A stressed cable maker's 8% bond trades at Rs 82 and its stock at Rs 40. Given three scenarios with probabilities and payoffs for each security, which offers the better risk-adjusted return?

On the analyst's odds the stock has the better expected return, 6.3% a year against 2.9% for the bond, but it loses 75% or everything in the two bad states, so it must be sized small; the bond's 16% yield is a promise, not an expectation. The bond's expected value is Rs 89.4 on Rs 82, 1.09x, and it needs about a 66% chance of recovery just to earn 7% a year. The stock needs about 51%. At Rs 82 the bond is the security that is mispriced against these odds.

A friend who promises to pay you back Rs 116 next year for Rs 100 today is offering 16% only if he pays. If there is a one in five chance he vanishes, what you expect is much less. Yield to maturity is the return if every promised rupee arrives; expected return weights each outcome by its probability, and for a stressed credit the two are far apart. Ekadanta's bond at Rs 82 promises 8, 8 and 108, 1.51x the price. Weighted across the three outcomes, expected cash is Rs 89.4: 1.09x over three years, about 2.9% a year. The yield to maturityThe single discount rate that makes the present value of all promised coupons and principal equal to the bond's price; it assumes they are all paid on time. of 16% exists only in the recovery state.

Expected value alone would say buy the stock. The portfolio manager's question has a second half. In the bad states the bond loses 17% and 57% of its price; the stock loses 75% and 100%, so the stock's expected loss across those states is 42% of the money against 17% for the bond. That is the structural difference between the two securities: the bond has a claim on the company's assets in a restructuring and the stock has whatever is left after every creditor, which in a restructuring is close to nothing. The price of the stock's higher expected return is a one in two chance of losing most of the capital, and that number sets the size of any position before anything else does.

Turn the sum around and ask what probability of recovery each price needs to earn a plain 7% a year, roughly what a government bond might offer, holding the split between restructuring and default at 3:2. The bond at Rs 82 needs about a 66% chance of recovery; the stock at Rs 40 needs about 51%. The analyst believes 50%. On that view the stock is roughly fairly priced for a 7% return with upside, and the bond is priced for odds the analyst does not believe. Say the limit: the three scenarios and their probabilities are the analyst's judgement, and a bond buyer who thinks recovery is likelier than two in three would reach the opposite conclusion. The exercise does not tell you who is right; it tells you where the disagreement with the market sits.

Buy the stock, sized so that losing all of it costs the fund no more than it can bear, and do not buy the bond at Rs 82. If the fund must own credit, the bond becomes interesting nearer Rs 70, where a 50% recovery probability earns about 7% a year. A better answer still asks whether the fund can own both in a ratio that pays in every state: a small stock position for the recovery case and the bond only once its price reflects the restructuring risk. The limitation to state is that the three-year horizon ignores when the cash arrives and whether coupons are reinvested; a restructuring that drags on for years lowers the bond's return further than the simple multiple shows.