Sellers won't sell back shares in a short sale?

2. Person B borrows 100 shares from Person A without Person A's knowledge (because that's how short selling is supposed to work?)

It's not legal to "borrow" something without the owner's knowledge so that should give you some idea that this is not how it works.

A short is essentially a financial derivative like a stock option or call, with the side performing the short (we'll call them the buyer) and the side that owns the share (we'll call them the seller) making a formal agreement that the seller will give the buyer the shares for a specific period of time for a (generally) flat fee. The seller doesn't really care what happens to the share in the meantime, and is happy to get money for letting the buyer "borrow" the share for a defined period of time. The buyer of the short will sell the shares they receive more or less immediately and then will buy the shares back when the term is up to be able to give it back to the buyer. Note here, the specific shares received from the seller are not necessarily the same shares the buyer will give back- the buyer sells the shares on the open market and buys them back on the open market. Person C is irrelevant here, all there needs to be is at least one seller.

That said, the short is a gamble for the buyer of the short. They are gambling that the price will fall so that when they buy the share back to give it to the seller they will make a profit. If people don't want to sell the share, the price will go up, and the buyer will have find a price at which someone is willing to buy, buy the shares at a huge loss to themselves to give it back to the seller, or skip on their contract and face legal and reputational backlash of reneging on their contract. Typically it will be extremely rare that no one will be willing to sell especially if the price is spiking, however illiquidity risk is something that both the buyer and seller will have to have taken into account in making the contract in the first place.

(A) who owns 100 shares does not know the identity of borrower (B) but by signing a margin agreement, (A) has agreed that his shares may be may be loaned out. Therefore he has knowledge that it's possible that his shares will be loaned but he has no knowledge if it occurs or who the counter party may be when it occurs.

Share borrower (B) sell the 100 shares to Buyer (C). Regardless of whether share price has risen or fallen, if (B) wants to buy the shares to cover his short position, he does so in the open market. He does not deal directly with Buyer (C) and while it's possible, the odds that they are on both sides of this closing trade are infinitesimal.

As per your question, let's assume that (B) and (C) transacted. When the short is covered, the shares are returned to the account of (A). (B) has a STO and a BTC so his transaction is complete and has a capital gain or loss. (C) has a BTO and a STC so his transaction is also complete along with a capital gain or loss. If (C) was not available to transact with, then borrower (B) bought shares from seller (D).

There will always be a seller of shares that borrower (B) can transact with. The question is, what will he have to pay to obtain shares (think short squeeze with share price rising quickly).

There is no thievery here. There is a book entry in the account of lender (A) for long 100 shares. The system (brokerage firm, regulatory agencies) guarantees that the shares are his.

Here's where it can get problematic. While the shares are loaned out, (A) decides that he wants to sell his shares. Technically, he can't sell what isn't in his account so his broker looks for 100 shares in other same firm accounts. If none are available, he looks to other brokerage firms to borrow 100 shares. If none are available anywhere, borrower (B) is sent a notice that he must cover his short position by the end of the day or there will be a forced buy in by his broker. Either way, 100 shares are purchased and these shares are returned to the account of (A) at EOD.

In reality, lender (A) wasn't prevented from selling his shares. He sells his shares whenever he wants to but since the shares are not in his account, it creates another book entry (+100 shares owned and loaned out followed by -100 shares sold but not available to deliver). At the EOD when the purchased shares to cover (B)'s short are returned to the account of (A), book entries are settled.

You have two main misunderstandings:

Person B borrows 100 shares from Person A without Person A's knowledge (because that's how short selling is supposed to work?)

I don't know where you got this idea. Lending shares, borrowing shares, and buying borrowed shares are all established parts of the market, and is done openly. Person B pays interest on the borrowed shares, and there are plenty of people who willingly lend their shares in exchange for that interest. The idea that short sellers are sneaking around grabbing shares when no one is looking is downright bizarre.

Person B buys back the shares from Person C at a value of $X-$delta

Person B buys back the shares on the open market, at the best price they can get. If they can't buy back the shares at a price lower than what they sold for, then the market is, by definition, not a bear market. Stock price is not some abstract thing separate from the market; it's the dollar amount at which transactions are taking place. If the price has gone down, then, by definition of "price", there are people willing to sell for less than the previous price. If no one is willing to sell for less than the previous price, then the price hasn't gone down. If no is willing to sell at all, then there is no well-defined price at all.

It is quite common for short-sellers to not be able to find anyone willing to sell for less than what they originally paid. In that case, they have to buy at a higher price, and take a loss. That's one of the risks of going short. If they can't buy back the stock, then they have to default on the loan, and the consequences of that depend on the exact conditions they agreed to when they placed the short sale. Short sellers are required to put up collateral to cover these losses, and if the price shoots up enough, they can lose all of their collateral, and they may be on the hook for even more if that's not enough to cover the loss.

