Correlation Between DCFs and Stocks?

I do not understand your question fully but I will still take a stab at it.

Yes, you're correct on the intrinsic value. If it's higher than the market price then it means the company is undervalued and it indicates that you should buy the stock. But to answer the very first question of yours, DCF cannot determine how big of a position you should hold in a company. DCF only tells you if the company is overvalued or undervalued.

(On a side note - Look up Aswath Damodaran, a very well-known professor, and look up his view on valuation and watch his videos to understand valuation more clearly)

A DCF will help you identify undervalued based on your perception of the company's future performance, but it won't really tell you "how much" to buy. That will depend on your own allocation strategy.

Overvalued and undervalued is just perception based on access to insider information, remember you need insider information to do a DCF. If you have all the data and your price is higher than the market price then the company is undervalued then you can buy. You are simply betting than this ‘insider’ information will be publicly available at some point. How much you buy depends on how rich you want to be.

I also feel like the biggest problem isn't really how much to allocate, I mean if it's undervalued it's undervalued - the other thing is afaik, DCF's are pretty inexact (at least if you vary assumptions for WACC, Perpetuity Growth Rate, etc.) so "undervalued" is just a perspective.

the dcf will give you a valuation and you can divide it by the # of shares outstanding. from there you can compare its value to what its currently trading at in the market and decide whether or not you want to buy.

if you are concerned about how much to buy, maybe you can run dcfs for a bunch of stocks you are considering and see which ones are outperforming its market price by the highest margin

note: only works on public companies stocks

DCF is an accounting question

how much of a stock to buy relative to the portfolio is a portfolio management/risk management question

so the answer is: No, a DCF will not help you with this.

I would use an FCF approach.

DCFs are extremely subjective and sensitive. I usually just look at fundamentals of the company - the PE, PEG, P/B, ROE to see under/overvalued stocks