Transcript Macroeconomics Chamberlin and Yueh

Macroeconomics
Chamberlin and Yueh
Chapter 6
Lecture slides
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Financial Markets
• Efficient Markets: Asset Pricing Models
Expected Dividend Model, Gordon Model
Uncertainty and the Capital Asset Pricing
Model
• Portfolio Selection: Tobin Model
• Financial Market Volatility: Efficient and
Inefficient Markets
• Bubbles and Crashes in Financial Markets
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Learning Objectives
• Understand the nature of financial markets and why they
are an important determinant of consumption and
investment.
• Analyse the expected dividends model and the process of
arbitrage.
• Introduce the Capital Asset Pricing Model (CAPM), which
is a consumption based model that implies that assets with
higher returns offer less opportunity to hedge against
income risks.
• Discuss the Tobin model of portfolio selection, which
describes how investors choose the optimal combination of
risk and return in their portfolios.
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Learning Objectives
• Investigate the Efficient Markets Hypothesis (EMH) that
financial asset prices should reflect all available information
and that asset prices follow a random walk process.
• Evaluate the empirical tests which tend to reject the EMH
because the volatility of asset prices is greater than the
volatility of news regarding fundamentals.
• Define and learn about bubbles in financial markets, such as
the dotcom bubble in the late 1990s.
• Learn about crashes, which refer to a large and sudden drop
in market values, and the role of traders.
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Importance of financial markets
• We introduced the main features of the money market. In
doing so, we only considered two types of assets, money
itself and interest bearing bonds.
• This topic extends the analysis to look at financial markets
– by which we predominately mean the stock market. The
stock market is where equities, such as stocks and shares,
are traded and prices are determined.
• We have seen that stock market valuations play a very
important role in the economy.
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Efficient Markets: Asset Pricing
Models
• Financial markets are at the centre of the circular flow of
income and play an important allocative role by
intermediating between savers and borrowers. We examine
both efficient and inefficient financial markets.
• If financial markets are efficient, then the price of a
financial asset should reflect all available information
concerning the fundamentals of risk and return.
• In these circumstances, it would be expected that assets
which offer relatively high and certain returns would
accordingly be highly priced.
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Efficient Markets: Asset Pricing
Models
• We introduce two models of asset price determination.
• The first is what has been termed the expected dividend
model. This relates the price of an asset to the stream of
expected future dividends that the asset pays. The Gordon
model is a commonly used variant of this mode.
• The second model we consider is widely used in corporate
finance. The Capital Asset Pricing Model, or CAPM,
argues that the value of an asset is strongly related to its
ability to diversify risks.
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Expected Dividend Model
• Dividends and Expected Discounted Values
• A firm listed on the stock market has been split into a
number of shares, with each share representing ownership
of a certain proportion of the company. These shares are
marketable so their value is determined by demand and
supply.
• The total value of the company is found by simply
calculating its market value, that is, the number of shares
multiplied by the price of each share:
Vt  Nt  Pt
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Expected Dividend Model
• There are two elements that make up the returns from
holding shares.
• The first is the entitlement to a share of the firm’s earnings,
which are usually paid as dividends.
• The second arises from the gains or losses that accrue from
the resale value of the share. If the share price rises (falls)
in the period of ownership, then a capital gain (loss) is
made.
• These returns, though, are uncertain. The motive for buying
or holding a certain share must therefore come from its
expected future returns given the information available at
the time.
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Expected Dividend Model
•
•
•
•
Assume that:
Pt is the price of the financial asset at time t.
It is the information set available at time t.
The expected dividend paid, given this
information, is EDt 1 It 
• And, also conditional on the information
available, the expected asset price next
period is
EPt 1 It 
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Expected Dividend Model
• These values, though, will only be obtained in the next
period at time t+1. In order to present them in present (time
t) values, they need to be discounted by the interest rate
(1+r).
• The efficient price of the financial asset will therefore be set
equal to the expected discounted value of the future
dividend payment and resale price:
(6.1)
 
 
Pt  E Dt 1 I t  E Pt 1 I t

1  r 
• If the asset price were to deviate from this, then there would
be opportunities for traders to make profits.
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Expected Dividend Model
• The process which drives asset prices to their efficient
values is known as arbitrage.
• When people think of financial markets, they often think of
traders who are buying and selling assets in order to achieve
trading profits. These traders can be thought of as
arbitrageurs, who try and profit from mis-pricings and can
trade aggressively to do so, but the outcome will be to drive
asset prices toward fundamental values.
• By combining long and short positions, it is possible for a
trader to hold a portfolio that does not cost anything. For
example, its long positions in certain assets are funded by
short positions in others. For this reason, arbitrage can be a
strong phenomenon as traders can take positions in order to
profit from expected movements in asset prices.
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Expected Dividend Model
• The expected dividend model implies that the efficient
price of an asset can be written in terms of the stream of
future expected discounted dividend payments the asset
generates.
• Rewriting solely in terms of future divident payments, the
expected price of the asset at time t+1 will be determined in
exactly the same fashion as it was in time t:
(6.2)
EPt 1 It   EDt  2 It   EPt  2 It  1  r 
• If priced efficiently, the expected price of the asset at time
t+1 will equal the sum of the expected discounted dividend
payment and asset price at time t+2.
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Expected Dividend Model
• If (6.2) is substituted into (6.1), then a new equation for the
asset price at time t can be derived:
(6.3) P  ED I   ED I   EP I  1  r  1  r 
t

