- One of the most profound ideas and models, I've read in my PhD studies
- Inspired me to think differently with the way we present :)
- Lo developed the "Adpative Markets Hypothesis" in a 2004 paper that tried to reconcile the efficient markets hypothesis with behavioral biases.
- Markets are effecient most of the time in a normal situation but investors need to adapt to survive changes in the environment
- This series of papers develops a more rigorous and formalized model to establish the foundations of the hypothesis

- Hope to is to develop a unified theory of social behavior that borrows from evolutionary biology - could span all social sciences from psychology, anthropology to political science and of course, economics.
- In traditional economics and finance, we're used to thinking about optimization given a set of known constraints (investors maximize utility subject to budget function, corporations maximize profits subject to resource constraints, agents maximize their self-interest subject to contractual constraints).
- Lo proposes an entirely different alternative: it's not about optimizing, it's about survival.
- There's still a maximization problem in there (maximize population growth) BUT the key difference is that optimization assumes a static known environment whereas survival assumes radical changes in the environment such that existing optimization approaches can fail entirely
- If goal is survival, then seemingly irrational behavior from an optimization perspective, now make sense because these types of behavioral ensure survival

- Can choose either a or b where each choice leads to reproductive outcome x_a and x_b. X's randomly distributed
- Individuals' type/behavior is indexed by how often they choose a (from 0 to 1, with possible mixing)
- Assume iid in time series and cross-sectionally (each period is the same and one individual's action doesn't affect the other)
- Individuals don't think, they just follow they're type and their descendants inherit the same type/behavior
- In previous paper, he assumes that individuals perfectly inherit their parent type but in this paper, he adds the possibility of mutation where each there's a chance that the next generation's type is evenly reshuffled across the other types

- People tend to randomize guesses even when they know that the dice is weighted. Clearly irrational in classic econ thinking.
- Suppose there's two choices (build in plateau or build in valley). Each choice has random outcome.
- Sunny on plateau kills you but rainy is good which leads to offspring. Opposite is true in valley.
- Symmetric so optimal choice for each individual depends on which is more likely to occur. Supposing it's more likely to be sunny, what would you do?
- Optimal individual choice to always pick building in the valley bc/ you have a greater chance of survival.
- However, this type that thinks this way will eventually go extinct, as soon as it rains, they all die (bc/ subject to the same systemic risk)
- Only types that randomize will survive...and the optimal way to randomize is to match building in valley with prob of how often it's sunny!

- Arise naturally from the fact that if you grow fast (3 kids) and slow (1 kid) each half the time, the population will grow much more slowly than if you always of 2 kids
- From Jensen's inequality

- When it comes to loses, ppl are risk seeking but when it comes to gains, ppl are risk averse
- We just showed risk aversion but that's assuming that both states leads to reproduction
- What if one state leads to extinction...then you might as well swing for the fences since at least you have a chance to survive

- mutations allow for chance that the a certain type is reshuffled equally across other types
- the type that is not optimal is then called "irrational"
- if the optimal type always survives, this will slow down population growth
- however, if there are regime changes, then the irrational type may be the optimal type under an alternative regime
- if this is true, mutation is optimal and the optimal amount of of mutation depends on how often the regime changes
- the more often the regime change the higher the mutation rate
- applies to industries and markets as well

- Forces us to rethink what's rational and not
- Forces us to rethink what equilibrium is
- Must more focused on robustness rather than efficiency
- Models still in infancy but would not be surprised if they become more and more powerful
- Just like Newton's laws can be seen as a special case of general relativity when masses are small and speed is slow, efficient market behavior may be special case when the environment is stable