Managerial Economics

1
Managerial Economics

• Lecture Ten
• Standard theory of finance

2
Recap

• Minskys Financial Instability Hypothesis
• Finance-driven cyclical behavior

3
Modern Finance?

• Modern Finance Theory has many components
• Sharpes Capital Asset Pricing Model (CAPM)
• Modigliani-Millers Dividend Irrelevance
  Theorem
• Markowitzs risk-averse portfolio optimisation
  model
• Arbitrage Pricing Theory (APT)
• Modern as compared to pre-1950 theories that
  emphasised behaviour of investors as explanation
  of stock prices, value investing, etc.
• Initially appeared to explain what old finance
  could not
• But 50 years on
• Foundation is Sharpes CAPM

4
The Capital Assets Pricing Model

• How to predict the behaviour of capital
  markets?
• Extend theories of investment under certainty...
• to investment under conditions of risk
• Based on neoclassical utility theory
• Investor maximises utility subject to constraints
• Utility
• Positive function of expected return ER
• Negative function of risk (standard deviation) sR
• Constraints are available spectrum of investment
  opportunities

5
The Capital Assets Pricing Model
Investment opportunities
Z inferior to C (lower ER) and B (higher sR)
Indifference curves
Border (AFBDCX) is Investment Opportunity Curve
(IOC)
6
The Capital Assets Pricing Model

• IOC reflects correlation of separate investments.
  Consider 3 investments A, B, C
• A contains investment A only
• Expected return is ERa,
• Risk is sRa
• B contains investment B only
• Expected return is ERb,
• Risk is sRb
• C some combination of a of A (1-a) of B
• ERcaERa (1-a)ERb

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The Capital Assets Pricing Model

• If rab1, C lies on straight line between A B

8
The Capital Assets Pricing Model

• If rab1, C lies on straight line between A B

9
The Capital Assets Pricing Model

• If rab1, C lies on straight line between A B

10
The Capital Assets Pricing Model
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The Capital Assets Pricing Model

• If rab0, C lies on curved path between A B

This is zero
Hence this is zero
12
The Capital Assets Pricing Model

• If rab0, C lies on curved path between A B

13
The Capital Assets Pricing Model

• If rab0, C lies on curved path between A B

Straight line relation
Hence lower risk for diversified portfolio (if
assets not perfectly correlated)
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The Capital Assets Pricing Model
15
The Capital Assets Pricing Model

• Sharpe assumes riskless asset P with ERPpure
  interest rate, sRP0.
• Investor can form portfolio of P with any other
  combination of assets
• One asset combination will initially dominate all
  others

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The Capital Assets Pricing Model
Efficiency maximise expected return minimise
risk given constraints
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The Capital Assets Pricing Model

• Assume limitless borrowing/lending at riskless
  interest rate return on asset P
• Investor can move to anywhere along PfZ line by
  borrowing/lending
• Problem
• P the same for all investors (simplifying
  assumption)
• But investor perceptions of expected return,
  risk, investment correlation will differ
• Solution
• assume homogeneity of investor expectations
• utterly unrealistic assumption, as is assumption
  of limitless borrowing by all borrowers at
  riskless interest rate. So...

18
The Capital Assets Pricing Model

• Defended by appeal to Friedmans
  Instrumentalism
• the proper test of a theory is not the realism
  of its assumptions but the acceptability of its
  implications
• Consequence of assumptions
• spectrum of available investments/IOC identical
  for all investors
• P same for all investors
• PfZ line same for all investors
• Investors distribute along line by
  borrowing/lending according to own risk
  preferences

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The Capital Assets Pricing Model
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The Capital Assets Pricing Model

• Next, the (perfect) market mechanism
• Price of assets in f will rise
• Price of assets not in f will fall
• Price changes shift expected returns
• Causes new pattern of efficient investments
  aligned with PfZ line

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The Capital Assets Pricing Model
Range of efficient assetcombinations after
market price adjustments more than just one
efficient portfolio
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The Capital Assets Pricing Model

