Please don't argue about how risky or irresponsible such a trading strategy is. Many financial publications described that Mr Hwang got a leverage of about 1:5 meaning for each $100 of his own money he could buy $500 in stocks. How can a normal person get such a leverage without using options or CFDs?
In the US, pretty much every provider that offers a margin account gives a 4:1 margin - you have 100k cash, you can buy 400k of stocks (or do other transactions, like short sales, write naked calls, etc.). Try eTrade, JPMorgan Chase, Vanguard, Robinhood, etc. The minimum to get a margin account is to have 25k equivalent in the account; that's regulation. Then you sign a form saying that you are an adult and you know what you are doing, and you can start burning your money.
If you care about the last 20% he seemed to have: other countries may have other regulations; or maybe if you have more than ten million you can ask for more margin. If you trade in two-digit millions, you might not have a run-of-the-mill eTrade account or such anyway, but use specialized software and / or connect directly to the exchanges.
The highest leverage you can get as a retail investor is limited by regulation. And to get anywhere near the level of leverage you're asking about you'd need to use Options and/or Futures.
If your requirement that no options or futures could be used was lifted though, the following inadvisable scenario would get you an incredible amount of leverage... maybe even halfway to the leverage Lehman took at the top of the mortgage bubble (they were at around 33x, I believe, when they imploded)!
Just as Hwang was able to layer leverage on top of leverage through SWAPS and most likely other agreements with Investment Banks (especially since the actual leverage, and therefore the actual risk of his business, was unknown from bank to bank), there are ways that you can get implied leverage far in excess of what's regulated in Margin accounts using Options. Yes, it's also far in excess of what a rational, risk-aware person with anything to lose would do.
But, as an entirely theoretical matter you can think about it this way: what if I were to borrow money from one non-securities markets related area or asset in my life, open a Margin account (borrowing from another area), and further leverage by engaging in Options or the even higher leverage Futures contracts? I could certainly attempt to do that. And in doing so I could achieve ridiculous levels of leverage.
Throwing caution and common sense completely to the wind, I could use the proceeds of a cash-out refinance to open an Options/Futures account and then use the Options to buy or sell optionable 3X Leveraged and Leveraged/Inverse exchange-traded funds. Right? Of course, I'd really, really have to know what I was doing just to play with the 3X Leveraged L/I funds in the first place. I'd have to have an expert-level understand of both the Volatility Decay such funds expose their holders to since they don't expose you to a multiple of a security or commodity's returns, but a multiple of the security or commodity's daily returns, resetting each night. I'd also have to understand the roll risk involved in the underlying securities and be able to live with not only those risks but the slippage eating away at my returns whether actively trading, or not. Oh, I'd also have to factor in the cost of both borrowing on Margin and embedded in the funds as expense ratios.
So to recap: I can borrow a large sum from my future through a house or other collateral: against my business, as cash advances from credit cards if I had that sort of capacity (at usurious rates that I'd have to keep a close eye on, too), from family and/or friends willing to lend to me, etc. Basically, borrowing in any way and against anything I could. Borrowing against an account set up with these proceeds and investing in securities with embedded leverage would then pump me up past even Bill, I'm certain.
None of this is either advisable or, frankly, possible without breaking several laws and/or violating several regulations, at a minimum, though. I'd have to deceive people or entities at every step in the process thereby exponentially increasing my risks. In addition to the risk of losing more than I had and being forced into bankruptcy (the lowest level of risk in this scenario) I'd be exposing myself to the additional risks of losing any rights I had under Securities Laws and/or the Account Terms of the entity I engaged to open the Margin account, the risk of losing my future ability to use the securities markets for anything, at all, and the risk of losing my freedom in the ensuing Credit & Securities Fraud cases against me (since I would have had to lie on the account opening form about where the money for the account came from in the first place).
I know you didn't want to hear about the risks, but the bottom line is that in order to leverage yourself up to the extent an Investment Bank or a Wall Street darling baring the promise of hundreds of millions in fees from his/her billions in transactions you'd have to sell your soul and risk... everything, more or less.
Hope this helps!