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Let's say, completely hypothetically, that I own 1,000,000 shares in Company X, and their share price is exactly $10.00. Theoretically, this is worth $10 million, but obviously if I wanted to liquidate this quickly and I placed an order saying "sell 1,000,000 shares at market," it would drive the price down and I'd end up getting significantly less than $10 million out of it.

Is there any accepted way to calculate (a reasonable approximation of) how much this sale would actually be worth? I figure it would probably have to take into account factors such as current trading volume on Company X and the total number of shares outstanding, but I don't know enough to know what I don't know...

Chris W. Rea
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Mason Wheeler
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4 Answers4

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I don't have a formula for anything like this, but it is important to note that the "current value" of any asset is really theoretical until you actually sell it.

For example, let's consider a house. You can get an appraisal done on your house, where your home is inspected, and the sales of similar houses in your area are compared. However, this value is only theoretical. If you found yourself in a situation where you absolutely had to sell your house in one week, you would most likely have to settle for much less than the appraised value.

The same hold true for collectibles. If I have something rare that I need cash for immediately, I can take it to a pawn shop and get cash. However, if I take my time and locate a genuinely interested collector, I can get more for it.

This is comparable to someone who holds a significant percentage of shares in a publicly held corporation. If the current market value of your shares is $10 million, but you absolutely need to sell your entire stake today, you aren't going to get $10 million. But if you take your time selling a little at a time, you are more likely to get much closer to this $10 million number.

A "motivated seller" means that the price will drop.

Ben Miller
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This is actually a very complicated question. The key reading in this area is a seminal paper by Almgren & Chriss, "Optimal Execution of Portfolio Transactions" (2000). They show that there's a tradeoff between liquidating your portfolio faster and knowing the value with more certainty, versus liquidating more slowly (and likely for a higher price) but with less certainty.

So for example, if you sold your entire position right now, you would know almost certainly how much you would get for the position. Or, you could sell off your position more slowly, and likely get more money, but you would have less certainty about how much you would get.

The paper is available online at http://www.courant.nyu.edu/~almgren/papers/optliq.pdf

Thomas Johnson
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One of two things is true:

You own less than 5% of the total shares outstanding. Your transaction will have little to no effect on the market. For most purposes you can use the current market price to value the position.

You own more than 5% of the total shares outstanding. You are probably restricted on when, where, and why you can sell the shares because you are considered part owner of the company. Regardless, how to estimate (not really "calculate," since some of the inputs to the formula are assumptions a.k.a. guesses) the value depends on exactly what you plan to with the result.

stannius
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Something like

cost = a × avg_spreadb + c × volatilityd × (order_size/avg_volume)e.

Different brokers have different formulas, and different trading patterns will have different coefficients.

TRiG
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Fardream
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