• Theory so far applies to combinations of assets
• Individual assets normally lie above capital
  market line (no diversification)
• Cant relate between ERi si
• Can relate ERi to systematic risk
• Investment i can be part of efficient combination
  g
• Can invest (additional) a in i and (1-a) in g
• a1 means invest solely in i
• a0 means some investment in i (since part of
  portfolio g)
• Some alt0 means no investment in i
• Only a0 is efficient

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The Capital Assets Pricing Model
24
The Capital Assets Pricing Model

• Slope of IOC and igg curve at tangency can be
  used to derive relation for expected return of
  single asset

• This allows correlation of variation in ERi to
  variation in ERg (undiversifiable, or systematic,
  or trade cycle risk)
• Remaining variation is due to risk inherent in i

25
The Capital Assets Pricing Model
26
The Capital Assets Pricing Model

• Efficient portfolio enables investor to minimise
  asset specific risk
• Systematic risk (risk inherent in efficient
  portfolio) cant be diversified against
• Hence market prices adjust to degree of
  responsiveness of investments to trade cycle
• Assets which are unaffected by changes in
  economic activity will return the pure interest
  rate those which move with economic activity
  will promise appropriately higher expected rates
  of return. OREF II

27
The Capital Assets Pricing Model

• Crux/basis of model markets efficiently value
  investments on basis of expected returns/risk
  tradeoff
• Modigliani-Miller extend model to argue valuation
  of firms independent of debt structure (see OREF
  II)
• Combination the efficient markets hypothesis
• Focus on portfolio allocation across investments
  at a point in time, rather than trend of value
  over time
• Argues investors focus on fundamentals
• Expected return
• Risk
• So long as assumptions are defensible

28
The Capital Assets Pricing Model

• In order to derive conditions for equilibrium in
  the capital market we invoke two assumptions.
  First, we assume a common pure rate of interest,
  with all investors able to borrow or lend funds
  on equal terms. Second, we assume homogeneity of
  investor expectations investors are assumed to
  agree on the prospects of various investmentsthe
  expected values, standard deviations and
  correlation coefficients described in Part II.
  Needless to say, these are highly restrictive and
  undoubtedly unrealistic assumptions.
• However, since the proper test of a theory is not
  the realism of its assumptions but the
  acceptability of its implications, and since
  these assumptions imply equilibrium conditions
  which form a major part of classical financial
  doctrine, it is far from clear that this
  formulation should be rejectedespecially in view
  of the dearth of alternative models leading to
  similar results.
• Sharpe later admits to qualms

29
The CAPM Reservations

• People often hold passionately to beliefs that
  are far from universal. The seller of a share of
  IBM stock may be convinced that it is worth
  considerably less than the sales price. The buyer
  may be convinced that it is worth considerably
  more. (Sharpe 1970)
• However, if we try to be more realistic
• The consequence of accommodating such aspects of
  reality are likely to be disastrous in terms of
  the usefulness of the resulting theory... The
  capital market line no longer exists. Instead,
  there is a capital market curvelinear over some
  ranges, perhaps, but becoming flatter as risk
  increases over other ranges. Moreover, there is
  no single optimal combination of risky
  securities the preferred combination depends
  upon the investors preferences... The demise of
  the capital market line is followed immediately
  by that of the security market line. The theory
  is in a shambles. (Sharpe 1970 emphasis added)

30
The CAPM Evidence

• Sharpes qualms ignored CAPM takes over
  economic theory of finance
• Initial evidence seemed to favour CAPM
• Essential ideas
• Price of shares accurately reflects future
  earnings
• With some error/volatility
• Shares with higher returns more strongly
  correlated to economic cycle
• Higher return necessarily paired with higher
  volatility
• Investors simply chose risk/return trade-off that
  suited their preferences
• Initial research found expected (positive)
  relation between return and degree of volatility
• But were these results a fluke?