t 1
t

t 2
t 2
t
• Alternatively, this can be written as:
(6.4)
Pt 
E Dt 1 I t 
1  r 

E Dt  2 I t 
1  r 2

t


E Pt  2 I t 
1  r 2
• Therefore, the current price of the asset is equal to the
expected discounted dividend payments over the next two
years and the expected discounted resale price in two periods’
time. Note that the payments which accrue two periods in the
future are discounted twice.
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Expected Dividend Model
• The expected asset price in two periods’ time would be
equal to the sum of the expected discounted dividend
payment and asset price in time t+3:
(6.5)
EPt  2 It   EDt 3 It   EPt 3 It  1  r 
• Substituting (6.5) into (6.3) gives the current asset price as a
function of dividends over the next three periods and the
asset price at time t+3:
(6.6) Pt  EDt 1 It   EDt 2 It   EDt 3 It   EPt 3 It  1  r  1  r  1  r 
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Expected Dividend Model
• This can be seen more clearly by rearranging
the above:
(6.7)
Pt 
E Dt 1 I t 
1  r 

E Dt  2 I t 
1  r 
2

E Dt  3 I t 
1  r 
3

E Pt  3 I t 
1  r 3
• Once again, note that the values which
accrue in three periods’ time are discounted
three times.
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Expected Dividend Model
• By continuing this repeated substitution to infinity, we can
derive a very simple formula for the fundamental value of
an asset solely in terms of its dividend stream:
(6.8) Pt  EDt 1 It   EDt  2 2It   EDt 3 3It   ...........  EPt  It 
1  r 
1  r 
1  r 
1  r 
• Payments that arise a substantial time in the future are
discounted more heavily, so in present value terms their
value will head to zero. Therefore, we would expect that as
time goes to infinity that the expected discounted asset price
will head towards zero.
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Expected Dividend Model
• This leaves the current asset price as being
determined by just the stream of expected
future discounted dividend payments:
(6.9)


Pt   E Dt i I t
i 1

1  r  i
• Equation (6.9) is the essentially the same as
(6.1).
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Expected Dividend Model
• The expected dividends model is fairly intuitive in
that it links asset values according to the returns
that the asset produces. If all assets are priced at
their efficient levels, then investors will obtain the
same rate of return regardless of which asset they
buy. This will be the rate of interest , so the
investor will also be indifferent between holding
any asset and bonds.
• This model is quite simple, but it can be used to
analyse the causes of stock market changes. These
broadly fall into two categories.
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Expected Dividend Model
• The first is any factor that is likely to affect the flow of
future dividend payments, which are in turn derived from
the firm’s earnings. This could be almost anything – a
technological breakthrough, changes in the management
structure, specific government regulations, the state of the
economy and consumer demand, the condition of the firm’s
competitors, and so on.
• The second is the interest rate, which represents the
opportunity cost of holding equities, as any investor could
always invest in bonds instead. It is easily seen from (6.9)
that higher interest rates imply future dividend payments are
more heavily discounted, so share prices would be expected
to fall.
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Gordon growth model
• A simple variant of the expected dividend model is
the Gordon model.
• This uses exactly the same framework as above,
but specifies a rule that describes how dividends
grow over time.
• This model reaches broadly the same conclusions,
but is widely used due to its simplicity.
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Gordon growth model
• The most important assumption is that
dividends grow at the rate of g each period.
Therefore:
Dt 1  (1  g ) Dt
Dt  2  (1  g )Dt 1  (1  g ) Dt
2
Dt 3  (1  g )Dt  2  (1  g ) Dt
3
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Gordon growth model
• If we substitute this dividend stream into
(6.8), then the current asset price can be
written as follows:
(6.10)
Dt 1  g  Dt 1  g  Dt 1  g 
Pt 


 ..........
2
3
1  r 
1  r 
1  r 
2
3
The expression in (6.10) can be simplified
further to produce a very simple rule for
asset prices.
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Gordon growth model
• The first step is to factorise (6.10) by collecting the
common term on the right hand side:
(6.11)
 1  g   1  g 2  1  g 3

P  Dt 

 
  .......
 1  r   1  r   1  r 

• Next, we need to make an assumption that the
growth rate is less than the interest rate:
1 g 

 1
 1 r 
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Gordon growth model
• In (6.11), the terms in the square brackets can be simplified by using the
 1 g  
rule for finding a sum to infinity:


