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

0

1000000

2000000

3000000

4000000

5000000

1995 1996 1997 1998 1999 2000

Debt Outstanding Market Capitalization

HK

$ M

illio

n

Markets are Closer as a Source of Funds

0

100000

200000

300000

400000

500000

1995 1996 1997 1998 1999 2000

New Capital Issued New Debt Issued

HK

$ M

illio

n

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.

• Gross Return

• Net Return = Capital Gain + Dividend Yield

P

DPR 111

P

D

P

PPR 11

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.

i

DPP

P

DPRihi

eeeee

beqb

1111 1111

,

Fundamental Value of Stock

i

D

i

D

i

D

ii

P

i

D

i

D

i

DP

i

P

i

D

i

D

i

D

ii

P

i

D

i

D

i

DP

i

P

i

D

i

D

i

D

ii

P

i

D

i

D

i

DP

i

P

i

DP

i

P

i

D

i

D

ii

Pi

D

i

DP

i

P

i

DP

i

P

i

D

i

DPP

eee

ee

ee

T

eT

T

eT

ee

ee

ee

eeee

ee

ee

eee

eee

ee

e

eee

eeee

1....

11)1(11

11

11....

11)1(11

11

1111)1(11

11

11

)1(11111

1

11

111

221

2

33

221

221

2

33

221

33

33

221

2

33

221

332

22

221

22

1

221

1111

Dividend Yields

• Assume that dividends grow at a constant rate g . This implies Dt+j = (1+g)j Dt

• If x < 1,

• For price,

Di

gD

i

gD

i

gD

i

gP

i

D

i

D

i

DP

eee

1

1....

1

1

1

1

1

)1(

1....

11

3

3

2

2

221

0

11

)1(......

1

)1(......

432

432

x

x

x

x

xxxxxxx

x

xxxxxxx

TT

gi

g

D

P

gi

gD

igig

D

i

g

i

g

i

g

i

gDP

1

1

1)1(

1

1)1(

1

1....

1

1

1

1

1

)1(3

3

2

2

Dividend Yield

• 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.

g

gi

P

D

1

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

gi

g

E

P

1

• 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 co-movement 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 well-

diversified 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.

• A stocks equity premium is proportional to its beta

m

j

)( femf

ej RRRR

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.

2.6

2.8

3.0

3.2

3.4

3.6

3.8

US Dividend Yield HK Dividend Yield

Average Dividend Yield on HKSE and NYSE 1985 -2001

PE Ratios

13

14

15

16

17

18

19

20

21

US PE Ratio HK PE Ratio

Average PE Ratio 1985-2001

Event Demand for Loanable Funds

Supply of Bonds

E

Capital Productivity

Business Taxes

Deficits