# Is there a mathematical formula to determine a stock's price at a given time?

I have been trying to find exact information on how stock prices are determined but still I haven't found any exact mathematical formulas how it happens. Wikipedia states:

When prospective buyers outnumber sellers, the price rises. Eventually, sellers attracted to the high selling price enter the market and/or buyers leave, achieving equilibrium between buyers and sellers. When sellers outnumber buyers, the price falls. Eventually buyers enter and/or sellers leave, again achieving equilibrium.

That still doesn't tell how the price is determined. The formulas must exist, because prices can be followed real time? I'll give a simple example. Let's consider that there is a Company X and parties A, B and C and there exists 6000 stocks in public market.

At moment 1

Current stock price: 100€

Stocks held:

Party A: 2000 stocks -> value = 2000*100€ = 200 000€
Party B: 3000 stocks -> value = 3000*100€ = 300 000€
Party C: 1000 stocks -> value = 1000*100€ = 100 000€

At moment 2

Party C wants to by 1000 stocks at price 110€ and Party B wants to sell 1000 stocks at price 120€. How is the correct price in the middle determined exactly? Is it just by negotiating or is there a formula to determine it?

In any case, let's then consider that the agreement is in the middle and agreed price is 115€ and transaction is made.

The most important question is: What is the the global stock price after such transaction?

At moment 3

Current stock price: NEW_STOCK_PRICE

Stocks held:

Party A: 2000 stocks -> value = 2000*NEW_STOCK_PRICE = ?
Party B: 2000 stocks -> value = 2000*NEW_STOCK_PRICE = ?
Party C: 2000 stocks -> value = 2000*NEW_STOCK_PRICE = ?

How is the NEW_STOCK_PRICE calculated and what is its value?

For instance in Yahoo Finance (during writing this) Microsoft is valued for 30.56. Where does that number come from?

• Similar question money.stackexchange.com/questions/15156/… Commented Aug 25, 2012 at 12:31
• This question may also shed light: money.stackexchange.com/questions/1063/… Commented Aug 25, 2012 at 16:17
• You don't seem to understand what I'm asking. I'm not interested in how traders value their shares. I'm simply asking what kind of mathematics is used to determine values that are published. So, just answer how is the value 30.56 determined in the Microsoft -case? Is it just a guess, a random number, or does it actually reflect something?
– M.L.
Commented Aug 25, 2012 at 18:34
• @M.L., it simply reflects the last price the stock was traded at. As Chris said, once the current price has been traded it becomes history, and the new current price is the next price the bid and offer prices meet to make a new transaction. Commented Aug 26, 2012 at 23:52
• Investors use mainly fundumental analysis to predict the value a stock should be, whilst traders mainly use technical analysis, whilst some use a combination of both. Both techniques provide an indication of where prices should be headed in the future, but both are by no means anywhere near 100% correct, because many factors, including peoples' emotions, will determine the actual price a stock is sold at at any particular time. And there is no formula to determine peoples' emotions and many other of these factors. Commented Aug 27, 2012 at 0:00

A stock market is just that, a market place where buyers and sellers come together to buy and sell shares in companies listed on that stock market. There is no global stock price, the price relates to the last price a stock was traded at on a particular stock market. However, a company can be listed on more than one stock exchange. For example, some Australian companies are listed both on the Australian Stock Exchange (ASX) and the NYSE, and they usually trade at different prices on the different exchanges.

Also, there is no formula to determine a stock price. In your example where C wants to buy at 110 and B wants to sell at 120, there will be no sale until one or both of them decides to change their bid or offer to match the opposite, or until new buyers and/or sellers come into the market closing the gap between the buy and sell prices and creating more liquidity. It is all to do with supply and demand and peoples' emotions.

• You should also note that the stock price is not necessarily the price that you can buy or sell at. In your example, if B wanted to sell all of his 3,000 shares, that would be half of the company, and it would force the price down in order to find enough buyers. Commented Aug 25, 2012 at 12:49
• I marked this as correct answer, because it answered the first part of the question.
– M.L.
Commented Aug 25, 2012 at 19:30
• Well, there are formulas used to determine stock price. Most are proprietary, used by the investment banks and mutual fund managers to determine one of the three key words: "buy", "hold", "sell". The core of most of those models, however, are the basic TVM equations for present and future value. Basically, calculate the expected gains (i.e. dividend payments) over a particular time period that you would like to grow your money. The share price of the stock is the "present value", and the "future value" is the stock's value plus the value of all gains. Find the yield. Is it good enough? Buy. Commented Aug 27, 2012 at 16:32
• The proprietary part is usually a prediction of the single largest part of the future value; the price of the stock at the end of the time period. These calculations are based on the entire market outlook, similar industries, related commodities futures, etc etc and much of the input is subjective. The judgments that determine input, and the quality of the output predictions of the models, are what separates a fund that beats the Lipper average from one that doesn't. Commented Aug 27, 2012 at 16:35
• @KeithS - that is not a stock's price, that is using assumptions to predict what the price should be at, but the assumptions used can and are often biased and wrong! The stock price is what it trades at on a stock market! Commented Jan 6, 2021 at 7:21

The fallacy in your question is in this statement:

"The formulas must exist, because prices can be followed real time."

What you see are snapshots of the current status of the stock, what was the last price a stock was traded at, what is the volume, is the price going up or down.

People who buy and hold their stock look at the status every few days or even every few months. Day traders look at the status every second of the trading day.

The math/formula comes in when people try to predict where the stock is going based on the squiggles in the line. These squiggles move based on how other people react to the squiggles.

The big movements occur when big pieces of news make large movements in the price. Company X announces the release of the key product will be delayed by a year; the founder is stepping down; the government just doubled the order for a new weapon system; the insiders are selling all the shares they can.

There are no formulas to determine the correct price, only formulas that try to predict where the price may go.

I found the answer. It was the Stock Ticker that I was looking for. So, if I understand correctly the price at certain moment is the price of the latest sale and can be used to get a global picture of what certain stock is worth at that certain instant.

• Actually, the stock ticker price is the last reported sale, but perhaps a better gauge of what stocks are worth at any given instant are the prices people are willing to pay to buy the stock (the bid) and the prices that people who own the stock are willing to sell them at (the ask). Refer to money.stackexchange.com/questions/1063/… .. when news comes out, especially after markets have closed, the last trade's price often isn't indicative; it's a historical number and gets stale. The bid and the ask are current. Commented Aug 26, 2012 at 13:52
• Oscar Wilde said that a cynic was someone who knew the price of everything and the value of nothing. There are algorithms that can be applied to balance sheets, audited accounts etc to come with a value for a share of stock, but the price is whatever the most recent buyer and seller agreed upon. If 100 shares traded most recently for \$10.40 a share, that does not mean that if someone holding 50,000 shares puts them up for sale, he will get the same price. Try to distinguish between what a stock is worth and what its current price is. Commented Aug 26, 2012 at 18:09
• @ChrisW.Rea I agree with what you said, one more addition: the last trade price is just as important (some argue it's more honest) because it's a record of someone actually putting money into the game. Commented Aug 29, 2012 at 6:02

Try to find the P/E ratio of the Company and then Multiply it with last E.P.S, this calculation gives the Fundamental Value of the share, anything higher than this Value is not acceptable and Vice versa.

• Sorry - P/E * E/S literally gives you P/S, the current price per share. One can use P/E to make some decisions, of course, and some even compare the P/E of other stocks in the same industry, but your answer seems to be circular. Commented Nov 19, 2013 at 0:42