Leverage can give arbitrarily high returns at arbitrarily high risk. With things easily available at a brokerage, this goes up to very high returns with insane risk. See St. Petersburg paradox for an illustration of what insane risk means. I like the variant where you continually bet everything on heads in an infinite series of fair coin tosses, doubling the bet if you win, so that for the originally invested $100 you get back the same $100 in expectation at each step (at first step, $200 with probability 1⁄2 and $0 with probability 1⁄2; by the third step, $800 with probability 1⁄8 and $0 with probability 7⁄8), yet you are guaranteed to eventually lose everything.
Diversification, if done correctly, reduces risk at the expense of some reduction in returns. At which point increasing leverage to move the risk back up to where it was originally increases returns to a level above what they were originally. Diversification without leverage can make things worse, because it reduces returns.
Not making use of leverage is an arbitrary choice, it’s unlikely to be optimal. For any given situation, there’s almost certainly some level of leverage that’s better than 1 (it might be higher or lower than 1). There are various heuristics for figuring out what to do, like Sharpe ratios and Kelly betting. As an outsider to finance, it was initially hard for me to make sense of this, as discussion of the heuristics is usually fairly unprincipled and relies on fluency with many finance-specific concepts. A math-heavy finance-agnostic path to this is to work out something along the lines of Black–Scholes model starting from expected utility maximization and geometric Brownian motion. For actual decisions, calculation through Monte Carlo simulations rather than analytical solutions lets utility functions, taxes, and other details be formulated more flexibly/straightforwardly.
Leverage can give arbitrarily high returns at arbitrarily high risk. With things easily available at a brokerage, this goes up to very high returns with insane risk. See St. Petersburg paradox for an illustration of what insane risk means. I like the variant where you continually bet everything on heads in an infinite series of fair coin tosses, doubling the bet if you win, so that for the originally invested $100 you get back the same $100 in expectation at each step (at first step, $200 with probability 1⁄2 and $0 with probability 1⁄2; by the third step, $800 with probability 1⁄8 and $0 with probability 7⁄8), yet you are guaranteed to eventually lose everything.
Diversification, if done correctly, reduces risk at the expense of some reduction in returns. At which point increasing leverage to move the risk back up to where it was originally increases returns to a level above what they were originally. Diversification without leverage can make things worse, because it reduces returns.
Not making use of leverage is an arbitrary choice, it’s unlikely to be optimal. For any given situation, there’s almost certainly some level of leverage that’s better than 1 (it might be higher or lower than 1). There are various heuristics for figuring out what to do, like Sharpe ratios and Kelly betting. As an outsider to finance, it was initially hard for me to make sense of this, as discussion of the heuristics is usually fairly unprincipled and relies on fluency with many finance-specific concepts. A math-heavy finance-agnostic path to this is to work out something along the lines of Black–Scholes model starting from expected utility maximization and geometric Brownian motion. For actual decisions, calculation through Monte Carlo simulations rather than analytical solutions lets utility functions, taxes, and other details be formulated more flexibly/straightforwardly.