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From my perspective you can't bet both sides and still expect gains on average. Sure you can be lucky that the one bet wins more than the other loses but typically that doesn't work if you bet on two opposite outcomes. There are no magical and safe ways to multiply money other than maybe being super rich and already too big to fail.
Hedging isn't about ensuring gains, it's about reducing losses.
So how does hedging prevail at the instititional level it does or it seems like it does as a viable tool in the investing toolkit? Does it consequently hard require insider info and basically its just investing uncertainty theatre?
Hedging is done in many different ways. One of the easiest, that requires zero insight is a future hedge.
Say I hold 1000 shares worth 5 bucks each in company Bob. If the price goes up, that's great, but I'll need to replace my car in three years, and I'll need at least 3000 bucks for that.
So, I'm going to spend some money now on buying an option in 2 years 11 months to sell 1000 shares for 3 bucks per share. That way, if Bob company completely collapses, I'll always have at minimum 3000 bucks.
Of course, those options cost money to buy, so I'll have to pay to reduce my risk, but I don't need any real insight into the market to use this kind of hedge.
In the example you give in the OP, it's relying on the guess that it would be unlikely that Kamala wins and Tesla goes up OR that Kamala loses and Tesla goes down. Those were still possible outcomes though.
Statistically you can. Firstly, when you invest you can limit how much that could be lost right off the bat by how you invest and via what amount. For example: BUYing $20k in 2 opposing stocks, split 10k each. Max possible loss? All $20k.
Let's say the Index goes up 10% which suggests on average that $20k is now $22k, or $11k/stock.
In actuality stock A loses 50% but stock B gains 60%. Had you luckily invest solely in the right stock (B) with all 20k you would have made $12k. Badly (stock A)? Lost $10k. By hedging you dilute max potential gains to mitigate catastrophic loses.