The Stock Market, Rational Expectations, and the Efficient markets Hypothesis
Expectations are important in every sector and market in the economy. This is certainly the case in stock
Oct 16, 2012 Edit
Computing the price of Common Stock
• Expectations are important in every sector and market in the economy
• This is certainly the case in stock valuation
• In an efficient capital market the price of a common stock today is equal to the present value of all future
expected dividend payments Plus the expected final price of the stock:
D D D D P
P 0 1 1+ 2 2 + 3 3 +......+ n n + n n (1)
(1+k e (1+k e (1+k e (1+k e (1+k )e
Where k eis the required rate of return on equity-typically higher that bond yields.
First examination of equation (1) leads to the conclusion that one cannot determine the price of the
cannot determine the price of the stock today (P0) Unless one Knows what the price of the stock is
going to be in the future (Pn).
Fortunately, an approximate valuation of the term in possible by ignoring the last term in equation (1).
The approximation is very close when one takes a long string of future dividends into consideration.
Then, the discount factor for the final price (Pn) is a very high number, and its present value is trivial.
This approximation is known as the generalized dividend model and is written as
P D t (2)
0 t(1 K ) t
The price of a stock according to this approximation is equal to the present value of an infinite stream of
dividends using a discount rate that is appropriate for stocks.
Equation (2) is still very different to compute because it requires forecasts of dividends into the indefinite
future. One possible shortcut is assume that dividends grow at a constant rate, g.
This is known as the Gordon growth model.
The model postulates that dividends evolve over time as follows:
D t (1 g) D 0 (3)
The constant dividend growth assumption allows us to write equation (2) as
D 01+g) D 01+g) D 01+g)
P 0 + 2 +...+ t
(1+k e (1+k )e (1+k )e
D (1 g) 1 g 1 g 1 g
P0 0 [1 ( ) ( ) .... ( ) ] (4)
(1 k e 1 k e 1 k e 1 k e
D (1 g) D0(1 g) (1 g) t
P 0 [1[ ]....[ ]] (5)
0 (1 k e 1 k e 1 k e
D (1 g) 1
P0 0 (6)
(1 ke) 1 g
1 ( )
1 k e D 01 g) 1 k e D 01 g)
P0= = (7)
(1 k e ke g ke g
Equation (7) allows the pricing of common stock in a