Here's my intuitive understanding of decay:
When you use leverage, there's always the risk of margin calls (when your net value becomes close to 0). If you can bear with a dip without triggering them and recover, you can then benefit from a multiplied average return; if not, you lose everything. Volatility influences the probability of margin calls, so what really matters for an investment is the ratio of average return to variance (see Sharpe ratio) because you can always leverage investments with the same Sharpe ratio to get the same return for the same risk of losing everything, roughly.
Now, there's a simple way to avoid margin calls: periodically "rebalance" your leverage to a set value, i.e. if the share value has gone down after a set time period, repay some debt, and if it has gone up, get more debt, so that your leverage stays on target. The more frequently you "rebalance", the less margin call risk you have. If you rebalance continuously every second, you have virtually 0 risk, assuming perfect liquidity. If you rebalance every month, then you need the dips to go up quickly enough without triggering the margin calls. Most leveraged ETFs will rebalance once a day, eliminating most of the margin-call risk* at the expense of efficiency.
Rebalancing frequently is the safest, but also the least efficient. The reason is if there are market fluctuations, and you rebalance once in a peak or a dip, then after a return to normal, you lose. This is because rebalancing in a low will reduce your leverage right before the increase; rebalancing in a high will increase your leverage right before the decrease; both are bad. Another way to see it is that rebalancing frequently will cause you to sell low and buy high, which is the opposite of what you want. The more fluctuations you capture, the more you'll lose. If there are ups and downs every second and you rebalance continuously, you'll lose big very fast.
The only strategy if you're going to make leverage work is to leverage and hold, and pray for no margin calls. When there's a dip, holding your loans will automatically increase your leverage, so that a future market recovery will put you exactly where you started. A dip puts you in a more vulnerable position, making you "double down" on your bet: either recover, or lose everything. You can rebalance after a few months if the market went up, i.e. buy more shares.
I'd never leverage the S&P 500 with more than 20% (1.2x). If you use 2x, you basically assume that the market always recovers above 50% (i.e. it never dips below 50% of any past value) which isn't true historically. If you use 3x, you assume the market never dips below 66.7%, etc. At 1.2x, you assume it never dips below 16.7% of any past value, which I think is true historically. At no leverage, you have no risk of margin calls, so in theory you can keep your shares forever and always hope for a rebound, although some shares do lose all value sometimes.
*Who knows what happens to the 3x ETFs in a single day at -33.3%? Shit must hit the fan in many ways anyway, but that's a possibility. They'll probably sell a little before they hit the margin call, call it a day, set the fund value to 0, and close it.
