The Stock Market, the Theory of Rational Expectations, and the Efficient Market Hypothesis

Chapter 7

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Theory of Stock Valuation

One period stock valuation

P

0  1

Div

1 

k e

 1 

P

1

k e

Generalized dividend valuation

P

0   1

D

1 

k e

1 

D

2

k e

 2  ...

  1 

D n k e

  1 

P n k e



n P

0 If n is fairly large, then 

t

   1  1 

D t k e



t

If the stock doesn’t pay dividends, t starts when dividends start.

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Theory of Stock Valuation

Gordon Growth Model

P

0 

D

0  1  1  

k



g

1  1 

D

0  1  1  

k



g

2  2  ...



D

0  1  1  

k g

    To simplify, multiply both sides by 1  1 

k g

and subtract the original equation from both sides

P

0 1 1  

k g P

0   1 1 

k g

  

P

0   1  1 

k g

 1   

D

0

P

0 

D

0   1 

k



g g

 

P

0 

k D

1 

g

3

Informed Buyer Bids Up the Price

 If two people both knew next period’s dividend and the growth rate, but one has more information about the future of the firm, the knowledgeable one will require a smaller k and pay a higher price.

 The uncertainty for the less informed shows up as higher k.

4

Examples

 Fed lowers interest rates => price of bonds rise => demand shifts to substitute: stocks => price of stocks rise  Subprime crisis => g down, k up => P 0 down 5

Expectations

 Static: expectations don’t change  Past has no trend  Adaptive: expectations are adjusted according to past with recent past having higher weight  Slope is small  Rational: expectations are forward looking  Slope is very discernable 6

Rational Expectations

 Approximate guesses impose high costs  Optimal forecasts can reduce costs  Predictions are on average accurate  Errors add up to zero: no trend 7

Efficient Market Hypothesis

Rational Expectations in Financial Markets  Investors decide on stock purchases according to expected returns.

 Expected returns rely on expected price in the future.

 Expected price is the optimal forecast price.

 Information on the variables affecting the supply and demand allow optimal forecast of returns to be the same as equilibrium return.

8

Efficient Markets Hypothesis

 Markets with extreme price flexibility adjust instantaneously to any shift in supply and demand.

 Optimal forecast equals the equilibrium value.

 Any deviation will immediately be recognized and allow arbitrage.

 There cannot be any profit opportunities.

9

Efficient Market Hypothesis

 Those who profit from the efficient market are the smart ones because the “dumb” ones make stupid choices.

 Prices are always right; they embody all the relevant information.

 Pangloss!

10

Efficient Market Hypothesis

 Random walk, throwing darts do as well as professional picks.

 Hot tips are already passé.

 Beware of the managers with high fees.

11

Efficient Market Hypothesis

 If there is market psychology, herd behavior, EMH is suspect.

 Bubbles question EMH.

 Animal Spirits (R. Shiller and G. Akerlof) won the 2009 TIAA-CREF Samuelson award.

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