If you actually knew that the drift on a certain investment was positive, you still have to be prepared to survive the losses you might accumulate on the way to profit. The greater the volatility the more painful this process can be. If you can just sock away your investment and not look at it for a long time it will become more valuable. On a day-to-day time scale, as an actual human watching this risky bet you've made wobble back and forth, it can require a lot of fortitude to remain invested even as the value dips significantly.
What I mean is that if we can assume that the wiggle for VTI or SPY on the long term is positive because of outside factors, does that make options on those larger market assets become a game of who has a large enough reserve
Imagine you have a model that establishes the price of used cars, it can be really really good but if you go to the market to buy one you will pay whatever is been asked for not what your model says.
EDIT: Although pricing models do not have direct affectation to market prices they do in an indirect manner. To manage risk are needed pricing models which somehow condition market participants and therefore prices indirectly. In the simile with cars, you can buy as many cars as you want at the price you want, but what you do when you have them and if you want to take wise decisions with them you have to know something about their value.
One car dealer trying to sell a 2023 Honda Accord with 60,000 miles can't just decide, independently, to forget the high mileage and price the car based solely on it being 1 year old. Sure that's "whatever is being asked" but that car will never sell until he brings the price down in line with other 60k mile cars - and that is because the pricing models are essentially agreed upon by all market participants.
But it might take quite some time, and it's still random, it might be much smaller or much bigger.
You could be tempted to employ leverage. However, that introduces the chance of being wiped out.
ETA: Real rates are normally positive. So you can achieve the same result by investing in long term bonds with less risk. Just have to wait even longer.
The limits may be very large, but they aren’t infinite.
Without expansion of population, consumption and production both stagnate. See what has happened in Japan in since the 90s.
Especially improvements in energy generation, fertilizer production, and efficient usage of both (often through information technology).
Given any stable state of technology/energy/space, a society will generally reach a high point, then go through cycles of growth/retraction.
But improvements in technology and energy generation means it won’t be at a stable state, eh?
It isn't crazy to think that there are physical limits to things.
Malthus projected that populations would grow exponentially, but agricultural yields would grow linearly. He was wrong in that ag yields did keep up and population growth slowed down. One thing to keep in mind is we used fossil fuels and fertile lands to do that, but we are hitting the limits for fossil fuels and we are burning through arable land.
However, there are other physical limits, and some of these are a bit harder to work around. Infinite growth isn't necessary, but a decent life and an equitable distribution of wealth is.
We have huge numbers of people 'rocking the boat' trying to create say.... a Gamma Squeeze.
The only reason everyone trusts a Gamma Squeeze can happen is because they trust the math in Black Scholes. The may not even understand the math, just trust that the YouTuber who told them about Gamma Squeezes had enough of an understanding
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Today's problem IMO, is now a bunch of malicious players who are willing to waste their money are trying to make 'interesting' things happen in the market, almost out of shear boredom. Rather than necessarily trying to find the right prices of various things.
Knowing that other groups follow say, Black Scholes, is taken as an opportunity to mess with market makers.
Specific to Black-Sholes the best option plays, when going long, are the ones which have incorrect assumptions about the volatility of the underlying. You can have far outta the money options, absolutely print, with a sufficient spike in the underlying. Even if the strike price will never be met (though you’ll also give that back if you ride them to expiration or let things settle down).
If that bets goes bad, the typical investor in Treasuries has perhaps bigger problems to worry about, but it’s still a bet IMO (and one which will inevitably eventually go bad).
1. Interest rates can be negative 2. Volatility reduces the average. Take an example of +10% then -10% (1+0.1)*(1-0.1) = 1 - 0.1² = 0.99 < 1. It's due to the "log normal returns"
edit: To address your specific observation, that the price of the stock is expected to go up, it's assumed that if the stock goes up, so do all other assets. In mathematical finance you never keep you money as cash, so if you sell the stock you put that money in an account that expected to grow at the "risk-free" rate. The major difference between the "risk-free" account and the stock is the variance of these asset prices.
However, in your scenario, you wouldn't need Black-scholes for the price of the stock itself since that should be theoretically equal to it's expected (in the mathematical sense of "expectation") future value assuming the risk-free rate.
Black-Scholes is used to price the variance of the underlying asset over time for the use of pricing derivatives. But again, if the stock moved exactly as modeled then the model would give you the perfect price such that neither the buyer nor the seller of the derivative was at a disadvantage.
The way you would make use of such a perfectly priced stock would be to search for cases where either buyers or sellers had mispriced the derivative and then take the opposite end of the mispriced position.
However you don't need a perfect ideal stock to make use of Black-Scholes (this is a common misconception). Black-Scholes can also be used to price the implied volatility of a given derivative. Again, derivatives fundamentally derive their values from the volatility/variance of an asset, not it's expectation. By using Black-Scholes you can assess what the market beliefs are regarding the future volatility. Based on this, and presumably your own models, you can determine whether you believe the market has mispriced the future volatility and purchase accordingly.
One final misconception of Black-Scholes is that it's always incorrect because stock price volatility is "fat-tailed" and has more variance than assumed under Black-Scholes. This was the case in the mid-80s and people did exploit this to make money, but today this is well understood. The "fat-tailed" nature of assets prices is modeled in the "Volatility smile" where the implied volatility is different at different prices points (which would not be expected under pure geometric Brownian motion), but this volatility can still be determined using Black-Scholes for any given derivative.
tl;dr Buying stocks is about your estimate of the expected future value of a stock, but Black-Scholes is used to price derivatives of a stock where you actually care about the expected future variance of a stock. Even in an unideal world you can still use Black-Scholes to quantify what the market believes about future behavior and buy/sell where you think you have an advantage.