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Sarthak Bagaria
Writing

Startup Salary

Pricing a startup offer against a big-tech salary, using derivative pricing.

Sarthak Bagaria

Problem

Last week, I posted job openings at www.mercurie.ai/careers. I spent some time thinking about how a candidate could begin comparing the compensation at a startup to the salary at a big company. As a former quant, I naturally started thinking in terms of financial derivative pricing.

Let's use my job posts as an example. I posted an opening for an engineering role with an annual salary of ₹25 L cash + ₹25 L equity. A reasonable binomial outcome is:

  • Success: the venture succeeds with 10x equity valuation growth in 4 years (I want to say 100x, but I will check my ambitions for now)
    ⇒ 4-year compensation is ₹1,100 L.
  • Failure: The venture fails in 2 years
    ⇒ 2-year compensation is ₹50 L.

I am looking for domain experts and possibly competing with BigTech firms paying ₹70 L per year to matching candidates.

What is the implied probability of the venture's success to the job-seeker at the posted salary?

Assumptions

  • No interest rates, no appraisals.
  • BigTech jobs are riskless and liquid (can join anytime, can leave anytime) (yes, I read the news, but let's just assume for now).
  • The job-seeker invests in Indian equities and demands a similar risk premium from their other life choices, let's say a Sharpe Ratio of 0.3.
  • The job-seeker demands an additional 5% premium on their salary for the illiquid nature of the startup equity.
  • The job-seeker demands an additional 20% premium on their salary for the anticipated tectonic shift in their work-life balance, but they are willing to discount that to 10% for the adventure and the thrill they will experience.

Approach

To begin, let's summarize our variables:

  • (CS) Startup Cash Salary: ₹
    L
  • (ES) Startup Equity Salary: ₹
    L
  • (GM) 4-year Startup Growth Multiple If Success:
  • (LP) Premium on Startup Salary for Illiquid Equity:
    %
  • (WL) Premium on Startup Salary for Work Life Balance:
    %
  • (BT) BigTech Salary: ₹
    L
  • (SR) Sharpe Ratio Demand:

First, we compute the excess returns the startup salary provides over the BigTech salary in the binomial model:

  • (ERS) Success:

    = ₹672 L.
  • (ERF) Failure:

    = ₹-97 L.

Let's define and let the implied probability of startup's success be . We can then write the excess returns as where is a Bernoulli trial with probability of success . The expectation and the standard deviation of the excess returns are then:

  • (ER) Expectation:
  • (SD) Standard Deviation:
The compensation-implied probablity of startup success is the that solves the equation:

Squaring both sides, we get the quadratic equation

Substituting values (rounded-off values shown here):

The unique valid solution to this equation is 0.2568 or 26%.

If the candidate believes the chances of the startup succeeding, with them working there, are higher than this, it may be worth applying!

Sharpe Ratio vs Success Probability

Additional Notes

An important consideration for the candidate should be whether the cash portion of the startup compensation meets their financial obligations.

This is a simplistic model which may give answers counter to intuition at times. For example, try 0 premium and the startup compensation cash portion equal to BigTech salary. In this case it seems obvious that the startup compensation is always equal or better, no matter if it succeeds or fails, but the model will see variance in the startup returns and demand a non-zero chance of startup success to satisfy the Sharpe Ratio demand.

Do not test the calculator's final suggestions by giving impractical values. It does not interpret all solutions well.