Cows aren't fungible, so that analogy isn't great. The key thing to keep in mind is that here you do legally own the share you bought, except that when buying it you also signed a contract that says you will resell a share to the original owner at the original price, plus interest.
This is exactly how loans from banks work. You took money from the bank and bought a house. You now do not have enough money to pay back the bank, but the bank doesn't mind, because they only care about the contract that says they will get their money back plus interest.
The bank has an "asset" in their account that is the debt note from you. This asset has the value of the money you borrowed, plus interest, and it can be sold for that. One dollar just became two. (If it's a mortgage it's called a mortgage-backed security which the Federal Reserve will gladly take off your hands currently. The money they pay is created from nothing.)
That asset has associated risk vs cash that for the most part doesn’t. The risk being you don’t get the cash back. One dollar did not become two. If you sell the asset you get your cash back from whoever bought it, and it comes out of their account, again one dollar did not become two, unless it’s the Fed sure, they can create money.
Shares aren’t created unless the company issues more right?
So I think you do actually have it right. That's why you'll see careful commenters in this thread referring to "synthetic shares", which are like normal shares but come with that risk that you don't get it back. Except, if I understand correctly there are also laws around shorts which say that you are required to have the money to cover the share, which helps diminish the risk.
"Synthetic Shares" just sounds like a fancy way of saying you have a loan on the books. Its like if I loan you money and saying now I have "Synthetic Money" in the form of the loan you owe me. Money people seem to love to make up new terminology to obfuscate the meaning.
The risk is priced. That's the excess interest (above the risk-free rate) embedded in the asset value.
I should also add that it's not the case that the bank "no longer has" the money lent out. The bank doesn't actually move money from some depositor to the borrower. The bank credits the borrower's account with money created from nothing, and it feels comfortable doing so because there is the asset backing it. The Federal Reserve doesn't have to be directly involved at this stage. It allows banks to do this as long as capital requirements are satisfied.
So fractional reserve banking, once they hit reserve fraction they can't legally lend more cash out right?
This also doesn't occur with shares, you either own the share to lend or you don't? There are no new shares created only loans on a fixed amount of shares in circulation unless the company issues more shares, right?
You don't own the share you lend as in it's no longer your property, but you own a new contract claim against the brokerage house whom you lent to. As with any loan, this is newly created financial property. It acts and is priced like the original share, plus additional compensation for the risk (payment for share lending).
It's not the same as company issuing a new share since there is no voting right and there is no SIPC insurance. But in all other ways, financially, it's as if the brokerage created a new share. Real share owners can lend again, so one real share can leverage into any number of outstanding synthetic shares. The only thing holding leverage in line is the margin requirement, and how many people who lent real shares want their loans back.
Right, risk plays into it, but the loan the bank creates is an asset, (a liability for the bloke that has to pay it back in the future) - If I can sell that loan to someone else great, I just have to make it look low risk. But whether or not I sell the contract/loan off, I do have an asset that I didn't have before. It may not be a dollar from the Fed, but it's worth a dollar as long as the risk is low.
This is exactly how loans from banks work. You took money from the bank and bought a house. You now do not have enough money to pay back the bank, but the bank doesn't mind, because they only care about the contract that says they will get their money back plus interest.