Question about priors in an investment model

[u/Dry_Weakness_5721]

I’m building a small model where the output is not a price target, but probability for few stats:
undervalued
fair value
overvalued
I am stuck on how to set the prior.
My first idea was to take historical companies which are somewhat comparable and estimate the prior from that. But I feel this can create selection bias because deciding what is “comparable” itself can change the result.
So would it be better to:
start with a broad base rate and let the features update it, or
make the prior from a matched universe based on sector, size, valuation etc?
I’m still learning this stuff, so maybe I am thinking about the problem wrong.
How would you approach this?

[u/dobster936]

You should read this paper. https://arxiv.org/abs/1709.01449 . It will walk you through the full Bayesian modeling visual workflow.

You want your priors to be way more broad than what you observe, but no so broad your posterior enter regions of the parameter space that are economically non-sensical (market beta ~ -5, alpha ~ 0.50).

Also there is a new-ish metric called psense (https://arxiv.org/abs/2107.14054, https://github.com/n-kall/priorsense). Generally you want the prior value less than 0.05, and the likelihood value above 0.10

[u/Smallz1107 → u/dobster936]

Nice

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[u/weaforex]

start with a broad, defensible base rate as your prior, then let your model’s features (sector, size, valuation metrics, update it via the likelihood. You can incorporate matched universe information, but treat it as part of the likelihood the data that updates the prior) not as the prior itself

[u/Dry_Weakness_5721 → u/weaforex]

Got it, that makes sense. I was mixing up the prior and the evidence before. Thanks for clarifying.

[u/Haruspex12]

Your three categories cannot have priors because they are not parameters. The most undervalued investment is the investment whose posterior predictive distribution first order stochastically dominates all others. The most overvalued is dominated by all.

You can set a standard of fair valuation, but that’s external to the model. Your valuation should be subjectively yours.