 1 r 
 
Pt  Dt  
 1 g 
1   1  r  


• Which, in turn, can be simplified to:
• Because
1  g 
Pt  Dt 

r

g


D1  (1  g ) D0
• The Gordon model is:
Dt 1
Pt 
rg
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Gordon growth model
• There are two factors which determine the price of a financial
asset.
– The first is the interest rate – as this rises, the efficient asset price falls.
– The second is the growth rate of dividend payments. The implication
here is that firms which experience higher earnings growth will be
valued more. We could reinsert the notion of uncertainty by arguing
that it was expected rather than actual growth which mattered. This
means that asset prices will be determined by any number of factors.
• The discounted dividend and Gordon models are essentially
the same and relate asset prices to company earnings.
However, these basic models do not consider the impact of
different risks and uncertainties on asset prices.
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Uncertainty and the Capital Asset
Pricing Model
• The expected discounted dividend model is widely used,
but lacks one important ingredient.
• Assets are valued in accordance with their income streams,
so assets with a command over higher future dividends will
have a greater price.
• However, there is one important ingredient that is missing
in valuing assets this way – risk.
• We now introduce the Capital Asset Pricing Model
(CAPM) in which assets are valued in terms of their ability
to diversify risks.
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Capital Asset Pricing Model
• This is a consumption-based model. Asset pricing
models of these types are driven by the law of
diminishing marginal utility of consumption. This
states that as consumption increases, total utility
increases but at a declining rate.
• This has important implications for the pattern of
consumption over time. One of the main features
of the Permanent Income Hypothesis is that
smoothing consumption over time is consistent
with utility maximising behaviour.
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Capital Asset Pricing Model
• Under the Permanent Income Hypothesis, consumption can
be smoothed over time by using saving and borrowing to
offset transitory movements in consumption. It is less
obvious how an individual can smooth consumption over
different states of the world, although it would be logical to
do so from the standpoint of maximising expected utility.
• This is where financial markets have a role to play.
Different assets will generate different returns in different
states of the world, giving investors an opportunity to
manage risks and uncertainty. Using financial assets to
diversify wealth or income uncertainties is the guiding
principal behind consumption-based models, which argue
that assets should be priced in accordance to their abilities
to do this.
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CAPM Model
• The CAPM model argues that assets should be valued
according to their degree of income diversification.
• The law of diminishing marginal utility of consumption
implies that as consumption increases, the marginal utility
of an extra unit of consumption falls.
• In terms of pricing assets, this implies that dividend
payments paid in periods of high income, and therefore high
consumption, should be weighted less than dividends paid
in periods of low income.
• This is because although they might have similar money
values, they have very different values in terms of utility.
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CAPM Model
• Incorporating this feature into the asset pricing model in
(6.9) yields the following:
MU E Ct i | I t  E Dt i I t 
Pt  
i


MU
C


1

r
i 1
t
• The expected dividend model is extended so that the
expected discounted dividends in the future are weighted
according to the marginal utility of expected consumption
in each period.
• This means that expected dividend payments in times when
expected consumption is expected to be high will be
weighted less than the same dividend payment in a time
where the level of expected consumption is low.
(6.15)

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CAPM Model
• This relationship underlies the CAPM model.
• The higher the covariance of an asset’s returns with the
marginal utility of consumption, the lower is the value of
the asset.
• An asset where returns are negatively correlated with the
marginal propensity to consume will be worth more because
it enables the holders to hedge against low consumption.
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CAPM Model
• The CAPM pricing rule can be derived in the following fashion:
• the expected return on an certain asset i is E R
 i
• the expected return from holding the market portfolio is
Erm 
• If Rrf is the expected return on a risk-free asset, then it is possible to
write the following identity:
(6.16) E Ri  Rrf  E Ri  Rrf
 


• The market portfolio is where the same amount of each asset is held.
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CAPM Model
• The CAPM relationship can now be written in the following
way:
(6.17) ERi   Rrf  i ERm   Rrf
• For each asset, the excess return over the risk-free rate is
related to the excess return of the market portfolio over the
risk-free rate of return by the coefficient, βi.
• This is the central element of the CAPM model.
• Each Beta gives an indication as to how an asset can be
used to diversify risks.


