Case 031Long pitches and valuationWarm up

Oskari Auto Components trades at Rs 420. Your one-week case gives a bear value of Rs 300 (30% chance), a base of Rs 480 (50%) and a bull of Rs 650 (20%). What is the probability-weighted value, what is the skew, and is this a long you size up or down?

The situation

Oskari Auto Components makes clutch and brake assemblies for two-wheeler makers and trades at Rs 420. You had one week to build a case on it. Your bear case, Rs 300, assumes its biggest customer moves a third of its volume to a rival supplier and margins fall back to their last trough. Your base case, Rs 480, has volumes growing with the market and margins holding. Your bull case, Rs 650, adds new orders for electric two-wheeler parts.

You put 30% on the bear case, 50% on the base and 20% on the bull, and the portfolio manager asks you to turn that into a view.

Your task

What is the probability-weighted value, how is the payoff skewed, and would you size this position up or down?

Quick check

What is Oskari's probability-weighted value?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

The probability-weighted value is Rs 460, only 9.5% above the Rs 420 price, with a 30% chance of losing Rs 120 a share. The upside tail is bigger in rupees than the downside, but the downside is more likely than the bull case. The reward is thin for the risk, so this is a small position, or a name to watch for a lower price, not one to size up.

Step 1How do you turn three scenarios into one number?

A shopkeeper deciding how many umbrellas to stock thinks about a weak, a normal and a heavy monsoon, and how likely each is; the stock he orders reflects all three, weighted by how likely he thinks they are. A probability-weighted value does the same for a share: each scenario's value times its probability, added up. For Oskari that is 0.3 x 300 plus 0.5 x 480 plus 0.2 x 650, which is 90 plus 240 plus 130, or Rs 460. Against Rs 420 that is 9.5% of expected upside.

The relationship

E[V] = 0.3 \times 300 + 0.5 \times 480 + 0.2 \times 650 = 460 \qquad \frac{460}{420} - 1 = 9.5\%

E[V]	the probability-weighted value of a share
0.3, 0.5, 0.2	your probabilities for the bear, base and bull cases
420	today's share price

What it says in wordsWeight each scenario by its probability, add them, and compare the result with the price.

Oskari's bear case of Rs 300 carries 30% of the probability, the base of Rs 480 carries 50% and the bull of Rs 650 carries 20%, so the weighted value is Rs 460, only 9.5% above the Rs 420 price.

Step 2What is the skew telling you?

Split the payoff into its two sides. The probability-weighted gain above the price is 0.5 x 60 plus 0.2 x 230, which is Rs 76; the probability-weighted loss below it is 0.3 x 120, Rs 36. The ratio of about 2 to 1 sounds attractive, but it nets to only Rs 40 of expected gain against a spread of outcomes worth about Rs 123 a share, roughly 29% of the price. The skewWhether the big outcomes sit on the upside or the downside. A positively skewed payoff has a long upside tail. is positive in rupees, because the bull case is far out, but the bear case is one and a half times as likely as the bull. Much of the expected gain depends on a 20% scenario you had a week to test.

Scenario	Value, Rs	Probability	Move from Rs 420	Weighted, Rs
Bear	300	30%	-28.6%	90
Base	480	50%	+14.3%	240
Bull	650	20%	+54.8%	130
Probability-weighted	460	100%	+9.5%	460

The three scenarios weight to Rs 460, a 9.5% gain on Rs 420, while the bear case alone, 30% likely, is a 28.6% loss.

Step 3Do you size it up or down?

Size by what the bear case costs, not by the upside. If the book allows any single name to lose at most 1% of NAV in its bear case, a 28.6% bear-case loss caps Oskari at about 3.5% of NAV, and at that size it adds only about 0.33% of NAV in expectation. That is a starter position at most. A better price changes the answer: to have 20% expected upside you would want to pay about Rs 383. So would more work on the bear case: if a customer check cut its probability to 15%, with the base case taking the difference, the weighted value rises to Rs 487, 16% upside.

Say the limitation before the portfolio manager does. The probabilities are your judgement after one week, and the answer moves a lot with them. The strongest version of this pitch names the one piece of evidence that would move the bear probability, such as the biggest customer's sourcing decision, and says how you would get it. That turns a thin idea into a trade with a trigger.

Where candidates lose it

The common loss is pitching the base case as the answer: Rs 480 is 14% upside and sounds like a buy. The base case is the most likely single outcome, not the expected value, and the 30% bear case drags the weighted value down to Rs 460.

The second is calling the idea attractive because the bull case is far away. A long upside tail that is only 20% likely does not make up for a more likely downside when the expected gain is under 10%; the portfolio manager is listening for a sizing answer, not enthusiasm.

What the interviewer asks next

What bear-case probability would make the weighted value equal to the price?
The stock falls to Rs 380 with no news. What do you do?
How would you test the 30% on the bear case in two days?
Would you short Oskari if you put 50% on the bear case?

Company names and figures are illustrative.