Money, Banking & Finance
Lecture 2
The Stock Market, Rational
Expectations and Efficient Markets
Aims
• Explain the theory of valuing stocks.
• Explore how expectations influence affect the
value of stocks.
• Understand the theory of rational expectations
• Understand the concept of the Efficient Markets
Hypothesis
Common Stock
• Common stock is the principal way that
listed companies raise equity capital.
• Common stock holders have an ownership
interest in the enterprise in the form of a
bundle of rights.
• The right to vote at the AGM. The right to
be the residual claimant of all cash flows
into the company. The right to sell stock.
• Dividends are paid quarterly or six monthly
One period valuation
• An analyst makes a forecast for the price of a
particular stock.
• Does the current price accurately reflect the
Analysts forecast?
• Need to discount the expected future cash flow.
• This is a one-period model where P0 = current
price of the stock
• P1 = the price of the stock in the next period
• D1 = the dividend paid at the end of next period.
• ke = required return on investments in equity
One period valuation
D1
P1
P0 

(1  ke ) (1  k e )
Generalised dividend valuation
model
D3
Dn
Pn
D1
D2
P0 


 ..... 

2
3
n
(1  ke ) (1  ke ) (1  ke )
(1  ke )
(1  ke ) n

Di
P0  
i
(
1

k
)
i 1
e
Pn
lim
0
n
(1  ke )
n 
Dividend Model
• The price of a stock depends only on the
discounted flow dividend payments.
• Some don’t pay out a dividend and so the
valuation is based on the expectation of
dividends to be paid out some time.
• Some stock are zero dividend stocks.
Valuation is based on expected capital gain.
Dividend growth
• Valuation of stocks is based on expected
dividend stream
• Difficult to estimate.
• Many companies aim to increase dividends
at a constant stream each year.
• Let g = the expected constant growth in
dividends.
Gordon growth model
D0 (1  g ) n
D0 (1  g ) D0 (1  g ) 2
 ..
 .... 

P0 
n
2
(1  ke )
(1  ke )
(1  ke )
D0 (1  g ) D0 (1  g ) 2
(1  ke )
 ..

 D0 
 P0
2
(1  ke )
(1  ke )
(1  g )
(1  ke )
 D0  P0
 P0
(1  g )
 (1  ke ) 
 1  D0
 P0 
 (1  g ) 
Gordon growth model
continued
 (1  k e )  (1  g ) 

P0 
 D0


(1  g )


 P0 ( k e  g )  D0 (1  g )
D0 (1  g )
D1
 P0 

(ke  g )
(ke  g )
D1
P0 
(ke  g )
Assumptions and Implications
• Dividends are assumed to continue growing at a constant rate forever.
• The growth rate is assumed to be less than the required return on
equity.
• We can see how this model can be applied to the setting of stock
prices.
• Let expected dividend payout next year be £2 per share. Market
analysts expect firm growth to be 3% but there is uncertainty about the
constancy of the dividend stream.
• To compensate for the higher risk the required rate of return is 15% for
investor A
• Investor B has researched industry insiders and is more confident and
therefore has a required rate of 12%.
• Investor C has inside information and feels that 10% is acceptable to
compensate for risk.
Stock prices setting
•
•
•
•
Investor A valuation = [2/(.15-.03)]=£16.67
Investor B valuation = [2/(.12-.03]=£22.22
Investor C valuation = [2/(.10-.03]=£28.57
If investor A holds stock, he/she would sell
it to C. The market price would depend on
which investor holds the stock, how much
stock and the market orders for the stock.
Implications
• Expectations about the firm changes as new information is
made available.
• Expectations of future dividends or growth will affect
investor valuations.
• Interest rates affect the market valuation of stock prices.
• When interest rates are lowered the rate on bonds (and
other safe assets) decline. As these are substitutes to
equity, the required return on equities decline also and
drive up stock prices.
• Lower rates also stimulate the economy and help the real
economy to expand which also helps firms and raise stock
prices.
Risk and Return
• Expected return of a share is the sum of the earnings per
share and expected percentage capital gain.
• For example if the current price of a share is 100 and the
expected price of the share in one years time is 114 and the
dividend is 3.
• The expected return is [(114-100)/100 + 3/100]= 17%
• But in this exercise the expectation will not be held by all
people or the expectation will be state-conditional.
• A distribution of estimates of expected return will exist based
on differing information state contingency
Expected return
E ( Pt 1 )  Pt E ( Dt 1 )
E (r ) 