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CAPM Model: β
• If βi=1, then the returns of asset i move directly in line with
the market portfolio. In fact, asset i is the market portfolio.
As the market portfolio is expected to move in line with the
economy as a whole, this asset would not be expected to
diversify income.
• If βi<1, then the returns of asset i move less than the market
portfolio. This offers individuals the ability to diversify
income shocks. For example, if 0< βi<1, then following a
fall in the overall stock market, the fall in the returns of
asset i would be correspondingly less.
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CAPM Model: β
• It is even better in terms of diversification if βi<0, as the
asset returns are negatively correlated with movements in
the market portfolio, which offers a more complete
opportunity to diversify income risks.
• If βi>1, then the returns on asset i would be more volatile
than movement in the market as a whole.
• The CAPM relationship in (6.17) is known as the market
line.
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CAPM Model: The market line
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CAPM Model: Summary
• Assets that offer higher expected returns have
higher betas, whereas the assets that offer lower
returns have lower betas.
• The market line reflects a trade-off between risk
and return from holding different portfolios of
assets.
• Those which offer high expected returns are more
risky, as they offer limited ability to diversify
income.
• On the other hand, assets with low expected returns
offer the compensation of a low beta, so are better
able to hedge against low income.
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Portfolio selection: Tobin model
• The relationship between risk and return, and the
optimal amount of each asset that an investor
desires to hold, is explained in the Tobin model of
portfolio selection.
• A portfolio represents the combination of different
assets that an investor holds.
• The overall risk and return of the portfolio will
reflect the composition of the assets in the
portfolio.
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Tobin model of portfolio selection
• Assume for simplicity there are two types of assets.
• The first is a risk-free asset which offers a
guaranteed rate of return Rrf with zero variance:
 rf2  0
• The second is a risky asset which offers a higher
rate of return, but these returns are uncertain and
have a positive variance:
 r2
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Tobin model of portfolio selection
• A portfolio can be constructed by choosing a combination of these two
assets, with a proportion w of the risky asset and (1-w) of the risk-free
asset.
• The expected return from the portfolio is derived as follows:
(6.18a)
ERp   w * ERr   1  w* Rrf
• As the proportion of the risky asset in the portfolio increases, the
expected return also increases.
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Tobin model of portfolio selection
• Equation (6.18a) can be rearranged,
 


(6.18b) E Rp  Rrf  w * ERr   Rrf
• The riskiness of the portfolio, though,
depends on the relative variances of the two
assets.
• The variance of the portfolio is then:
(6.19) 2
2
2
2
2,
 2  w2 * 2
 p  w *  r  1  w *  rf
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p
r
Tobin model of portfolio selection
• This can be rearranged so that the weight w
can be expressed as the ratio of the standard
deviation of the portfolio to the risky asset:
2
2


w
*

(6.20) p
r  w * r ,
p
w  gives us an
Substituting this ratio into (6.18)
r
equation which describes the risk return
trade-off that the investor faces:

