Chapter 10
Information and Financial Market
Efficiency
Stocks
• Equities like common or ordinary stocks are a claim to the profits of a
corporation
• Stocks have no maturity date. Firms may buy back stock at market
prices as they choose.
• Stock owners receive periodic but not fixed payments called dividends.
Dividends reflect the profitability of the business and are not known in
advance.
• Stock owners are the owners of the firms. Holders of shares vote for
the directors of firms on a one share-one vote basis.
• Stock owners are the residual claimants to a firms income meaning a
firm that goes out of business must repay all debt before stock owners
get any income.
• Stock owners enjoy limited liability. Unlike the owners of private
firms, stock owners cannot lose more than the value of their stock.
Stock Outstanding Far Exceeds Debt Outstanding
5000000
HK$ Million
4000000
3000000
2000000
1000000
0
1995
1996
1997
Debt Outstanding
1998
1999
2000
Market Capitalization
Markets are Closer as a Source of Funds
500000
HK$ Million
400000
300000
200000
100000
0
1995
1996
1997
New Capital Issued
1998
1999
New Debt Issued
2000
Rational Expectations and Market
Forecasts
• Pay-offs to owners of equity are uncertain. To assess the
value of stocks, portfolio holders must make forecasts
about future dividends.
• One often used hypothesis about forecasts is that they
are based on rational expectations
• Rational expectations: Expectations that reflect optimal
forecasts (the best guess of the future) using all
available information.
• Statistically, rational expectations recognizes that people
will inevitably make forecast errors. However, no
systematic errors
– Average of forecasts equal average of dividends
– Errors are unpredictable, I.e. uncorrelated with all
information available at time forecast was made.
Efficient Markets Hypothesis
• When traders have rational expectations and
when the cost of trading is low, equilibrium price
= market forecast of fundamental value.
• When prices are below fundamental value,
portfolio holders will buy more of the asset
bidding up the price.
• Prices will change in reaction to changes in
expected future returns, or in risk, liquidity, or
information costs.
• New information incorporated into stock price
immediately.
Stock Returns
• Returns are defined as the payoff after one
period divided by price.
• Pay-off of stocks is dividend payment plus
price next period PAYOFF = P+1 + D+1.
P D
1

R

• Gross Return
P
• Net Return = Capital Gain + Dividend Yield
1
P1  P
D1
R

P
P
1
Stock Prices
• Stocks are riskier than bonds. Thus, if portfolio
holders are risk averse, stocks will pay a higher
average return. Let ib be the interest rate on
risk free bonds. Let heq,b be the risk premium
on equity. Define a risk adjusted interest rate,
i= ib + heq,b.
• Returns on stocks, Bonds are perfect
substitutes for stocks, in this case. Expected
return to holding stock share for 1 period
should be equal to expected return on 1 period
bond.
e
e
e
e
P

D
P

D
1
1
1  i b  heq ,b  1  i  1  R e  1
 P  1
P
1 i
Fundamental Value of Stock
Pe1  De1
De1
Pe

 1
1 i
1 i 1 i
e
e
D 2
P
Pe1 
 2
1 i 1 i
De 2
Pe
 2
e
D1
De1
De 2
Pe2
1

i
1

i
P




1 i
1 i
1 i
1  i 2 (1  i ) 2
P
Pe2 
P
P
P
De3
Pe
 3
1 i 1 i
De1
De 2

1 i
1  i 2
De3
Pe
 3
De3
Pe3
De1
De 2
 1  i 12 i 



(1  i )
1 i
1  i 2 1  i 3 1  i 3
e
1
e
2
De3
Pe
 3
De1
De 2
DeT
PeT
1

i
1

i



 .... 

(1  i ) 2
1 i
1  i 2
1  i T 1  i T
e
1
e
2
De3
Pe
 3
De1
De 2
De 
 1  i 12 i 


....

(1  i )
1 i
1  i 2
1  i 
D
D

1 i
1  i 2
D
D

1 i
1  i 2
Dividend Yields
• Assume that dividends grow at a constant rate g . This implies Dt+j =
(1+g)j Dt
P
De1
De 2
De 


....

