Thursday, September 20, 2007

Portfolio Math

There has been a great deal of discussion about the viability of the venture capital industry.

What types of returns are required to justify the asset class' risk? Are such returns available in today's market? How much risk does an early stage venture capitalist need to take to justify the premise of the business?

To find out, I constructed a simple model of a portfolio with the following characteristics:

  1. # of companies in portfolio
    1. 10

  2. $ per company ($m)
    1. $10

  3. management fee
    1. $0 (to keep this simple:))
  4. Probability of Success
    1. 40%

  5. Probability of Failure
    1. 60%

  6. Definition of Success
    1. 5x money

  7. Definition of Failure
    1. 0x money
The table below illustrates the probability of N successes, the value of the Nth success, and the expected value of the Nth success:

For example, in a portfolio of 10 companies:

  • the probability of 4 successful outcomes is 25%
  • or, 10!/4!6!*(.4)^4*(.6)^6
  • the value of 4 successes is $200m, or 4x5x10
  • the expected value (prob * value) of the fund, the sum of the total distribution of expected values, is also $200m

To 3x a fund, one would need:

  • $300m,
  • given a 40% success rate, and 7.5x your money/success
To 5x a fund, one would need:
  • $500m, or
  • given a 40% hit rate, 12.5x your money/success
To 8x a fund, one would need:
  • $800m, or
  • given a 40% hit rate, 20x your money/success
Now, if the hit rate falls to 20%, to 3x a fund, one would need:
  • $300m, and
  • 15x your money/success
If you hold 5x money/success, each 1% improvement in the hit rate is worth $5m.

If you hold the hit rate constant at 40%, each .5x money/success is worth $20m.

In summary, given that early stage venture capital often experiences binary outcomes, individual firms should look to ensure that deals support the possibility, if not the probability, of a 10x or better outcome.

Furthermore, LPs should diversify across multiple partnerships and look for firms that look to create large winners, not incremental winners. Conventional wisdom holds that 10x returns are required for Series A investors, however, the math exercise helps illustrate why that is the case.

Back to the original question...The early stage very capitalist appears to only be able to justify the risk involved in the asset class if they can either
  • materially increase the hit rate, ie reduce probability of failure per deal
  • create deals with 10x+ returns on invested capital

Are there 10x or greater deals in the market? Of course, however, great funds will need to find quite a few in order to justify their existence.

Hitting doubles or triples, in the face of a high mortality rate, will not cut it.

Note: thank you to Hunter Hancock for his valuable feedback and help on this post.


  1. What made you pick a 40% chance of success? That number seems high (this is not my area of expertise, but I would've guessed it to be more like 10-20%?)

  2. Each investment has its own independent EV. Unless the return on the whole fund (to the investors or the VCs) isn't linear, I don't really see the utility of the binomial distribution. If it isn't linear, it probably should be.