Risk/reward: two outcomes, a probability, and a date
Every pod pitch ends in the same three numbers: what you make if you are right, what you lose if you are wrong, and how likely each is. A takeover is the cleanest version, so that is the model.
- Price a position as an upside case, a downside case and a probability
- Back out the odds the market is already pricing from where the stock sits
- Say what your edge is in probability points, and what it is worth per share
- Turn a third outcome, the beat-and-raise case, into value
The intuition
You are offered a coin flip: heads you win $12, tails you lose $6. Two to one is a good skew, but only if the coin is fair. At a 25% chance of heads the flip loses money on average. A pitch is that flip with a company attached: an upside case if the catalyst goes your way, a downside case if it does not, and your honest odds. The PM wants all three, and then wants to know where the price sits between the two cases, because that is the odds the market is already using.
The recipe uses the purest version, a takeover: the stock is worth the offer if the deal closes and the break price if it does not, and today's price sits somewhere between. Read "offer" as your upside case and "break price" as your downside case and every line is the same for an earnings pitch. Expected value weights the two cases by your odds. The implied probability is the weight that makes expected value equal today's price: the market's odds. Your edge is the gap between the two.
Expected value = p × upside + (1 − p) × downside. Implied probability = (price − downside) ÷ (upside − downside). Edge = your probability − implied. A skew is only a pitch once you attach a probability to it and a date to the catalyst.
Why it works
- The conventions here: two outcomes, each with a price; undiscounted, so time is the catalyst's date rather than a rate. A bump (a higher offer, or for an earnings pitch a beat-and-raise) is a third outcome whose probability is carved out of the chance of the plain upside, not out of the downside.
- Skew without odds is not a pitch. Upside of $12 against downside of $6 is 2:1, and a 2:1 skew loses money at 25% odds. Say the probability, and show the expected value is above the price.
- The market already has odds. Where today's price sits between the downside and the upside is the probability it is pricing. "Cheap" means your probability is higher than that; "expensive" means lower. A wide gap between the two cases is not an edge by itself.
- The catalyst dates the trade. In a pod, an undated idea costs risk budget and borrow while it waits, and the PM cannot hold it through a drawdown. The catalyst is usually the next print, guidance, a contract award, a product launch, an investor day; the horizon is the next one to three quarters.
- The downside case is where you are wrong, not where the chart has support. Price the miss: the lower earnings on the lower multiple a miss brings. That is the number the stop in chapter 5 is built from.
- Hold the probability as a range. Most pitches that lose money did not have the wrong number; they had the wrong confidence in it. Ask whether the trade still works at the bottom of the range.
| Skew: (92 − 80) ÷ (80 − 74) | 2 to 1 |
| Odds the market is pricing: (80 − 74) ÷ (92 − 74) | 33% |
| Your odds | 60%, so 27 points of edge |
| Expected value on your odds: 60% × 92 + 40% × 74 | $84.80, 6% above the price |
| Expected value at 25% odds: 25% × 92 + 75% × 74 | $78.50, below the price |
Same skew both times. The pitch is the odds, and the evidence for them.
The formulas
The two cases, weighted by your odds.
What the position is worth against what it costs.
The odds the market is using: how far the price has traveled from the downside toward the upside.
Points of odds the market is not paying for.
The bump's probability comes out of the plain upside's.
Worked example
Your odds against the market's. The market's come from where the price sits between the two cases; the difference is your edge, and the expected value on your odds is what the stock is worth to you.
See it move
Same company and the same downside case. Change how far above it the upside sits, the gap from today's price to the upside, your own odds, and the size and chance of a bump.
- Raise your odds. The worth on your odds and your edge rise; the market's odds do not move, because they come from the price.
- Widen the gap from today's price to the upside. Today's price falls, the market's odds fall, and your edge grows: the same view is now cheaper to own.
- Raise the upside's premium with the gap held. The market's odds rise: today's price now sits further from the downside.
- Raise the size or the chance of the bump. The bump bar grows; the two-outcome worth does not move.
Run it backwards
The PM's reflex question: the two cases and today's price are known, so what odds is the market already pricing? Then compare with yours.
Set expected value equal to the price and solve for p: the distance from the downside to today's price, over the distance from the downside to the upside. It is a fraction of the way traveled.
The follow-up is the whole pitch in one line: your odds against the market's. If yours are higher, the stock is worth more to you than it costs; if not, the skew does not matter.
Traps
Say it in the interview
“What's the risk/reward?”
Check yourself
4 fresh questions, with new numbers. Answer each one correctly to finish the chapter. Get one wrong and you will see the full working, then you can try it again with new numbers.
Answers within 1% are marked right. Type the number; $, %, x and M are fine. First tries count toward Learned: the topic is Learned once every chapter is done and 75% of first tries were right.
- Expected value = p × upside + (1 − p) × downside; compare it with the price.
- Implied probability = (price − downside) ÷ (upside − downside): the market's odds.
- Edge is your odds minus the market's, not the skew.
- A catalyst with a date; a downside case that is a price, not a chart level.