Venture Capital puzzles, solved step by step

About 1.24x, down from 3.0x. The other 29 companies returned Rs 360 crore, an average of Rs 12.4 crore each. Replace the Rs 540 crore winner with one more average company and the fund returns Rs 372 crore on Rs 300 crore. Missing that one company costs Rs 528 crore, more than three times what all 15 write-offs cost together.

Why does one company out of thirty move the whole fund?

Picture a cricket team that scores 900 runs in a series, 540 of them from one batter. Drop that batter for an average player and the team's total collapses, however steady the rest were. A venture fund works the same way: returns are so uneven that the best company is often worth more than all the others put together. Here the winner returned 54x its cheque. The other 29 returned Rs 360 crore between them, an average of Rs 12.4 crore on Rs 10 crore each, about 1.24x.

How does that compare with the cost of the failures?

Fifteen companies went to zero. At Rs 10 crore each, that is Rs 150 crore of lost capital, the most a write-off can ever cost. A write-off loses at most the cheque; a missed winner loses everything the winner would have returned, which has no ceiling. In this fund the one miss costs Rs 528 crore, about 3.5 times every write-off combined. This asymmetry is why venture investors say the error that matters is the company they passed on, not the one that failed.

What do you add after the number?

Say what it implies for how a fund behaves. A partner who rejects a deal because it might fail is guarding against the smaller of the two errors. The right question at the investment committee is whether a company could return the fund if it works. The limit is worth one sentence too: this is one fund's numbers, and a portfolio with a flatter spread of outcomes would care less about any single company.

About 36% of such funds find no winner, even though the expected multiple is 2.48x. Each bet misses with probability 0.96, so all 25 miss with probability 0.96 to the power 25, which is 0.360. Each bet is worth 0.04 x 50 plus 0.96 x 0.5 on average, 2.48x. The average hides a wide spread: a fund with no winner returns 0.5x.

Why is one winner not guaranteed when 25 times 4% is 100%?

A batsman who hits a six once every 25 balls on average can still face 25 balls and hit none. Twenty five times 4% gives the expected number of winners, one, not the chance of getting at least one. To find that chance, count the way the fund fails: every bet must miss, and since the bets are independent the misses multiply, 0.96 x 0.96 and so on, 25 times. That is 0.360, so about 36% of identical funds never see a 50x company.

What does the spread tell you about running a seed fund?

Each extra winner adds 49.5x on one twenty-fifth of the fund, about 1.98 turns of the whole fund. So the fund's result is set almost entirely by how many winners it happens to land: none gives 0.5x, one gives 2.48x and two give 4.46x. The most likely single outcome is exactly one winner, at 37.5%, but no winner at all is nearly as likely. This is why seed managers want more shots on goal: with 57 bets the chance of finding no winner falls below 10%.

Say the limitation too. Real outcomes are not two-point, and they are not independent: a funding drought hurts every company in a vintage at once, which fattens the no-winner tail rather than thinning it.

The portfolio must distribute Rs 1,750 crore, 3.5x the fund, which is exactly five Rs 350 crore exits. LPs want Rs 1,500 crore: Rs 500 crore of capital plus Rs 1,000 crore of profit. Their profit is 80% of the total, so total profit is Rs 1,250 crore and gross is Rs 1,750 crore. At Rs 350 crore an exit that needs five exits, where ignoring carry suggests just over four.

How do you work back from net to gross?

Picture a sales agent who keeps a fifth of whatever the house sells for above the owner's purchase price. If the owner wants to walk away with Rs 1 crore of profit, the house has to make Rs 1.25 crore of profit, because the agent takes a fifth of it. Carry only touches profit, so gross up the LPs' profit by 0.8 and leave their capital alone. LPs need Rs 1,000 crore of profit on top of their Rs 500 crore, so total profit is 1,000 divided by 0.8, Rs 1,250 crore, and gross distributions are Rs 1,750 crore.

Why does the exit count matter more than the multiple?

