Saptavik Seed Fund I has Rs 60 crore of reserves and five portfolio companies raising their next rounds, all aiming at the same Rs 3,000 crore outcome. Allocate the reserves by expected multiple per rupee.

Rank by probability times payoff: A 2.63x, B 2.40x, C 2.00x, E 1.67x, D 0.94x; fund A, B, C and E for Rs 55 crore and hold the last Rs 5 crore back. D is the portfolio's best-known company, but at Rs 800 crore post its price already assumes a 26.7% chance of the outcome, more than the fund's 25%. Following the favourites instead returns about 1.87x expected against 2.18x.

At a horse race the favourite wins most often, yet betting on it is not the best bet if the odds on offer are short: a horse that wins one race in four pays poorly if the bookmaker already prices it at one in three. A follow-on is a bet at the round's price, so its value per rupee is the chance of the outcome times the multiple a win pays at that price: probability times Rs 3,000 crore divided by the post-money. A rupee in A at Rs 400 crore becomes 7.5 rupees if A wins, and at 35% odds is worth 2.625 rupees today. A rupee in D at Rs 800 crore becomes 3.75 rupees if D wins, and at 25% odds is worth 0.938: less than it cost.

Because its price has already counted what everyone likes about it. Divide each post-money by the Rs 3,000 crore outcome and you get the probability at which a rupee in that round just returns itself. D's Rs 800 crore post-money assumes a 26.7% chance of the outcome; the fund's own estimate is 25%, so on the fund's own view the round is overpriced, however good the company is. A's price assumes 13.3% against the fund's 35%, and E's assumes 3.0% against 5%. The ratio of the fund's odds to the price's odds is the expected multiple, which is why A leads and D trails.

The ranked allocation puts Rs 55 crore into A, B, C and E for an expected Rs 125.8 crore, 2.29x, and with the Rs 5 crore kept at face value the whole Rs 60 crore is expected to return 2.18x. The tempting alternative, following the three most likely winners, A, D and B, uses the same Rs 60 crore for an expected 1.87x, because Rs 25 crore goes into the one round priced above the fund's own odds. The held Rs 5 crore is not idle: it is a bridge for whichever company stumbles.

Three limitations to say aloud. First, the probabilities are the fund's own guesses, and the answer is only as good as them; if the fund thinks D is 35% likely, D's expected multiple becomes 1.31x and the ranking changes. Second, the method ignores dilution after this round, which hurts the cheaper, earlier companies more, so C's and E's numbers are flattering. Third, expected value is not the whole story for a small fund: C and E are long shots, and a fund that only buys long shots may return nothing in most outcomes. The judgement stands: decline D's pro rata, tell D's founders why in terms of price rather than quality, and keep the relationship for a later round.