I'm never one from shying away from giving my opinion, but I have no idea whether the Food and Drug Administration will approve Arena Pharmaceuticals' (Nasdaq: ARNA) obesity drug lorcaserin tomorrow.

Not being 100% certain about a binary event isn't necessarily a deal-breaker for buying ahead of the event. The fair value of a company is described by this fairly simple formula:

Fair value = Expected price if positive * Likelihood of success Expected price if negative * Likelihood of failure

If a drug has a 75% chance at success and the shares will be $10 if successful and $4 if unsuccessful, then the fair value is $8.50 (10*0.75+4*0.25). If shares are trading below that price, and you're willing to risk the 25% chance of it going to $4, buying shares makes empirical sense.

Good luck filling out the formula for loracserin
First of all, you probably have to add another layer to the formula, because there are two potentials for negative events. The FDA could reject the drug, asking for something extreme, or it could reject the drug for a minor issue that would have a negligible effect on the price.

Calculating the potential price after the events is a little hard with share prices whipping around widely, but options can give you some clues.

Determining the likelihood of success or failure is more difficult. If you look at the advisory committee minutes, it's fairly clear the panel was content with the risk-benefit analysis given the current body of information, but many panel members wanted the drug studied further after it's put on the market.

Everything since then is a black box
Did the FDA follow the panel's advice and ask for post-approval commitments? And if it did, did Arena have enough time to submit documents and have the FDA review them? The FDA delayed a decision on VIVUS' (Nasdaq: VVUS) obesity drug Qnexa after it turned in post-panel paperwork, but Arena seems to have a date with destiny tomorrow, which could be a bad sign.

There's a real possibility that the FDA doesn't want to deal with post-approval issues because it plans to reject the drug. In the briefing documents for the advisory panel, one FDA reviewer was worried that compiled data that included patient information added after the first review had pushed the potential risk of heart valve issues beyond an acceptable level.

The advisory committee wasn't worried about it, but that doesn't necessarily mean the agency won't ignore the advice as it did with Orexigen Therapeutics' (Nasdaq: OREX) Contrave. The company went from leader of the pack to trailing wildly when the agency made the biotech run a large preapproval trial to study potential heart problems.

A similar requirement would sink Arena. If it fell to Orexigen's market cap, Arena would lose more than 80% of its value. What's the likelihood of that? There's no way to know for certain without being in the FDA meetings. I tend to think it's pretty low, but putting an exact number on it is difficult. Plugging in 5% versus 25% in my formula gives wildly different valuations because it has so far to potentially fall.

Most investors would be best off waiting until after the FDA makes its decision and then base the valuation on potential sales of the drug, which is certainly less opaque and a little more straightforward.

But that's no fun
Then buy it or short it. It's your money. Just realize that you're investing into a black box and anyone who tells you with certainty that the drug will or won't be approved is delusional. I'd strongly suggest you keep your investment to a reasonable portion of your portfolio.

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Fool contributor Brian Orelli holds no position in any company mentioned. Check out his holdings and a short bio. The Motley Fool has a disclosure policy. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. Try any of our Foolish newsletter services free for 30 days.