31
The CAPM Evidence

• Volatile but superficially exponential trend
• As it should be if economy growing smoothly

But looking more closely...
32
The CAPM Evidence

• Sharpes CAPM paper published 1964
• Initial CAPM empirical research on period
  1950-1960s
• Period of financial tranquility by Minskys
  theory
• Low debt to equity ratios, low levels of
  speculation
• But rising as memory of Depression recedes
• Steady growth, high employment, low inflation
• Dow Jones advance steadily from 1949-1965
• July 19 1949 DJIA cracks 175
• Feb 9 1966 DJIA sits on verge of 1000 (995.15)
• 467 increase over 17 years
• Continued for 2 years after Sharpes paper
• Then period of near stagnant stock prices

33
The CAPM Evidence

• Dow Jones treads water from 1965-1982
• Jan 27 1965 Dow Jones cracks 900 for 1st time
• Jan 27 1972 DJIA still below 900! (close 899.83)
• Seven years for zero appreciation in nominal
  terms
• Falling stock values in real terms
• Nov. 17 1972 DJIA cracks 1000 for 1st time
• Then all hell breaks loose
• Index peaks at 1052 in Jan. 73
• falls 45 in 23 months to low of 578 in Dec. 74
• Another 7 years of stagnation
• And then liftoff

34
The CAPM Evidence
21 years ahead of trend...

• Fit shows average exponential growth 1915-1999
• index well above or below except for 1955-1973

Crash of 73 45 fall in 23 months
Sharpes paper published
Jan 11 73 Peaks at 1052
Dec 12 1974 bottoms at 578
Bubble takes off in 82
CAPM fit doesnt look so hot any more
Steady above trend growth 1949-1966 Minskys
financial tranquility
CAPM fit to this data looks pretty good!
35
An aside what caused 73 crash?

• Many blame OPEC Oil Embargo for economic downturn
• October 17, 1973 OPEC bans export of oil to
  countries that supported Israel in 1973
  Arab-Israeli War
• Oil price rises 4-fold from US2.50 to 10 a
  barrel
• BUT embargo occurred 9 months after market peak
• Quarterly GDP growth fell from 10.1 in Q1 1973
  to -1.6 in Q3 73 before embargo
• Market already down 8 by October 17 to 963
• Rose in immediate aftermath to embargo
• Real acceleration of crash occurred with Franklin
  National Bank of New York crisis from May-October
  1974
• May 1 854 Dec 12 578 32 fall in 7 months
• Minskys financial fragility more important
• OPEC-inspired inflation may have made crisis less
  severe reduction of real debt burden

36
The CAPM Evidence

• By mid-1990s, clear CAPM and reality werent
  related
• The Dow ... stood at around 3,600 in early 1994.
• By 1999, it had passed 11,000, more than tripling
  in five years...
• However, over the same period, basic economic
  indicators did not come close to tripling.
• U.S. gross domestic product rose less than 30,
  and almost half of this increase was due to
  inflation.
• Corporate profits rose less than 60, and that
  from a temporary recession-depressed base.
• Viewed in the light of these figures, the stock
  price increase appears unwarranted and, certainly
  by historical standards, unlikely to persist
  (Schiller 4)

37
The CAPM Evidence

• Schillers inflation adjusted SP PE ratio

• Very cyclical
• Notice peak in 1966 Minskys nominated date for
  transition from robust to fragile financial
  system
• 2000 valuations highest in history
• Not rational calculation of CAPM but
  irrational exuberance

38
The CAPM Evidence

• Price far more volatile than earnings
• Volatility should be similar if CAPM true

• Growth in earnings slow steady compared to
  highly volatile prices

39
The CAPM Evidence

• CAPM predicts no cyclical behavior to prices
  (apart from that caused by earnings) you cant
  time the market

• Schiller finds clear cyclicality when PE ratio
  high, next ten year stock market returns low
  vice versa
• 1990-2000 valuation off the chart!
• Negative returns for next decade highly likely