1 i
1  i 2
1  i 
1  g  D  1  g  D  ....  1  g  D
(1  g )
P
D
1 i
1  i 2
1  i 3
1  i 
2
• If x < 1,
• For price,
3

x  (1  xT )
1 x
x  (1  x  )
x
x  x 2  x 3  x 4  ......x  

1 x
1 x

x 0
x  x 2  x 3  x 4  ......xT 
 (1  g )
1  g 2  1  g 3  ....  1  g  
P  D

1  i 2
1  i 3
1  i  
 1 i
(1  g )
1 g
1 i
 D
 D
(1  g )
ig
1
1 i
P
1 g

D
ig
Dividend Yield
D
ig

P
1 g
• High future growth means that agents will pay a higher
price for a stock with a current level of dividends.
• High interest rates means that agents can earn high returns
on bonds. Portfolio holders will pay a lower price for a
given alternative stream of income.
Price Earnings Ratio
• Dividend payments can be
varied through time for a
number of reasons.
• Earnings = Dividends +
Retained Earnings
• The idea that earnings grow
constantly through time may be
closer to reality than constant
dividend growth.
• Applying this equation to
the price earnings ratio
may be more useful
P 1 g

E ig
• The value of a stock is equivalent to the
present value of the expected future
dividend stream.
• Efficient markets hypothesis suggests that
any information about future dividend
levels will be reflected in current prices.
• Equivalently, efficient markets hypothesis
suggests that excess returns are zero
Excess Returns
• Forecast Errors: fe = R - Re
• Efficient markets Re = i
• Forecast errors = Excess Returns
• fe = R - i
• Rational Expectations: Excess returns are
unpredictable.
Implications of Efficient Markets for Portfolio
Strategies
• Since all stocks should be expected to have no
excess returns, better not to put all your money in
one stock.
• Investment strategies based on public information
cannot do better than average. Mutual funds that
hold a constant, broad-based portfolio will do as
well as funds that are actively traded on the basis
of some strategy.
• Since active trading has transactions costs,
churning portfolio on the basis of some strategy is
counter-productive.
Tests of Efficient Market Hypothesis
•
•
•
Early tests supported efficient markets.
Portfolios based on random stock
selection usually did as well as investment
experts. [Possible Exception – Value
Investors]
Early tests found that stock prices
followed a random walk. Since current
prices reflect all information, price
changes reflect unforecastable information
Recent Rejections of Efficient
Markets
1. Evidence of Pricing Anomalies
– January Effect: High Returns in January
– Small Firm Effect: Small firms have higher returns.
2. Evidence of Long-term Mean Reversion: Stocks with
positive excess returns will tend to do worse over long
term.
3. Evidence of Excess Volatility: Stock prices much more
volatile than discounted set of returns.
Explanations
• Noise Traders Many uninformed traders
lead to poor market performance
• Bubbles: Portfolio holders buy stocks at
prices higher than their fundamental value,
because they believe that others will buy
stocks at even higher prices.
– Bubbles are like musical chairs. Eventually,
someone will be left holding assets when price
returns to fundamental value.
Chapter 5 Part 2.
The Theory of Portfolio Allocation
Theory of Risk
• The fundamental insight of the theory of
finance is that the risk of an asset is not
measured by the volatility of the assets
returns, but by the amount that it adds
volatility to your portfolio.
• A well diversified portfolio can reduce the
average risk of the assets in the portfolio.
Example: Coin Flipping Stocks
• The interest rate is i = .1
• Consider a portfolio with a 1.1 million shares of
Heads or Tails Inc. At the end of the year, HoT
will flip a coin. If Heads comes up, the company
will pay a dividend of a dollar per share. If tails
comes up, the company will pay 0. Either way, the
company will close down. Present value of the
expected dividend is $.5 million.
• However, price that a portfolio investor will pay
for this portfolio should be considerably less than
$.5 million because of the high risk of the
portfolio.
Well Diversified Portfolio
• Consider a portfolio of 1.1 million shares of stocks in 1.1
million different coin-flipping companies.
• At the end of the year, each company will independently
flip a coin (for a total of 1.1 million coin flips). If heads
come up, they will pay a dollar. If tails come up, they will
pay nothing.
• Each individual share has the same risk characteristics as
share of Heads or Tails Inc.
• Expected PV = $.5 Million
• However, Law of Large Numbers says that if you flip a
coin 1.1 million times, there is an extremely high
probability that you will come very close to getting .55
million heads.
• Perfectly diversified portfolio of independent coin-flipping
stocks has very low risk.
Comovement as Risk
• The individual shares in the first portfolio have the
same properties as the shares in the second portfolio,
but the second portfolio has more risk overall.
• The reason is the pay-offs of the shares in the first
portfolio have a strong mutual covariance. The shares
in the second portfolio.
• A stock will add more volatility to your portfolio if its
return has a high covariance with the assets in your
portfolio than a stock whose return is independent of
the assets.
• A stock that is negatively correlated with your
portfolio may reduce the volatility of your portfolio.
Idiosyncratic vs. Systematic Risk
• Stock returns in a market tend to move together to a
certain extent.
• Most companies tend to have common movements in
returns due to business cycles.
• Common or systematic risk cannot be diversified away.
• All firms have idiosyncratic risk which is independent of
systematic risk. This risk can be diversified away.
• Different firms have different exposure to systematic
risk. Firms whose returns drop especially sharply when
the market as a whole drops, have larger exposure to
market risk. Adding these stocks to your portfolio adds
proportionately more to the volatility to your portfolio.
Capital Asset Pricing Model
• The CAPM takes the point of view that the risk
premium for an individual stock j demanded by
the market as a whole are a function of the extra
volatility added to a diversified portifolio by the
individual stock.
• The degree to which a stock adds to the volatility
of a diversified portfolio depends on its comovement with the overall market return.
• Stocks which have greater exposure to systematic
risk display greater comovement with the market
portfolio.

