2020-11-20

Correlated Returns are Insufficient for True Alignment

When people talk about incentive alignment, what they really mean is correlated returns.

Consider equity as a solution principal-agent problems. Since founders and employees are both paid as a percent of company valuation, their returns are correlated, and incentives are mostly aligned. [1]

But even where returns are perfectly correlated, there’s no guarantee that actors actually have each other’s best interests in mind. A more concrete way to think about this is: would you be willing to delegate your decisions to the other party? This is what I mean by “true alignment”.

This can go wrong in at least three ways:

Returns are correlated, but with different opportunity cost
Returns are correlated, but with different levels of risk
Returns are correlated, but with different second degree utility

1. Returns are correlated, but with different opportunity cost

Real estate agents are typically paid on commission of a home’s sale price. As a result, their returns are really well correlated with the homeowner’s:

In theory, this ought to mean that real estate agents and homeowners are truly aligned.

In practice, the real estate agent is the one doing work, which means that they’re the one paying opportunity cost.

Let’s say an agent can expect to earn $200/day, and gets paid 6% of home sale price. It’s not worth it for them to spend another 5 days of work pushing up your home price from $500k to $510k when this only nets them $600 against an opportunity cost of $1000.

In contrast, a homeowner would happily wait a week to get another $10k, or $9.4k after commission. Even factoring into account the time value of money, an additional 2% week-over-week is great.

If both sides were explicit about incentives and willing to broker a side deal, the homeowner would happily pay the full $1000 opportunity cost to get an extra $9000. But in the absence of transparency, the real estate agent will do their best to convince the owner to sell, even at net loss to their collective interests.

The result is correlated returns without true alignment. Neither side ought to trust the other.

2. Returns are correlated, but with different levels of risk

Another classic example is Venture Capitalists versus Founders. For any given startup, a founder might own 30%, and the VC 10%, so their returns are really well correlated:

In theory, this ought to mean that VCs and Founders are truly aligned.

In practice, VCs are massively diversified across startups, providing insulation against any one failure. As a result, they’re eager to push for riskier bets, even when it’s against the interests of an individual founder.

3. Returns are correlated, but with different second degree utility

Say you’re going out to dinner with a wealthier friend, and you’ve agreed to split the bill. No matter where you go, you’ll be paying the same amount, and getting the same consumption, so returns are really well correlated:

In theory, this ought to mean that wealthy and less wealthy diners are well aligned. You should be willing to let your friend pick the restaurant, and visa-versa.

In practice, each party may pay the same financial cost, but has a different marginal utility for their money. Assuming utility is something like log(wealth), the utility cost to a $100 dinner are far greater for you than for your wealthier friend.

Even assuming you have the same gastronomic tastes, your incentives are not actually aligned. You should not trust your friend to pick a restaurant. [2]

Conclusion

Taking “true alignment” to mean “would be willing to delegate decisions”, and “correlated returns” to mean “correlated first order financial returns”, everything I’ve said is true.

But in all these cases, the trick is just to think about the actual experienced utility rather than first order financial returns.

It’s presumably pretty straightforward to sell a home for a fair price, but much more work to sell for substantially more than what it’s worth. So the opportunity cost increases faster than the price of the home. Taking that into consideration, we can chart the agent’s returns with a consideration of non-linearly growing opportunity cost:

Which makes it clear that returns were never really correlated to begin with.

Similarly, risk-avoidance is a function of diminishing returns from wealth. As a result, founders would prefer a more certain return, while diversified VCs can afford to pay in risk for higher expected returns.

So the conclusion is not that something wacky is going on and alignment is impossible. It’s just that we have to take into account returns to actual utility rather than just naively looking at immediate finances.

Postscript

I framed these as three different examples, but in a sense, they’re all the same.

The Venture Capitalist is risk-indifferent because they’re diversified. The founder is risk-averse because they experience diminishing returns from wealth to utility. Otherwise, a 1% chance of a billion dollar exit would be just as good as a guaranteed $10 million exit. So this is outwardly about risk, but really about second degree utility.

Arguably, diminishing returns to wealth are also just a function of opportunity cost. The more money you have, the less consumption in one place becomes a substitute for consumption elsewhere. This is also the case of a concave production-possibility frontier: the more you produce one good, the more the opportunity cost increases. This gives us a sense of diminishing returns, even without appeal to the hedonic treadmill or other psychological effects.

[1] Note that this only works for early employees at startups. The more your compensation is defined by salary rather than equity, the more your returns are fixed, and the less aligned you’ll be with your founders.

[2] Unless of course, they offer to treat you.