Venture Capital puzzles, solved step by step

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  1. 045Investor A is right 40% of the time, and each winner returns 3x. Investor B is right 10% of the time, and each winner returns 25x. Losers return 0.2x for both. Whose portfolio returns more?Power law and portfolio mathsWarm upSeed and early-stage VCSeries A to C VC

    Try it first

    What does each portfolio return per rupee, on average?

    Show the worked solution

    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.

    The relationship
    E[M]=p W+(1−p) LA:0.4×3+0.6×0.2=1.32B:0.1×25+0.9×0.2=2.68E[M] = p \, W + (1 - p) \, L \qquad A: 0.4 \times 3 + 0.6 \times 0.2 = 1.32 \qquad B: 0.1 \times 25 + 0.9 \times 0.2 = 2.68
    pthe hit rate, the share of investments that win
    Wthe multiple a winner returns
    Lthe multiple a loser returns, 0.2x for both investors
    What it says in wordsWeight the winners' multiple by the hit rate and the losers' by the miss rate, and add.
    Expected multiple per rupee: what winners and losers each contribute0x1x2x3xmoney backlosers 0.12xwinners 1.20x1.32xInvestor A40% right, 3x winnerslosers 0.18xwinners 2.50x2.68xInvestor B10% right, 25x winnersTo draw level with BA's winners need 6.4xTo fall back to AB's hit rate need onlydrop to 4.5%But with 20 deals, B findsno winner 12% of the time
    Investor A's winners contribute 1.20x and B's contribute 2.50x, so B's portfolio returns 2.68x against A's 1.32x even though B is wrong nine times in ten.

    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.

    Where candidates lose it

    The common loss is picking A because 40% sounds like a much better investor than 10%. Hit rate is half the calculation; the other half is how much each win returns, and in venture that half usually dominates.

    The second loss is forgetting the losers' 0.2x and answering 1.20x and 2.50x. The order is right but the numbers are wrong, and the interviewer asked for the portfolio return.

    What the interviewer asks next

    • How many investments does B need for at least a 95% chance of one or more winners?
    • If B's winners return 15x instead of 25x, who wins now?
    • Why might a later-stage fund deliberately run A's strategy?