You've got a number of misconceptions here. Let's make up some numbers.

• Alice and Dave both have 100 shares of XYZ that they bought for $10 each.
• Bob has $15.
• Carol has $1000.
• XYZ is trading at $10 today.
• Bob makes a deal with Alice: loan me 100 shares of XYZ today and I will give them back to you tomorrow, plus my fifteen bucks. (See below)
• Alice thinks "I can't lose on this deal; I'm going to make a 1.5% return on my investment!"
• Bob takes the shares from Alice and sells them to Carol for $10 each.
• Now Alice has nothing, Bob has $1015, Carol and Dave have 100 shares.
• The next day, the price of XYZ has fallen to $9.
• Bob offers to buy Dave's shares for $9 each and Dave agrees.
• Bob now has 100 shares and $115.
• Bob returns the shares to Alice and pays her the $15.
• Bob now has $100. Alice has 100 shares and $15. Carol has 100 shares. Dave has $900.
• Bob started with $15 and ended up with $100 one day later. So Bob is up 567% in one day. Alice is down 8.5%. Carol and Dave are both down 10%.

Looks great for Bob!

Now run the math and see what happens if Bob guesses wrong and the price of XYZ goes up a dollar instead of down a dollar. Leverage works both ways.

Note that things are also good for Alice. She's long in a stock that declined in value, but her fee to Bob decreased her loss; that's pure profit.

The figure of "and fifteen bucks" for the interest is unreasonably high if the sale really is happening "tomorrow"; for pedagogical reasons I'm exaggerating. In reality the interest on the loan of a heavily traded stock would be in the ballpark of 3% or 4% per year, and some of that would go to the broker who brokered this deal.

What happens if at point 5, Person C does not want to sell shares back to Person B?

Carol doesn't sell back to Bob. Dave sells to Bob.

And even if Person B tries to buy from other people other than Person C, they all say no.

The supposition of the exercise is that the price of XYZ went down. If no one is willing to sell then the price did not go down. If no one is willing to sell then the price went up, and we have not yet determined what the price is. The price is determined exactly when someone is willing to sell at the same price that someone else is willing to buy!

Seriously, do the exercise again and see what happens if the price goes up instead of down. Bob ends up in a bad way. Short selling is dangerous.

How does Bob find Alice?

Now of course in practice, Bob probably doesn't call up Alice directly. Bob calls up his broker, and the broker figures out who is willing to lend shares, and who will get what cut of the fee.

How that works can vary, but typically it goes like this.

We know that a short sale is: Bob borrows stock, sells it now, buys it later, pays the stock back plus interest. That's not the only way to trade on a borrowed asset. Consider the following scenario:

Alice has $1000. She believes XYZ is going to go way up tomorrow, so she buys 100 shares for $10 each. If it goes up to $11 tomorrow, she sells and now she has $1100, for a total profit of 10%. But then Alice has a brilliant idea. She asks her broker "Can I borrow $1000 from you with my 100 shares of XYZ as collateral?" Alice takes the $1000 and buys 100 more shares for $10. Now if the stock goes up to $11, Alice sells her 200 shares for $2200, pays back the $1000 she owes, pays a couple bucks in interest on the loan, and now she has, say, $1198. She just doubled her profit for $2!

This strategy is called buying on margin, and like short selling it is super dangerous because, well, run the numbers again if the stock goes down instead of up.

Alice and Bob are therefore made for each other. They're both gambling with borrowed assets; Alice is gambling with borrowed money and betting the stock will go up; Bob is gambling with borrowed stock and betting it will go down. One of them will be wrong and get totally screwed.

So Alice's broker makes a deal with Alice: "I'll lend you the $1000 under the following conditions: (1) you pay me back with interest, (2) if XYZ goes down a lot, I get to sell your XYZ on your behalf, to ensure that you don't go bankrupt before you pay me back the $1000 you owe me, (3) I get to lend your XYZ to my buddy Bob the short seller over here, and I'll give you a cut of the fee that I'm going to charge him".

So when you say

Bob borrows 100 shares from Alice without Alice's knowledge (because that's how short selling is supposed to work?)

that's not right. Alice agreed to possibly lend to Bob when Alice opened a margin trading account, and Alice is getting a cut of the interest when that happens.

Of course all of this is super dangerous and there are additional restrictions in place to make sure that margin buyers and short sellers don't default on their loans. Bob's broker will not let Bob get away with selling short with $15 in his account; Bob's broker knows that Bob will need to sell assets to cover the short position if things go wrong for Bob. Bob's got to have a whole lot more than that $15 in order to make a short sale.

