Alright, so the bank would still, then, agree to lend 10K against the 10K in equity, right? That still significantly increases profits (24% vs 15%) and would afford the same loophole.
As a general rule, no. The bank will loan the LLC money if the LLC has a proven income record. Banks will generally not loan money secured by stocks for this exact reason. In the US, that's likely to be covered legally. Consumer banks are legally prevented from loaning with stocks as collateral.
An investment bank could do this, but absent chicanery, they won't. This is a turkey of a loan. A brand new LLC with no income history and no business plan. Its only assets are 10k in stocks. Perhaps they might loan 5k on the 10k in stocks at 18% interest (like a credit card). So your upside would be 4.5% (lower than the original 15%) minus the LLC fees. And your downside is a 100% loss of 10k plus any LLC fees (bankruptcy).
6% on a line of credit is the kind of thing that banks offer long term customers or people with separate income. I.e. if you are making 100k a year and launching a side business, banks will give you 6% interest on the side business knowing they can collect from your regular job.
Also be aware that it is possible to pierce the corporate veil. This is generally an option when someone creates a corporate form (e.g. an LLC) for the sole purpose of shielding from legal liability. So it is possible that your LLC's debts could be shifted onto you.
There are ways to make something like this work. Most of them involve having an established (not new) LLC owning real property (i.e. real estate). This is essentially the house flipper model. The problem is that you really need cash to make cash. Borrowing will eat up most of your profit.
The proper use of loans here is as short term bridges. For example, you have an opportunity to buy a new property, but all your cash is tied up with a property that is currently in escrow. You take out a short term loan against the property in escrow so as to make the purchase. As soon as the sale closes, you pay off the loan. The property that you purchase may offer enough of a discount to justify the interest charges. But most of the time, you would be better off waiting for a different deal.
A leverage ratio of 4-5 is reasonable; this is based on typical mortgage down payments. However, even a leverage ratio of 1 results in profit increase from 15 to 24%, while limiting risks.
Sure, but that's on a house. You are buying a 100k house with a 20k downpayment. So if the house loses 20% of its value, they still get 80k on an 80k loan. And again, a brand new LLC is unlikely to be able to get even a mortgage on its own. You would probably have to cosign the loan personally.
Houses are less likely to lose value than stocks. And if they do lose value, they tend to lose less value. Extrapolating from houses to stocks is unreliable. They're different kinds of investments.
If you really want, try it. You'll be out the LLC fees, but that's survivable. The most likely result is that you'll talk to a bunch of banks that will say no. A waste of your time, but again survivable.