(6.21) ER   R   * ER   R 
p
p
rf
r
rf
r
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Tobin model of portfolio selection
• Equation (6.21) fully describes the risk return
trade-off an investor faces.
• The excess expected return of the portfolio over the
risk-free asset increases as the proportion of the
risky asset in the portfolio increases. However, the
variance of the returns will increase as a result.
• Plotting (6.21) on a set of axis graphically shows
the risk return trade-off, which has a very similar
form to the market line derived in the CAPM.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Tobin model of portfolio selection
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
CAPM vs. Tobin’s model
• The only difference between the CAPM and Tobin
models is how risk is measured.
• In the CAPM model, risk is determined in terms of
the beta – with a higher beta indicating that the
portfolio has less ability to hedge against income
uncertainties.
• In Tobin’s model, the risk of a portfolio is defined
in terms of the variance or uncertainty of asset
returns.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Tobin model of portfolio selection
• The assumption of there being only two assets is just a
simplifying assumption. If there were many assets, the
same trade-off between risk and return would exist, but
would reflect the minimum variance of each portfolio for
every level of expected returns.
• It would still be the case that as the portfolio becomes more
risky, the expected returns would increase to reflecting a
risk premium.
• The Tobin model describes how investors choose the risk
and return composition of their portfolio.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Tobin model of portfolio selection
• It is assumed that each trader has preferences over risk and
return which can be represented in a utility function:
(6.22)
U  U R, 
• This utility function generates a suite of indifferences
curves, which shows the combinations of risks and return
that gives the investor a given level of utility. These
indifference curves are upward sloping because investors
see returns as a good thing, but risk as a bad thing.
Therefore, as the investor is forced to hold a portfolio with
greater risk, they require higher returns in order to keep
their utility at the same level.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Investor’s utility function
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Tobin model of portfolio selection
• The slope of the indifference return reflects the rate at
which the investor is prepared to trade-off risk for return.
• The utility maximising decision of the risk and return
structure of the portfolio is found by moving on to the
highest possible indifference curve, subject to the market
line which determines the feasible risk-return combinations
available.
• The choice of portfolio will be predominately determined
by the preferences of the investor. Those who are less risk
averse will likely have an optimal portfolio offering higher
risks but also higher expected returns. The opposite would
apply to more risk adverse investors.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Utility maximisation
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
CAPM vs. Tobin’s model: Summary
• The CAPM and Tobin model both introduce the element of
risk into asset pricing.
• The expected dividend model implies that assets which
offer higher returns should be valued more highly.
• However, if these greater risks simply reflect the existence
of a risk premium, then it is not necessarily the case that
investors will choose to hold assets with higher expected
returns.
• If investors are sufficiently risk averse, their optimal
portfolio might consist of lower return but safer assets.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Financial Market Volatility: Efficient
and Inefficient Markets
• The Efficient Markets Hypothesis (EMH) has been the
central proposition in finance theory since Fama first
presented the idea in 1970.
• In its most basic form, it just implies that prices in financial
markets fully reflect the available information as in the
expected dividend model in (6.9).
• The strong implication is that any investor cannot hope to
consistently beat the market because arbitrage is strong
enough to correct any mis-pricings. Spending vast
resources on trying to gain an informational advantage
would be wasted as all information will be correctly and
quickly incorporated into asset prices; it would be better to
passively hold the market portfolio.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The Theoretical Foundations of the
EMH: Arbitrage
• There are several foundations to the EMH. Firstly,
investors are assumed to be rational so that financial assets
are valued according to the expected discounted value of
future dividends as explained in (6.9).
• If investors are rational, financial asset prices will reflect all
available and relevant information, and market efficiency
will prevail as assets are priced according to their
fundamental values.
• To the extent that some traders are irrational, then their
trades are assumed to be random and therefore will cancel
each other out. Hence, asset prices will continue to trade at
prices close to fundamental values.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The Theoretical Foundations of the
EMH: Arbitrage
• However, it is the force of arbitrage that acts as the ultimate
defensive line for the EMH driving asset prices towards
their fundamental values.
• Arbitrage has a further implication. Irrational investors lose
money, but as Friedman pointed out in 1953, they cannot
continue to lose money forever. Eventually they will
become less wealthy and disappear from the market. So,
even if arbitrage cannot eliminate their effects on asset
prices, market forces will eventually act to eliminate them
from the market. Therefore, even if arbitrage is limited,
competitive selection means that market efficiency will
prevail.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The Econometrics of the EMH
• The EMH implies that the prices of financial assets include
all the available information regarding the expected future
earnings of that asset.
• Because this new information is unpredictable, financial
assets are said to follow a random walk process:
(6.23)
Pt  Pt 1   t
where εt is a stochastic term which represents news
innovations.
• The change in asset prices solely reflects the arrival of new
news:
Pt   t
(6.24)
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The Econometrics of the EMH
• As new information is always arriving in the
market, we would expect prices to be continuously
changing.
• Therefore, volatility in financial asset prices
shouldn’t necessarily be unexpected or regarded as
unfavourable.
• As new information is always coming to markets,
the quick and continuous reaction of asset prices is
part of the efficient pricing process.
• Volatility in financial asset prices is not at in
conflict with the predictions of the EMH.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Financial Times Stock Exchange
(FTSE)
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The Econometrics of the EMH
• It is clear that daily changes in prices are indeed volatile.
• We see that stock market prices, although volatile on a daily
basis, tend to trend upward over time.
• This reflects the fact that economies grow over time and