Because exits come in whole companies. Forgetting carry gives Rs 1,500 crore, which looks like 4.3 exits and invites a partner to think four big outcomes plus some smaller ones will do; with carry it is exactly five, with nothing to spare. Each exit returning Rs 350 crore to the fund is itself rare: if the fund owns 10% at exit, each one is a Rs 3,500 crore company. Seen this way, a 3x net target is a statement about how many very large companies the fund must back and keep a meaningful stake in.

Say the simplifications. The rest of the portfolio is assumed to return nothing, which overstates the exits needed, while fees, which the question told you to ignore, would reduce the capital invested and raise the bar again. A real model would net the two.

The Series B follow-on, at 1.50x against 1.25x. Rs 10 crore at Rs 400 crore post buys 2.5%, worth Rs 50 crore in a Rs 2,000 crore exit; at a 30% chance that is Rs 15 crore expected. The seed buys 25%, halved to 12.5% by exit, worth Rs 250 crore; at 5% that is Rs 12.5 crore. The seed would need a 6% chance of the exit to draw level.

Why is the cheaper entry not automatically the better bet?

A lottery ticket costs very little and a fixed deposit costs a lot per rupee of payout, yet nobody thinks the ticket is the better deal just because it is cheap. What matters is the price multiplied by the chance of being paid. The expected multiple of a venture cheque is the chance of the exit times the stake you hold at exit times the exit value, divided by the cheque. The seed price is 10 times lower, so the stake starts 10 times bigger, but halving by dilution leaves it only 5 times bigger, and the odds are 6 times worse.

How do you compare them quickly in the room?

Compare the three ratios rather than the full sums. The seed stake at exit is 5 times the Series B stake, but its odds are 6 times lower, so its expected value is five sixths of the follow-on's. Five sixths of 1.5x is 1.25x. The same logic gives the break-even: the seed draws level only if its chance of the exit rises from 5% to 6%, or the Series B chance falls from 30% to 25%.

What does the expected multiple leave out?

Say the limits before the interviewer does. The seed's 1.25x comes with a 95% chance of losing everything, against 70% for the follow-on, so the two bets carry very different risk even before you compare averages. Time matters too: a Series B company is closer to exit, so the same multiple earns a higher annual rate. Against that, a seed fund's strategy depends on owning large stakes in a few outliers, and a partner may accept a lower expected multiple for the bigger stake. The arithmetic decides the comparison only once those preferences are stated.

Investor B, at 2.68x against 1.32x. Expected multiple is each outcome times its chance. A gets 0.4 x 3 from winners and 0.6 x 0.2 from losers, 1.32x. B gets 0.1 x 25 and 0.9 x 0.2, 2.68x. B is wrong nine times in ten but its winners are big enough to carry the portfolio; A's winners need to be 6.4x to draw level.

Why does the investor who is usually wrong do better?

A shopkeeper who makes a small profit on four sales in ten and a small loss on the rest earns steadily but slowly. A fisherman who comes back empty nine days in ten but lands one huge catch on the tenth can still earn far more. In venture the size of the winners matters more than how often you win, because losses are capped at the cheque while winners are not. A's high hit rate buys only 1.20x from winners; B's one-in-ten rate buys 2.50x.

How far would either number have to move to flip the answer?

Solve for the break-even, because it tells you how robust the answer is. A's winners would need to return 6.4x, more than twice their 3x, to draw level, while B's hit rate could fall from 10% to 4.5% before B dropped to A's 1.32x. B's lead survives a large error in its hit rate, which is why venture investors talk about the size of possible outcomes before the chance of success: an investment that cannot return 25x cannot carry a portfolio like this.

What does the average hide about investor B?

Variance. With 20 investments and a 10% hit rate, B finds no winner at all 12% of the time and returns 0.2x. One winner is enough to lift B's 20-company portfolio to 1.44x, above A's expected 1.32x, so B's result depends heavily on whether it lands at least one outlier. That is the case for venture portfolios of 25 or more companies, and the limitation of the clean comparison: a fund with too few bets can follow B's strategy correctly and still lose money.

