Vishrant Finance's one-year commercial paper yields 11% while AAA paper of the same term yields 8%. With a 30% recovery in default, what default probability makes you indifferent between them, and how do you use that number?

The spread pays for a default probability of about 4% a year: 4.3% on the standard shortcut, 3.7% when you count every rupee. The shortcut is spread divided by loss in default, 3% over 70%. The number is a hurdle, not an answer. Vishrant's paper is worth buying only if your own estimate of its default risk sits clearly below it, with room left for illiquidity and error.

Lending Rs 1,000 to a friend who promises Rs 1,110 back, rather than taking Rs 1,080 from a bank deposit, only makes sense if the extra Rs 30 covers the chance the friend does not pay. A credit spread is the price of expected loss: roughly the chance of default times the share of your money you lose when it happens. Here a default costs 70% of the money lent, because 30% comes back. Credit desks call this the credit triangleThe rough link between spread, default probability and recovery: spread is about default probability times one minus recovery, so knowing any two gives the third..

Write out both outcomes for Rs 100. If Vishrant pays, you get Rs 111. If it defaults, you get Rs 30. The AAA paper pays Rs 108 either way. In a default you lose Rs 81 against the Rs 111 you were promised, not Rs 70, because the coupon disappears along with the principal. Setting the expected payoff equal to Rs 108 gives p = 3 / 81, which is 3.7%. The shortcut ignores the lost coupon, which is why it runs a little high; over one year at these yields the gap rarely changes a decision.

Your own estimate of Vishrant's default risk, built from the lender's books: its capital, the quality of its loans, how much of its funding falls due within a year, and whether banks will keep rolling its credit lines. The breakeven is a hurdle, not a forecast: the paper is worth buying only if your view of default risk sits well below about 4%. If you think the true figure is 2%, the paper returns Rs 109.38 on average against Rs 108, a gain of Rs 1.38 on every Rs 100. If you think 6%, it returns Rs 106.14, a loss of Rs 1.86.

Two limits keep the answer honest. First, part of any spread pays for things other than default: paper from a smaller lender is hard to sell before it matures, and buyers demand extra yield for that. So the default rate the market truly implies is below the breakeven, and a spread that looks generous may simply be paying for illiquidity. Second, recovery is a guess. At 10% recovery the same spread covers only 3.3% a year; at 50% it covers 6.0%. For current default and recovery rates by rating, read the rating agencies' latest published default studies rather than relying on a remembered figure.