this growth is reflected in the fundamental values of assets.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
The Econometrics of the EMH
• Because of this, a better description of the process
driving asset prices is a random walk with drift:
(6.25) Pt     t
• This states that the change in asset prices is equal
to a constant and an innovative factor.
• A random walk with drift process will be a series
that is volatile, but fluctuates around a trend line,
so will grow over time.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Efficient Markets Hypothesis: A Critique
• In the first decade after its inception, the EMH was an
enormous empirical and theoretical success.
• However, over the course of the following 20 years, there
have been a growing number of challenges to the theoretical
foundation of the EMH and the evidence supporting it.
• The key forces by which markets are supposed to attain
efficiency, such as arbitrage, are likely to be less powerful
than efficient markets theorists first believed.
• With new theory and evidence, behavioural finance has
emerged to provide an alternative view of financial markets.
Systematic and significant deviations from efficient prices
can therefore be expected to persist for long periods of time.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Efficient Markets Hypothesis: A Critique
• A simple empirical/econometric test for the EMH is simply
to test asset prices for the presence of a random walk. From
the above, it must be true that if the EMH holds, then the
variance of stock market changes should equal the variance
of the innovations that underlie them.
• This presents an intuitive way to test the ramifications of
the EMH: can changes in asset prices be related to changes
in news about fundamentals?
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Efficient Markets Hypothesis: A Critique
• Shiller’s (1981) work on stock market volatility, which
showed that stock market prices are far more volatile than
can be justified by a simple model in which prices are equal
to the expected net present value of future dividends. This
suggests that financial markets may react to noninformation.
• The most salient piece of evidence concerning this is the
1987 stock market crash. The surprising feature of this
crash is that no news or announcements could be identified
as the source of this crash. In fact, many sharp movements
in asset prices seem not to appear to accompany significant
news.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Efficient Markets Hypothesis: A Critique
• An interesting and similar conclusion was reached by Roll
(1988).
• He calculates the share variation in the returns of large
stocks explained by aggregate economic influences, the
contemporary returns on other stocks in the same industry,
and public firm-specific news events.
• He finds that only 35% of the total volatility in share prices
can be accounted for by this information on monthly data,
and only 20% on daily data. This again implies that
movements in stock prices are largely unaccounted for by
public news.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Efficient Markets Hypothesis: A Critique
• According to the EMH, changes in asset prices should be
unpredictable from past data.
• This is simply because past information will have already
been incorporated into asset prices if traders are rational and
markets are efficient. In this case:
(6.26)
Pt  Pt 1   t
• For the EMH to describe asset prices, it is required that β=0,
i.e., no past changes in prices are significant determinants of
current price changes.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Efficient Markets Hypothesis: A Critique
• Work by DeBondt and Thaler (1985) finds against the
notion that past information cannot be used to predict future
asset prices, implying that β0.
• They compare the performance of two groups of
companies: extreme losers and extreme winners. For each
year since 1933, they form portfolios of the best and the
worst performing stocks over the previous three years.
They then compute the returns of these portfolios over the
following five years and find that the extreme loser
portfolio does significantly better than the extreme winner
portfolio. The explanation is that stock prices overreact;
extreme losers become too cheap and bounce backwards,
whereas the extreme winners become too expensive and
must subsequently fall.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Efficient Markets Hypothesis: A Critique
• The upshot is that there is substantial empirical evidence
which points towards a rejection of the EMH.
• Volatility analysis (event studies) implies that financial asset
prices appear to have larger variance than the fundamentals
they claim to be built upon.
• Also, changes in asset prices may not be totally
unpredictable, with past price changes being an indicator of
current and future movements.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Theoretical Challenges to the EMH
• There are countless examples of where contagion,
mimicking or herding may be important in financial markets.
It can also offer an intuitive explanation as to why financial
asset prices may be excessively volatile.
• It is now no longer the case that financial market participants
just react to news about fundamentals; they must also react
to the reactions of other financial agents.
• Ultimately though, the theoretical case for efficient markets
depends upon the effectiveness of arbitrage. Even if
irrational traders lead asset prices away from fundamental
values, arbitrageurs will seek to profit from the mis-pricings
and in so doing reinforce efficient pricing. However, a
central concept of behavioural finance is that arbitrage is
risky, and therefore limited. The finite risk bearing capacity
of arbitrageurs reduces their ability to bring prices fully into
line.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Noise Trader Risk in Financial
Markets and the EMH
• Arbitrage is an important feature of financial markets, as its
effect is to bring prices towards fundamentals and keep
markets efficient.
• The most common explanation for complete arbitrage is the
presence of transaction costs or imperfect substitutes.
• The type of risk we are concerned with here is mis-pricing
that can worsen in the short run. These types of movements
are very important for short horizon investors engaged in
arbitrage against noise traders: this is the risk that noise
traders’ beliefs become more extreme before reverting to
the mean.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Noise Trader Risk in Financial
Markets and the EMH
• If noise traders are pessimistic about an asset and have
driven its price downwards, an arbitrageur who buys this
asset must accept the possibility that in the near future noise
traders may become even more pessimistic and drive the
price down further.
• If the arbitrageur is forced to liquidate his asset holding
before the price recovers, then they face a loss. Fear of this
loss may limit the original arbitrage position.
• It is the risk of further movements in noise traders’ beliefs
away from the mean (this is what noise trader risk is
defined by) that must limit the willingness to bet against
noise traders.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Noise Trader Risk in Financial
Markets and the EMH
• The result of limited arbitrage is that substitute
assets may end up selling at two different prices, an