Pt
Pt
Example
• The current price of a common stock is 100
• State contingency is, good, average, bad
• Expected future price in each state is, 128,117,
105 respectively
• Expected dividends are, 7, 3, 0 respectively
• The state contingent expected returns are; [(128100)+7]/100=0.35; [(117-100)+3]/100=.2; [(105100)+0]100=.05.
• Probability of each state; 0.3, 0.4, 0.3.
Expected return over all
contingencies
E (r )    i ri
  E (r )  E (r )
2
2
2
   i r   ri  i 
2
 
2
2
Calculation of expected return
and risk
• E(r) = (35%x0.3) + (20%x0.4) + (5%x0.3)
= 20%
• Variance of returns calculation
• [(35%)2x(0.3)
+
(20%)2x(0.4)
+
(5%)2x(0.3)] – (20%)2 = 535 – 400 = 135.
• Standard deviation = √135 = 11.62%
• This is an example of three contingencies
only
Distribution of returns
Frequency
- Return
0
E(r)
+ Return
Expectations
• Stock price valuation depends on
expectations
• But how are expectations formed?
• One model of expectations formation is the
theory of rational expectations.
• John Muth ‘Expectations will be identical to
optimal forecasts (the best guess of the
future) using all available information’
Optimal forecast
• Rational expectation is the optimal forecast using
all the available information but the forecast will
not always be right.
• Why? Each forecast has an error that is given by
all the possible outcomes.
• But it will be an optimal forecast meaning it will
be unbiased.
• Unbiasedness means that there is no bias in any
forecast.
Rational Expectation
X t  EX t    t
E  X t   E X  t 1 
E ( X t )  E E X  t 1   E  t 
E ( X t )  E X  t 1 
Implications of RE theory
• 1. If there is a change in the way a variable
moves, the way in which expectations of
this variable are formed will change as well.
• 2. The forecast errors will on average be
zero and cannot be predicted ahead of time.
If information set θ changes
then expectations of X changes
~
 t 1   t

E X  t 1   E X  t
~

Forecast errors are on average
zero
X t  E X t 1    t
E  t   0
Concepts of efficiency
• Economics provides concepts of efficiency –
allocative and operational efficiency
• An allocationally efficient market is one where
prices are determined where market demand
equals market supply.
• An operationally efficient market is one where
transactions costs of moving resources around are
zero. Eg: perfect capital markets
Efficient Capital Markets
• Efficient markets in finance is less restrictive than
the concept of perfect capital markets.
• In an efficient capital market, prices fully and
instantaneously reflect all available relevant
information – informationally efficient.
• A capital market may be informationally efficient
but not allocatively or operationally efficient. E.g.
imperfect competition (allocatively inefficient) or
transactions costs like the proposed Tobin tax
(operationally inefficient).
Efficient Markets Hypothesis
• Expectations are unobserved and we need expectations of
future stock price to calculate expected return.
• The theory of rational expectations tells us that
expectations are the optimal forecasts based on all the
available information.
• The supply and demand for securities will determine an
equilibrium price of securities therefore the expected price
of stocks will be given by the market equilibrium.
• The expected return on a security will equal the
equilibrium return given by the market conditions for that
particular security.
Weak form efficiency
• Weak form efficiency – no investor can
earn excess returns by developing trading
rules based on historical price/returns data.
So technical analysis or chartists rules
cannot beat the market.
• All past information is reflected in the spot
price of an asset.
Semi-strong form efficiency
• No investor can earn excess returns from trading
rules based on any publicly available information.
• Implication is that all publicly available
information is fully reflected in the actual asset
price.
• Market reaction to new publicly available
information is instantaneous and unbiased. No
over- or under-reaction. Fundamental analysis
based on publicly available information shouldn’t
result in abnormal returns.
Strong form efficiency
• No investor can earn excess returns using
any information – public or private.
• Strong form efficiency implies that all
information is fully reflected in the price of
the asset.
• Even private information! – Insider trading
is ineffective
Implication of EMH
• Let equilibrium return for stock A is 10%.
• The current price Pt is lower than the optimal forecast price
Pot+1 so that the optimal forecast return is actually 50%.
• This has created an unexploited profit opportunity.
• So investors buy more stock A and drive up the current
price relative to expected future price thus lowering the
optimal forecast return to equal the equilibrium return.
• Vice versa if the current price was above the expected
future price.
• In an efficient market all unexploited profits are
eliminated.
• Not all investors have to be informed or have rational
expectations for the price to be driven to its equilibrium
point.
Evidence in favour of EMH
• Empirical studies confirm that stock pickers or mutual
fund managers cannot outperform the market over a long
period of time.
• The EMH states that stock prices reflect all available
information so that earnings announcements that are
already known will not affect stock prices when the
announcements are made. Only ‘new’ news causes stock
prices to change.
• Future changes in stock prices should follow a random
walk (future changes in prices are unpredictable).
Random Walk-assume
expected dividend stream is
constant
 E ( Dt 1  t  E Pt 1  t  E Dt 1  t 

