How are prices being set on stock markets? For your explanation, start by (i) stating the optimization principle that reflects the pricing criteria, then (ii) provide your own (!) example of a pricing calculation. Further, (iii) please explain under which circumstances the method you have described is fair, and under which circumstances it would not work well to define a fair price.

Price setting is fundamentally driven by the demand and supply scenario. When demand is higher than supply, the price tends to move up and when the supply is higher than demand, the price tends to move down. This is basic principle of market price. Stock market being a public market, the price in the stock market is a mere supply demand situation for the traded security.

There are various methods to value stock price in the market. Absolue valuations such as Discounted cash flow, Sum of parts etc..and relative valuations like Price to Earnings, Price to Book etc..

Discounted cash flow valuation method of stock price is deriving a price by discounting the future cash flows at an appropriate cost rate with terminal value assumption. Lets say the DCF price indicates $100 for a unit of script. If the publicly traded price is > than $100, then it is considered to be trading with premium valuations above fair value and if it is trading < $100, then it is trading below the fair value with a potential to offer returns on investment.

One other method of assessing the fair value of stock is on the basis of Price to earnings ration. Lets say the price of stock is $100 and the expected future earnings is $10, then the PE is 100/10 = 10 times. In case the comparitive stocks in the same sector / same geography / same market trades above the 10 times PE valuation, the the said script is considered to be trading below fair value and vice-versa for trading above fair value.

Further, determination of fair price is also based on the purpose and use of the price reference. Example, in order to declare the value of investments in the balance sheet of a company, publicly available price is considered as fair price regardless of whether they are under or over valued. Similarly in cases where public traded price is not available, then the sum of parts valuation based on similar assets is considered as fair price. Even in instances when there is no comparitive price availbe, then the price at which arms length transaction between unrelated parties can be executed is considered as fair price.