outright contradiction of the EMH.
• Mis-pricing can lead to enormous inefficiencies
that in the absence of arbitrage behaviour can be
sustained.
• As a result large deviations of prices from
fundamental values may arise from risky arbitrage
that takes some time to correct.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Example: U.S. Stocks
• An example may help to illuminate the idea of risky and
limited arbitrage.
• Consider the case of American stocks in the late 1990s. At
the end of 1998, large U.S. corporations were trading at
some of their historically highest market values relative to
most measures of their profitability. For example, the ratio
of market value of the S&P 500 relative to the aggregate
earnings of the underlying companies stood at 32, compared
to the post war average of 15.
• However, there are not many good substitutes for the whole
S&P 500 market. In fact, any arbitrageur that tried to
exploit this apparent mis-pricing would probably have gone
out of business.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
S&P 500, 1990-2003
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Example: Royal Dutch Shell
• Fundamentally identical assets should trade at identical
prices; this is just the workings of arbitrage. However, this
is not always the case, and the presence of noise trader risk
appears to explain price divergences.
• A 1907 alliance between Royal Dutch and Shell Transport
in which the two companies agreed to merge their interests
on a 60:40 basis, while remaining separate and distinct
entities. The only real difference between the two firms is
that Royal Dutch trades in Holland and on the U.S. S&P
500, whilst Shell trades predominately in the UK on the
FTSE.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Royal Dutch Shell: percentage deviation from the
60:40 ratio in market values
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© 2006 Cengage Learning
Example: Royal Dutch Shell
• Between September 1980 and September 1995, there was a
tremendous amount of deviation, from an underpricing of
35% to an overpricing of 10% of Royal Dutch relative to
Shell. It takes about 4 years for the 30% mis-pricing of
Royal Dutch and Shell that was prevalent in September
1980 to eventually disappear. In return for bearing this risk,
the arbitrageur earns about 7% per year.
• For reasons such as the costs of leveraging, and the
presence of possible liquidation should further mis-pricing
occur, arbitrageurs may have found it unattractive to
arbitrage in September 1980, even with a 30% mis-pricing
of two identical securities.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Noise Trader Risk in Financial
Markets and the EMH
• Therefore, mis-pricing can be seen to take a while
to correct, and so enormous inefficiencies can be
maintained without aggressive arbitrage activity
coming in to correct them.
• From the point of view of the EMH, this is crucial
as it suggests that even with identical securities
noise trader risk may be large enough to cause
large and sustained price deviations from
fundamental values.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Professional Arbitrage
• Effectively, so far we have considered arbitrageurs who use
their own wealth to trade, and therefore are limited by their
own risk aversion.
• In reality, arbitrage is conducted by relatively few
professional, highly specialised investors who combine
their knowledge with the resources of outside investors to
take large positions. In this respect, traders and financers
are separated by an agency relationship.
• When the arbitrageur is managing other people’s money,
and his investors do not fully understand what he is doing,
they can only observe him losing money if prices happen to
move further out of line from fundamental values.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Performance based arbitrage
• The responsiveness of funds under management to past
returns is referred to as performance based arbitrage
(PBA). Investors may rationally allocate funds based on the
past returns of arbitrageurs, and withdraw funds after poor
performance.
• Consequently, arbitrageurs become less aggressive in
betting against mis-pricing.
• Performance based arbitrage is extremely ineffective in
extreme circumstances when prices are substantially out of
line and arbitrageurs are fully invested. In such panics,
arbitrageurs may bail out of the market, voluntarily or not,
exactly at the point of time where their participation is most
needed.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Bubbles and crashes in financial markets
• Much volatility in financial markets thus results
because herding behaviour or irrational investors
are allowed to influence market prices, as their
actions will not be corrected by arbitrage.
• This means that trading on noise rather than
fundamentals may come to drive market prices.
• We now turn to look at two important cases of
financial market volatility – bubbles and crashes.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Bubbles and crashes in financial markets
• A bubble sees long sustained rises in prices away from
fundamental values. Bubbles are characterised by their
self-fulfilling nature. Even if investors know that prices are
over-valued, the anticipation that prices will rise further
makes further acquisition of the asset profitable. Therefore,
prices can rise in a marked fashion for a considerable period
of time.
• Crashes refer to sudden and sharp drops in market prices.
This need not be at odds with market rationality. It could be
the case that a crash results from the arrival of very bad
news. Also, a crash may manifest itself in a collapsing
bubble, which should just be seen as a correction in market
prices.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Bubbles and crashes in financial markets
• However, there are also examples of sharp asset price drops
that cannot be related to either of these explanations;
therefore, there may be something inherently irrational
about them in that prices are driven down to unjustifiably
low levels.
• The October 1987 stock market crash is a recent example
which will form the basis of some brief analysis.
• The next figure plots the recent history of the NASDAQ
and the S&P500 stock market indices since 1990.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
NASDAQ, S&P, 1990-2002
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Dot Com Mania
• There is clear evidence of a dramatic rise in U.S. share
prices during the period 1995-2000, followed by a large
collapse over the following two years, a pattern which is
highly indicative of a bubble and its bursting.
• Between 1995 and 2000, it is possible to see that the S&P
500 doubled in value, but this trend is hard to observe when
it is pitted against the almost 10-fold increase in the
NASDAQ. The NASDAQ is the index on which the new
technology shares are traded.
• Because the dramatic rise in the stock market was driven by
IT companies, and especially those involved in internet
technologies, this period has been widely christened as Dot
Com Mania.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Bubbles and crashes in financial markets
• When stock prices start to increase quickly, further price
rises are fuelled by others who jump on the bandwagon
through fear of missing out on easy profits. However, for
this process to begin, there has to be something that justifies
an initial strong rise in prices. These reasons will also