EXERCISE: Run the numbers on our original scenario again, this time with Alice having 200 shares of XYZ and owing her broker $1000. Try running the scenario where XYZ goes up, and where XYZ goes down, and see how much Alice and Bob end up ahead or behind.

Trading with borrowed assets is called leverage because its like pushing on the small end of a lever: a small movement on the small end translates into a big movement at the big end. But leverage works both ways; a small movement in the wrong direction leads to a big bad outcome for you.

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Some follow-up questions:

What is the price of a stock if no one is willing to sell?

There is no price. The price of a thing is only defined when there is a seller and a buyer and they agree on a price.

We can make estimates of a price -- or, less charitably, guesses -- of varying qualities depending on the information we have available.

When a stock price is quoted, that's an estimate of the current price simply computed by taking the price of the most recent transaction. Odds are pretty good that the next transaction will be at a similar price.

You can also get quotes of the current "ask price" -- that is the highest price where a seller says "I'd be willing to sell at this price". And you can also get the "bid price", which is the lowest price that any buyer is willing to buy at. Normally they are very close together, and when someone budges, the trade happens.

You can also get an idea of the price of a thing by looking at all the shares that everyone wants to sell and the price they'd sell at, and similarly for buyers. That's called a "depth chart" and you can learn a lot about the demand for a stock by studying it. There are many tutorials on the internet that will show you how to read a depth chart.

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What if someone sells short and then the price goes way up, so high that the short seller cannot afford to buy back the stock?

Then the short seller is bankrupt, and the person they borrowed the stock from is a creditor who has a claim. A bankruptcy court will determine how the assets of the short seller are distributed amongst the creditors.

Of course in practice this does not happen too often. If you are doing a short sale through a broker and the price started to shoot up then they would probably require you to buy back while you still can, to cover your obligation. There are many mechanisms in place designed to ensure that irresponsible short selling does not bankrupt people. They don't always work.

When you loan out anything, whether its a stock or cash, you run the risk of not being paid back. That's called counterparty risk. (There are a variety of things you can do to mitigate counterparty risk -- do some research on Credit Default Swaps, for instance.) But in general, the reason why you justify charging interest for the loan is to cover the risk that you won't get paid back. If you make more on interest from people who do pay you back than you lose on defaults, you're ahead.

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What if I am very wealthy and I successfully buy all of a stock. Can I then charge the short sellers a price of my choice, or bankrupt them?

Yep.

In my hypothetical situation, because I now own ALL of XYZ, that means creditor Alice who loaned XYZ to the short seller Bob lost their stocks? And they accepted that risk in exchange for interest from Bob?

That's correct. Look at our scenario again:

• Alice and Dave both have 100 shares of XYZ that they bought for $10 each.
• Bob has $15.
• Carol has $1000.
• XYZ is trading at $10 today.
• Bob makes a deal with Alice: loan me 100 shares of XYZ today and I will give them back to you tomorrow, plus my fifteen bucks.
• Bob takes the shares from Alice and sells them to Carol for $10 each.
• Now Alice has nothing, Bob has $1015, Carol and Dave have 100 shares.
• The next day, John buys Carol and Dave's shares for $20 each, which they gladly accept.
• John buys up everyone else's XYZ for whatever they want to be paid, outbidding everyone else.
• Alice, who would love to sell to John for $20 calls up Bob and says hey buddy, I'd like those shares of XYZ and my $15 back RIGHT NOW please.
• Bob has no ability to buy XYZ at any price because John is outbidding him.
• At the end of the day, Bob has $1015, Alice has empty promises, Carol and Dave have $2000, and John just spent twice the previous day's market price in order to gain control of XYZ. Bob owes Alice $15, which he can repay, and 100 shares of XYZ, which he cannot. Alice and Bob are going to court.

Of course this scenario is extremely rare in real life.

If these sorts of shenanigans interest you, consider watching the classic comedy "Trading Places". It is about controlling a market, but not in order to screw over short sellers. Rather, it's about using psychological tricks and insider information to manipulate the price of frozen concentrated orange juice futures. I believe there was an episode of Planet Money that dissected the (now illegal) techniques used in that movie.

First thing I noticed is everyone claims person A agreed. Nope, their broker can loan out their stock without telling them. I think the questions is legit.

When a trader wishes to take a short position, they borrow the shares from a broker without knowing where the shares come from or to whom they belong. The borrowed shares may be coming out of another trader's margin account, out of the shares being held in the broker's inventory, or even from another brokerage firm. It is important to note that once the transaction has been placed, the broker is the party doing the lending, not the individual investor. So, any benefit received (along with any risk) belongs to the broker. (from "Investopedia" They said it better than I could..)