40
The CAPM Evidence

• The relation between price-earnings ratios and
  subsequent returns appears to be moderately
  strong...
• longterm investors who can commit their money to
  an investment for ten full years do well when
  prices were low relative to earnings at the
  beginning of the ten years and do poorly when
  prices were high at the beginning of the ten
  years.
• Long-term investors would be well advised,
  individually, to stay mostly out of the market
  when it is high, as it is today, and get into the
  market when it is low. (12)
• Critics of CAPM thus dismiss itbut even its
  one-time champions do too
• Fama French

41
The CAPM Evidence According to Fama 1969

• Evidence supports the CAPM
• This paper reviews the theoretical and empirical
  literature on the efficient markets model We
  shall conclude that, with but a few exceptions,
  the efficient markets model stands up well.
  (383)
• Assumptions unrealistic but that doesnt matter
• the results of tests based on this assumption
  depend to some extent on its validity as well as
  on the efficiency of the market. But some such
  assumption is the unavoidable price one must pay
  to give the theory of efficient markets empirical
  content. (384)

42
The CAPM Evidence According to Fama 1969

• CAPM good guide to market behaviour
• For the purposes of most investors the efficient
  markets model seems a good first (and second)
  approximation to reality. (416)
• Results conclusive
• In short, the evidence in support of the
  efficient markets model is extensive, and
  (somewhat uniquely in economics) contradictory
  evidence is sparse. (416)
• Just one anomaly admitted to
• Large movements one day often followed by large
  movements the nextvolatility clustering

43
The CAPM Evidence According to Fama 1969

• one departure from the pure independence
  assumption of the random walk model has been
  noted large daily price changes tend to be
  followed by large daily changes. The signs of the
  successor changes are apparently random, however,
  which indicates that the phenomenon represents a
  denial of the random walk model but not of the
  market efficiency hypothesis But since the
  evidence indicates that the price changes on days
  follow ing the initial large change are random in
  sign, the initial large change at least
  represents an unbiased adjustment to the ultimate
  price effects of the information, and this is
  sufficient for the expected return efficient
  markets model. (396)
• 35 years later, picture somewhat different

44
The CAPM Evidence According to Fama 2004

• The attraction of the CAPM is that it offers
  powerful and intuitively pleasing predictions
  about how to measure risk and the relation
  between expected return and risk.
• Unfortunately, the empirical record of the model
  is poorpoor enough to invalidate the way it is
  used in applications.
• The CAPM's empirical problems may reflect
  theoretical failings, the result of many
  simplifying assumptions
• In the end, we argue that whether the model's
  problems reflect weaknesses in the theory or in
  its empirical implementation, the failure of the
  CAPM in empirical tests implies that most
  applications of the model are invalid. (Fama
  French 2004 25)

45
The CAPM Evidence According to FF 2004

• Clearly admits assumptions dangerously
  unrealistic
• The first assumption is complete agreement given
  market clearing asset prices at t-1, investors
  agree on the joint distribution of asset returns
  from t-1 to t. And this distribution is the true
  onethat is, it is the distribution from which
  the returns we use to test the model are drawn.
  The second assumption is that there is borrowing
  and lending at a risk free rate, which is the
  same for all investors and does not depend on the
  amount borrowed or lent. (26)
• Bold emphasis model assumes all investors
  effectively know the future
• Assumptions, which once didnt matter (see
  Sharpe earlier) are now crucial

46
The CAPM Evidence According to FF 2004

• The assumption that short selling is
  unrestricted is as unrealistic as unrestricted
  risk-free borrowing and lending But when there
  is no short selling of risky assets and no
  risk-free asset, the algebra of portfolio
  efficiency says that portfolios made up of
  efficient portfolios are not typically efficient.
  This means that the market portfolio, which is a
  portfolio of the efficient portfolios chosen by
  investors, is not typically efficient. And the
  CAPM relation between expected return and market
  beta is lost. (32)
• Still some hope that, despite lack of realism,
  data might save the model