provide comfort for those who continue to buy at higher and
higher prices who can be convinced that stock markets offer
a one-way bet.
• Two of the arguments put forward justifying the strong rise
in share prices were as follows.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Bubbles and crashes in financial markets
• Firstly, the New Economy over the late 1990s. This
galvanised the strong belief that the U.S. was at the outset
of a new golden economic era and asset prices should rise
to reflect this.
• The second relates to the idea that it takes time for new
technology to be represented in asset prices. Information
technology began to emerge in the 1960s; the sharp rise in
asset prices during the 1990s simply reflects the New
Economy firms replacing the Old Economy firms in the
stock market listings.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Irrational exuberance
• The emergence of ICT and the New Economy may certainly
have provided some grounds for an increase in stock market
prices. However, was the scale of this rise justified when
compared to fundamentals such as earnings?
• The price-earnings ratio is the price of a share divided by
the level of corporate earnings per share. The next figure
plots the price-earnings ratio for the S&P 500 index over a
120 year period. It is clear that this ratio grows
dramatically during the latter half of the 1990s, indicating
that share prices had risen substantially compared to
earnings.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Price-earnings ratio for the S&P 500
index over a 120 year period
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Irrational exuberance
• It is justifiable for current share prices to rise without seeing
an increase in current earnings?
• This is because the current share price will reflect the
present discounted value of future earnings, so the
expectation of strong future earnings would lead to an
increase in current prices. However, with hindsight, it
appears that share prices had been driven to values way in
excess of fundamentals.
• Alan Greenspan famously referred to this as irrational
exuberance. The large downward correction in share prices
between 2000 and 2002 acted to bring the price-earnings
ratio back towards its long run average.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Crashes: The 1987 Stock Market
Crash and the Trading Mechanism
• While financial markets are intrinsically volatile, some of
the sharper movements are harder to explain in terms of
existing models. The crash on October 19th, 1987 led to
losses of around $700 billion, amounting to about 20% of
the total pre-crash stock value of $3.5 trillion.
• This dramatic fall, though, was brought on by a much
smaller amount of selling in comparative terms. Although
trading on this day was three times the average, only $6
billion (0.2% of total equity value) worth of trades were
responsible for this huge collapse in prices.
• The curiosity was how such a small amount of selling could
explain such a large decline in stock prices.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
NYSE, Jan.-Oct. 1987
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© 2006 Cengage Learning
Fundamentals vs. the market mechanism
• According to the predictions of the EMH, the large decline
in asset values should be associated with announcements of
bad news concerning the fundamental values of equities.
Preceding the crash, there were pieces of bad economic
news:
– Press speculation concerning the Federal Reserve raising the
discount rate.
– Fed announced decision to depreciate the $ against the DM
– U.S. bombing of an Iranian oil platform in the Gulf
– Trade deficit was worse than expected by about $1.5 billion
• However, none of these could be deemed significant enough
to match the huge fall in asset prices.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Fundamentals vs. the market mechanism
• In financial markets a wide variety of order types can be
found. The most common are price contingent orders.
• In the years preceding the crash, two important changes
occurred in the U.S. and also in other global stock
exchanges.
• Firstly, trading became electronic.
• Secondly, over the course of the 1980s, trading came to be
dominated by large institutional investors. The execution of
one stop order could create a cascade of similar executions.
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by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Summary
• Financial markets are where financial assets are traded. The
value of financial assets is an important determinant of
consumption and investment.
• The expected dividends model implies that the value of an
asset is equal to the expected present discounted value of its
earnings (such as dividends). This can be thought of as the
fundamental value of an asset. The Gordon model is a
simplified version of the expected dividends model which
relates asset valuations to the growth in dividend payments.
The process of arbitrage- where traders act to profit from
the over or under pricing of financial assets- acts to drive
asset prices towards fundamental values.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Summary
• Assets with higher returns might be riskier- and therefore
asset pricing models ought to value both risk and return.
The Capital Asset Pricing Model (CAPM) is a consumption
based model which implies that assets with higher returns
offer less opportunity to hedge against income risks. The
CAPM beta reflects the covariance between an asset’s
returns and those of the market portfolio. The higher the
beta, the lower the ability to hedge.
• The Tobin model of portfolio selection describes how
investors choose the optimal combination of risk and return
in their portfolios.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Summary
• The Efficient Markets Hypothesis (EMH) states that
financial asset prices should reflect all available
information. As a result, whenever new information arrives
at the market asset prices will change quickly to reflect it.
This implies that asset prices follow a random walk process.
• Empirical tests tend to reject the EMH as the volatility of
asset prices is greater than the volatility of news regarding
fundamentals. One of the explanations for this is the
presence of noise trader risks. Because asset prices might
become more mis-priced before moving to fundamental
values the power of arbitrage is less than the EMH suggests.
Therefore, financial market mis-pricings (inefficiencies) can
be sustained for long periods of time.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning
Summary
• A bubble refers to the self-fulfilling process where asset
prices are driven upwards by the expectation of further
increases in prices. As a result asset prices can rise to levels
far in excess of fundamentals. The strong rise in US stock
markets (particularly the NASDAQ) during the second half
of the 1990s is an example relating to the boom in the share
prices of new technology firms.
• A crash refers to a large and sudden drop in market values.
These can result from a sudden deterioration in
fundamentals, but also through the sharp unwinding of a
bubble. The October 1987 crash demonstrates the roles that
the market-mechanism and the strategies of traders can play
in precipitating a sudden collapse in prices.
Use with Macroeconomics
by Graeme Chamberlin and Linda Yueh ISBN 1-84480-042-1
© 2006 Cengage Learning