About 9.1x, not 7.5x. Take a Rs 100 crore fund. Fees take Rs 17.5 crore, leaving Rs 82.5 crore to invest. 60% of that, Rs 49.5 crore, goes to companies that return nothing, so only Rs 33 crore survives. To return Rs 300 crore, those survivors must earn 300 divided by 33, about 9.1x. Forgetting fees gives 300 over 40, or 7.5x, which understates the bar by a fifth.

Why does the base shrink twice before you divide?

A farmer who must sell 3 tonnes of grain for every tonne of seed bought, after setting aside some seed for the birds and losing most fields to flood, needs the surviving fields to yield far more than 3 tonnes each. A fund's target is set on every rupee committed, but only the rupees that are invested and survive can earn it, so the required survivor multiple is the target divided by the surviving share of commitments. Fees remove 17.5%; failures remove 60% of what is left. The surviving share is 0.825 x 0.4, which is 33% of commitments.

Is 3x on commitments the number LPs actually receive?

No, and saying so earns credit. The 3x here is before the manager's carried interest. If LPs want 3x after a 20% carry on profits, the fund must return about Rs 350 crore gross, and the survivors must earn about 10.6x. Recycling, where a fund reinvests early proceeds to put more than 82.5% of commitments to work, pushes the bar back down. Either way, the shape of the answer is the point: venture survivors need near ten-times outcomes as a group, which is why a fund cannot be built from companies that can only triple.

One honest limit: the 60% that returns nothing is a round assumption. Real portfolios have a middle band of companies returning 0.5x to 2x, which lowers the bar for the top performers, and the fee load varies by fund size and terms, so confirm both before using the figure.

64% from the top 4%, and 51.2% from the top 0.8%. Each application of the rule keeps a fifth of the companies and four-fifths of the returns. The top 20% earn 80%. A fifth of those, the top 4%, earn 80% of 80%, or 64%. A fifth of those, the top 0.8%, earn 80% of 64%, or 51.2%. So fewer than one company in a hundred produces more than half of all returns.

Why do the shares multiply at each step?

If a fifth of a city's shops make four-fifths of its sales, and among those top shops a fifth again make four-fifths of their group's sales, then the very top shops make four-fifths of four-fifths. A rule that repeats inside itself compounds: k steps leave 0.2 to the power k of the companies with 0.8 to the power k of the returns. Three steps give 0.8% of companies and 51.2% of returns. The pattern is the signature of a power lawA distribution where a small number of very large outcomes account for most of the total, and the same shape repeats at every scale., and it is why venture is described as a business of outliers.

What does this mean for how a venture fund is built?

Half the returns come from the top 0.67% of companies, fewer than one in a hundred. A fund of 30 companies, picked at random from this population, has only about a 21% chance of owning even one company from that top 0.8%, so portfolio size and access to the best deals matter more than average picking skill. That is the logic behind funds holding more companies, reserving money to double down on the winners, and refusing to cap the upside of any single investment. A fund cannot diversify its way to the median here; the median company returns little.

State the limit. A clean, repeating 80/20 rule is a stylised model, not a measured fact about any dataset; real venture returns are lumpy and vary by vintage and stage. The value of the puzzle is the shape: concentration at the top is far more extreme than one application of 80/20 suggests.

About Rs 4,167 crore, against Rs 2,667 crore if the fund had kept 15%. A round that sells 20% leaves existing holders 80% of what they had, so 15% becomes 12% and then 9.6%. Returning Rs 400 crore from 9.6% needs an exit of 400 divided by 0.096. Skipping pro rata raised the bar by about 56%, and later rounds would raise it further.

Why does a round that sells 20% not cut your stake by 20 points?

Think of a pizza shared by four friends. A fifth friend arrives and is given a fifth of the whole pizza; every original slice shrinks by a fifth of itself, not by a fixed number of slices. Dilution is multiplicative: a round that sells 20% of the company leaves every existing holder with 80% of their previous stake. So 15% becomes 15 x 0.8 = 12%, and the next round makes it 12 x 0.8 = 9.6%. The fund has lost 5.4 points, 36% of what it bought, without selling a single share.

How do you turn a stake into a fund-returner exit?