• The degree to which a stock adds to the risk of a welldiversified portfolio is measured by its beta coefficient
–
–
–
–
Rf : Risk-free return
Rm: Return on Market Portfolio
Rj : Return on Stock j
: Correlation of Excess Returns on Stock j (Rj-Rf)
with the excess returns on market portfolio (Rm-Rf)
– m : Standard Deviation of Excess Returns on Market
Portfolio
– j : Standard Deviation of Excess Returns on Stock j
Model of Equity Premium
• Beta is the product of the correlation of the excess returns
on a stock with the excess returns on a market portfolio
and the relative volatility of the stocks returns.
j
  
m
• A stocks equity premium is proportional to
its beta
R  R f    (R  R f )
e
j
e
m
CAPM and Dividend Yield
• Stock is forecast to have constant dividend
growth of 4%. The interest rate is 5%. The
average market return is 15%. The stock has
a beta of 1.5.
• Rje = .05 + 1.2·(.15-.05) = .17
• P = D· 1.04/(.17-.04)
• P/D = 8
Hong Kong PE Ratios
• A number of critics have argued that managers may pay
themselves high salaries rather than pay dividends which
would have to be paid to minority shareholders.
• In Hong Kong, insider managers own a majority or a near
majority of shares of virtually all of the stocks listed on
Hong Kong Stock Exchange
• A number of critics have argued that regulatory regime in
Hong Kong does not do enough to protect minority
shareholders.
Average Dividend Yield on HKSE and NYSE 1985 -2001
3.8
3.6
3.4
3.2
3.0
2.8
2.6
US Dividend Yield
HK Dividend Yield
PE Ratios
Average PE Ratio 1985-2001
21
20
19
18
17
16
15
14
13
US PE Ratio
HK PE Ratio
Event
Demand for
Loanable Funds
E 

Capital Productivity 

Business Taxes 

Deficits 

Supply of Bonds



