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I'm taking a course on the fundamentals of financial mathematics. This is my first quantitative finance course, so I'm still getting acquainted with a lot of the ideas.

We covered the notion of a frictionless market. According to the lecture notes, in such a market we assume there is no restriction on short selling.

I would think this implies that in the real world, there $\textit{is}$ a restriction on short sales. My questions:

  1. What is meant by short sales (in the context of general models),
  2. why do we need to restrict them,
  3. and how are they restricted.
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There is indeed a legal angle to this. There are restrictions around naked short selling i.e. selling the stock and then failing to deliver it. See https://en.wikipedia.org/wiki/Naked_short_selling

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  • $\begingroup$ Oh, thanks! Makes sense. $\endgroup$ – PaleBlueDot Jan 18 at 18:40
  • $\begingroup$ Historically governments and regulators have been dubious (if not actually outraged) about the practice of short selling (blaming it for stock market crashes for ex.), and in some periods or some countries have banned short sales temporarily or permanently. However the trend is away from such restrictions. Nowadays it is generally permissible almost everyehere subject to some technical rules such as those dm63 mentioned. $\endgroup$ – noob2 Jan 18 at 20:08
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1) short sales are a type of transaction of stock Z where you try to profit from the fact that you believe that the stock price of Z is going down ( rather than up ). you do this by borrowing shares of stock Z from person X, selling it to person Y, waiting for it to go down, buying it in the market and then returning it to person X. ( make an example where the person shorts 1 share of Z, Z is initially 100 and Z goes down to 98 to see why you profit in this case ).

2) In the real world, it's not always possible to borrow the stock from someone so sometimes this makes it not possible to do the short.

3) they are restricted in the sense that there is no one available who wants to lend it to you.

I hope this helps.

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  • $\begingroup$ Ah I see, thanks. When I read about this restriction, I thought it would be some kind of legal matter. $\endgroup$ – PaleBlueDot Jan 18 at 12:44
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    $\begingroup$ it can also be a legal matter but I think that's getting less and less over time. $\endgroup$ – mark leeds Jan 19 at 4:22

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