability and the expected IRR is 12.5%, not 15.3%, because annualising is not linear: the loss branch hurts more in return terms than its share of the recovery average suggests. Investment committees usually see both, with the IRR on the expected recovery as the headline and the weighted figure as the reminder that the average outcome is not an outcome anyone receives. Either way the trade misses a 20% hurdle at 40; the price that clears it on the expected recovery is 49.5 over 1.2 to the power of 1.5, about 37.7.

Start with the downside branch, because that is what a committee asks about first. A 30% chance of recovering 20 is a 30% chance of losing half the position; if that probability is really 40%, the expected recovery drops to 46.0, and above about 53% the trade loses money in expectation. A distressed bond is a bet on recovery, and the question that decides it is how sure you are about the worst branch, not the average. Then timing: the same 49.5 received at 30 months is 8.9% a year, at 36 months 7.4%; restructurings slip, and at 40 the 20% hurdle survives only if the money arrives within about 14 months.

Then the things the three numbers hide. Where do the bonds sit: if secured lenders rank ahead, the 20 in liquidation may be optimistic. What does the 55 consist of: reinstated debt is worth close to face, but new equity in a chemicals company fresh out of restructuring may trade well below the plan value it is given, so the 55 could be a 45 the day it is received. Who else is in the bonds: a holder group that controls the plan can tilt the recovery, and a small position has no say. On these numbers, at 40, with a 20% hurdle, the honest recommendation is to pass or bid lower; around 38 the expected recovery clears the hurdle, and below that the downside branch is at least paid for.