Money, Banking

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Money, Banking FinanceLecture 2

• The Stock Market, Rational Expectations and
  Efficient Markets

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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

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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

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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

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One period valuation
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Generalised dividend valuation model
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Dividend Model

• The price of a stock depends only on the
  discounted flow dividend payments.
• Some dont 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.

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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.

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Gordon growth model
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Gordon growth model continued
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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.

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Stock prices setting

• Investor A valuation 2/(.15-.03)16.67
• Investor B valuation 2/(.12-.0322.22
• Investor C valuation 2/(.10-.0328.57
• 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.

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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.

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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
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• 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

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Expected return
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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
  (128-100)7/1000.35 (117-100)3/100.2
  (105-100)0100.05.
• Probability of each state 0.3, 0.4, 0.3.

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Expected return over all contingencies
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Calculation of expected return and risk

• E(r) (35x0.3) (20x0.4) (5x0.3) 20
• Variance of returns calculation
• (35)2x(0.3) (20)2x(0.4) (5)2x(0.3)
  (20)2 535 400 135.
• Standard deviation v135 11.62
• This is an example of three contingencies only

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Distribution of returns
Frequency
Return
- Return
0
E(r)
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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

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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.

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Rational Expectation
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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.

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If information set ? changes then expectations
of X changes
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Forecast errors are on average zero
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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

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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).

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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.

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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.

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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 shouldnt
  result in abnormal returns.

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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

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Implication of EMH

• Let equilibrium return for stock A is 10.
• The current price Pt is lower than the optimal
  forecast price Pot1 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.

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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).

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Random Walk-assume expected dividend stream is
constant
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Random Walk

• Since the expectation of Pt conditional on
  information at time t is simply itself Pt.
• The difference between expected dividends in t1
  given information at time t and dividends in t2
  given information at time t1 is new news and
  is therefore unpredictable. Hence its expectation
  is ZERO.

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Random Walk
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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.

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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.

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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)

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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.