47
The CAPM Evidence According to FF 2004

• The efficiency of the market portfolio is based
  on many unrealistic assumptions, including
  complete agreement and either unrestricted
  risk-free borrowing and lending or unrestricted
  short selling of risky assets. But all
  interesting models involve unrealistic
  simplifications, which is why they must be tested
  against data. (32)
• Unfortunately, no such luck
• 40 years of data strongly contradict all versions
  of CAPM
• Returns not related to betas
• Other variables (book to market ratios etc.)
  matter
• Linear regressions on data differ strongly from
  risk free rate (intercept) beta (slope)
  calculations from CAPM

48
The CAPM Evidence According to FF 2004

• Tests of the CAPM are based on three
  implications
• First, expected returns on all assets are
  linearly related to their betas, and no other
  variable has marginal explanatory power.
• Second, the beta premium is positive, meaning
  that the expected return on the market portfolio
  exceeds the expected return on assets whose
  returns are uncorrelated with the market return.
• Third, assets uncorrelated with the market have
  expected returns equal to the risk-free interest
  rate, and the beta premium is the expected market
  return minus the risk-free rate. (32)

49
The CAPM Evidence According to FF 2004

• There is a positive relation between beta and
  average return, but it is too "flat." the
  Sharpe-Lintner model predicts that
• the intercept is the risk free rate and
• the coefficient on beta is the expected market
  return in excess of the risk-free rate, E(RM) -
  R.
• The regressions consistently find that the
  intercept is greater than the average risk-free
  rate, and the coefficient on beta is less than
  the average excess market return (32)

50
The CAPM Evidence According to FF 2004

• Average Annualized Monthly Return versus Beta for
  Value Weight Portfolios Formed on Prior Beta,
  1928-2003

• the predicted return on the portfolio with the
  lowest beta is 8.3 percent per year the actual
  return is 11.1 percent. The predicted return on
  the portfolio with the highest beta is 16.8
  percent per year the actual is 13.7 percent.
  (33)

51
The CAPM Evidence According to FF 2004

• The hypothesis that market betas completely
  explain expected returns
• Starting in the late 1970s evidence mounts that
  much of the variation in expected return is
  unrelated to market beta (34)
• Fama and French (1992) update and synthesize the
  evidence on the empirical failures of the CAPM
  they confirm that size, earnings-price, debt
  equity and book-to-market ratios add to the
  explanation of expected stock returns provided by
  market beta. (36)
• Best example of failure of CAPM as guide to
  building investment portfolios Book to Market
  (B/M) ratios provide far better guide than Beta

52
The CAPM Evidence According to FF 2004

• Average returns on the B/M portfolios increase
  almost monotonically, from 10.1 percent per year
  for the lowest B/M group to an impressive 16.7
  percent for the highest.
• But the positive relation between beta and
  average return predicted by the CAPM is notably
  absent the portfolio with the lowest
  book-to-market ratio has the highest beta but the
  lowest average return.
• The estimated beta for the portfolio with the
  highest book-tomarket ratio and the highest
  average return is only 0.98. With an average
  annualized value of the riskfree interest rate,
  Rf, of 5.8 percent and an average annualized
  market premium, Rm - Rf, of 11.3 percent, the
  Sharpe-Lintner CAPM predicts an average return of
  11.8 percent for the lowest B/M portfolio and
  11.2 percent for the highest, far from the
  observed values, 10.1 and 16.7 percent.

53
The CAPM Evidence According to FF 2004

• Average Annualized Monthly Return versus Beta for
  Value Weight Portfolios Formed on B/M, 1963-2003

• Simple regression of data gives opposite
  relationship to CAPM return rises as beta falls!

54
Beta is dead, long live?

• CAPM clearly a failure
• As predictor of stock market behaviour
• As guide to formation of return-maximising,
  risk-minimising portfolio
• Early success possibly due to unusual
  financial tranquility nature of post-WWII to
  1966 stock market
• New model of finance needed
• To explain behaviour of asset markets in general
• To guide portfolio selection
• Next week the developing Really New Finance
• The Inefficient Market Hypothesis
• The Fractal Market Hypothesis
• Chaos, heterogeneity and minority games