A fund returnerA single investment whose proceeds alone equal the whole fund size, the bar many seed funds use when they decide whether a company could matter. is one company whose proceeds alone pay back the whole fund. The exit it needs is the fund size divided by the ownership held at exit. At 15%, Rs 400 crore needs 400 / 0.15 = Rs 2,667 crore. At 9.6%, it needs 400 / 0.096 = Rs 4,167 crore. Same company, same fund, and the bar moved up by Rs 1,500 crore because of two decisions not to write a cheque.

What should you say about the assumptions?

Say three out loud: no further rounds before exit, no option pool top-up, and a clean sale in which preferences do not change the split. Each of those would push the number higher, never lower. Rs 4,167 crore is therefore a floor, not an estimate. Then add the reason the question exists: a seed fund keeps reserves precisely so it can defend its stake in the companies that are working, because the seed cheque buys the option and the pro rata cheque keeps it.

One seed bet has a 4% chance, and it takes 57 independent bets to have a 90% chance of at least one such exit. Multiply the stage rates: 0.4 x 0.5 x 0.5 x 0.4 = 0.04. For a portfolio, find the chance that every bet misses: 0.96 to the power n. It first falls below 10% at n = 57, where the chance of at least one exit is 90.2%. Correlated bets would need more.

How do the stage rates turn into one chance?

A cricket team must win the quarter final, the semi final and the final; its chance of the trophy is the product of the three, not the average. Each financing stage is a gate the company must pass, so the chance of reaching the end is the product of the conversion rates. 40% to Series A, then half, then half, then 40% to the large exit: 0.4 x 0.5 x 0.5 x 0.4 is 0.04. Out of 100 seed companies, 4 get there.

Why can you not just add the chances across bets?

Adding 4% twenty five times gives 100%, which would mean 25 bets make a hit certain. For at least one success, work with the opposite: the chance that every bet misses, which multiplies. Each bet misses with probability 0.96, so n independent bets all miss with probability 0.96 to the power n. Twenty five bets all miss 36% of the time, so the chance of at least one hit is only 64%. To push the miss chance under 10%, take logs: n is at least ln 0.1 over ln 0.96, which is 56.4, so 57 bets. At 56 bets the chance is still 89.8%.

What does this tell you about how seed funds are built?

It explains why seed portfolios hold dozens of companies rather than a handful. With a 4% hit rate, a portfolio of 25 companies misses entirely about a third of the time, however good the picks look one by one. Then say the limit: the bets are not independent. Companies from the same year share a funding climate and an exit window, so a weak market lowers every stage rate at once. Correlation makes the true number of bets needed higher than 57, and the 4% itself is an assumption to test against a fund's own record.

About 12% for 20 bets and 59% for 5 bets. In both strategies a single hit returns at least the whole fund: 20x on 5% is 1x, and 20x on 20% is 4x. So a strategy loses money only when every bet misses. Twenty bets all miss with chance 0.9 to the twentieth, 12.2%; five bets all miss with chance 0.9 to the fifth, 59.0%. Expected value is 2x either way.

When does each strategy lose money?

Buying one lottery ticket in each of twenty draws and buying four tickets in each of five draws can cost the same and win the same on average, yet the second leaves you empty-handed far more often. Find the outcome that loses money first: here one hit already pays back the whole fund in both strategies, so losing means getting no hits at all. With 20 bets each worth 5% of the fund, a hit returns 20 x 5% = 1x the fund, exactly the money back. With 5 bets of 20%, a hit returns 4x. Either way, zero hits is the only losing outcome.

If the expected value is the same, why does it matter?

Because a fund's investors live through one draw, not the average of many. Concentration leaves the expected multiple at 2x but stretches the outcomes: B loses money 59% of the time, yet also returns 4x or more 41% of the time, against 13% for A. A returns at least 3x 32% of the time and rarely does spectacularly. Neither is better in the abstract; the choice depends on how much the fund's investors can bear a blank.

What does the model leave out?

It assumes the bets are independent and identical. In practice a concentrated fund argues that it can pick better and support each company more, raising p; a diversified one argues that nobody can pick reliably at seed. Correlation also matters: if all twenty companies depend on the same funding climate, the 12% understates how often A has a blank decade. Say the result, then say which assumption you would test first.