# How to calculate how much a large stock position is really worth?

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...

• This depends on the average trading volume of the stock during the time in which you are executing the sale. I can't find a good link, but there's a measure called "# of Days to Liquidate". See here gladmainnew.morningstar.com/directhelp/Ownership/… If this measure is low, your sale probably won't effect the price as much. Oh, and you want to sell when trading volume is high. This happens at the beginning and the end of the day, and maybe at certain times in the month/quarter/year. Commented May 4, 2015 at 19:23
• Days to liquidate and volume weighted average price is a good metric. It is also possible to find a buyer outside of the stock exchanges.
– CQM
Commented May 4, 2015 at 19:35
• If you really had 1 million shares you probably wouldn't sell them on the open market anyway. It would be better to negotiate with a brokerage and buy the put options from them OTC. Then you both would benefit(assuming you can negotiate favorable terms.) Commented May 4, 2015 at 19:36
• @Mr.Mascaro: ...and then you lose the price of the put options, which can be a non-trivial amount for 10,000 contracts. So either way, you get less than the nominal \$10M. Commented May 4, 2015 at 19:40
• And you think you wouldn't have to pay transaction fees to sell them on the open market? To shift that many shares would be very expensive. You can buy 1,000,000 OTC put options for literally pennies each. Market-traded options would be a lot more. Commented May 4, 2015 at 19:56

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

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.

• How about when the stock position is distributed as a bequest? There's no sale, but wouldn't you need a current value for capital gains purposes? Commented May 4, 2015 at 18:24
• @User58220, the current value would be closing price on the date of the bequest transfer aka market value. Whether you can actually convert this value to cash is irrelevant on a liquid asset. Commented May 4, 2015 at 19:28

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.

• I guess your 5%-rule heavily depends on the jurisdiction (of the company, or maybe of the stock market) – maybe add this in your answer? Commented May 4, 2015 at 19:08
• I added the words "probably," and also "regardless" as the meat of the more-than-5% paragraph is that it depends. Commented May 4, 2015 at 20:31
• You really think the market wouldn't move significantly if you try to sell just under 5% of the total shares in a company? I don't have any concrete experience of this but it seems intuitively unlikely. Commented May 6, 2015 at 6:38

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.

• Hi Fardream, and welcome to the site. Do you have a reference for the above equation, in particular one that shows how to determine the coefficients and what they stand for?
– Joe
Commented May 5, 2015 at 1:22
• Hi, Joe. Sorry about the late reply. The particular form of the equation is from a certain broker. But a general search for transaction cost or market impact on ssrn.com should yield you some pretty decent results. Since most people will fix the exponential terms, the only remaining coefficients would be a, c - then just find a large enough sample (and to be honest, this is the most difficult part) and fit the equation. Commented Jun 5, 2015 at 20:41