Pt  


(1  r )
r
 (1  r ) 
 E ( Dt  2  t 1  E Pt  2  t 1  E Dt  2  t 1 

Pt 1  


(1  r )
r
 (1  r ) 
E Dt  2  t 1  E Dt 1  t 
Pt 1  Pt 

 ut 1
r
r
Pt 1  Pt  ut 1
E Pt 1  t   E Pt  t   E ut 1  t 
Random Walk
• Since the expectation of Pt conditional on
information at time t is simply itself Pt.
• The difference between expected dividends
in t+1 given information at time t and
dividends in t+2 given information at time
t+1 is ‘new’ news and is therefore
unpredictable. Hence its expectation is
ZERO.
Random Walk
Pt 1  Pt  ut 1
E ut 1  t   0
Empirical evidence against
EMH
• Size effect – Empirical studies show that small firms earn abnormal
returns over long periods.
• January effect – studies have confirmed an abnormal price rise from
December to January.
• Market overreaction – over/under shooting following ‘new’ news.
• Excessive volatility – fluctuations in stock prices are greater than the
fluctuations in the fundamentals.
• Mean reversion – low returns stock tend to be followed by high returns
and vice versa. Stocks that have done poorly in the past tend to do
better in the future. But the evidence on this is controversial.
• Lag in effect of ‘new’ news – stock prices do not always react to news
instantly. Some evidence of autocorrelation.
• If capital markets are informationally efficient, why is there so much
between people that take different views about the same future.
Behavioural Finance
• Doubts about EMH particularly after the stock market crash of 1987
(and probably 2008) have led to the emergence of a new field in
finance.
• Applies psychology, social anthropology and sociology to understand
the behaviour of stock markets.
• One of the arguments of EMH is that unexploited profit is eliminated
by knowledgeable investors. For this to happen they must engage in
short selling.
• Short selling – borrowing the stock from brokers and then sell it in the
market with the aim of making a profit by buying the stock back at a
lower price.
• Psychologists suggest that people are subject to ‘loss aversion’. They
are more unhappy from losses than happy with equivalent gains.
Because the potential losses can be huge from short selling in reality
short selling occurs only in special circumstances.
• Psychologists also find that people tend to be overconfident in their
own judgements. Overconfidence and social contagion explain the
creation of speculative bubbles.
The final say?
• “Observing correctly that the market was
frequently efficient they [academics, investment
professionals, corporate mangers] went on to
conclude incorrectly that it was always efficient”
Warren Buffet
• “Economics is not so much the Queen of the
social sciences but the servant, and needs to base
itself on anthropology, psychology – and the
sociology of ideologies” John Kay (FT 7/10/09)
Summary
• The theory of stock market valuation
• Expectations govern the valuation of stocks.
• Different expectations result in different expected
returns and a distribution of expected capital
gains.
• The theory of rational expectations provides a
market equilibrium basis for expectations based on
available information.
• The EMH is the application of rational
expectations to the securities market.