1Market Efficiency

1
1Market Efficiency

• This section is all about how information is
  used. Information determines prices in
  derivative markets.
• Suppose that
• Markets are frictionless in that there are no
  transactions costs assets are divisible can be
  bought or sold and there are no trade-impeding
  regulations.
• There is perfect competition in product and
  security markets.
• Information is free and available to all at the
  same time.
• All economic agents are rational and seek to
  maximize expected utility.

2
2Perfect Capital Markets

• Under these circumstances, capital markets are
  said to be perfect. The assumptions may be
  criticized in many ways. How?
• As investors, we are interested in whether asset
  prices fully and immediately reflect available
  information. Under perfect capital markets, this
  will be true. If conditions 3 and 4 hold, then
  capital markets are said to be informationally
  efficient.
• Venn diagram.

3
3Informationally Efficient Capital Markets
Market Environment Space
Informationally Efficient Capital Markets
Perfect Capital Markets
4
4Are Markets IE?

• Perfection is a bit too much to ask for. We
  might have to settle for informational
  efficiency. Are markets IE?
• Academics have concluded that markets are
  probably fairly IE, but not totally so. They are
  certainly not perfect.
• To test for IE, we must clarify what constitutes
  information in our definition. There are three
  main forms.
• Defn Weak Form IE (WFE) is where all information
  that can be extracted from past prices in the
  market (i.e., past returns) is already reflected
  in present prices.

5
5WFE

• If true, then the WFE hypothesis is satisfied.
  Its implication for investors is that the
  analysis of any past prices cannot assist in
  generating returns surplus to those due to the
  opportunity cost of capital and due to the
  systemic risk taken on.
• If a) the CAPM returns generating process
  pertains, and b) markets are WFE, then your rate
  of return should be rj,t1 rf
  Et(rm,t1) - rf ?j ej,t1.
• Here, rj,t1 return on asset j over (t, t1,
  rf risk-free rate of return, Et(rm,t1) time
  t expected rate of return on the overall market
  over (t, t1, ?j sensitivity of asset j to
  market rates of return, ej,t1 random
  component with mean value 0 and is independent of
  past prices.

6
6Semi-Strong Form IE

• Defn In a semi-strong form informationally
  efficient market (SSFE), all information that can
  be extracted from the set of all publicly
  available data is already reflected in present
  prices. If true, then the semi-strong form
  efficient market hypothesis pertains.
• Note, if the big speculators can cheaply obtain
  and analyze all pertinent publicly available
  information, then this hypothesis should hold.
  The advent of cheap information technology makes
  it more likely to hold. But if you get the
  information before the rest of the public, then
  there are profit opportunities (Battle of
  Waterloo).

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7Strong Form IE

• Defn In strong form informationally efficient
  market (SSFE), all information that can be
  extracted from the set of all data (public or
  private) is already reflected in present prices.
  If true, then the strong form efficient market
  hypothesis pertains.
• We can compare the three hypotheses and the
  associated information sets in two different
  ways as contained data sets and as contained
  spaces of environmental circumstances.

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8IE Data Set Relations

• Sizes of Data Sets

All Information
WFE
SSFE
SFE
9
9IE Relationships between Environmental
Circumstances

• The circumstances under which SFE hold are far
  more stringent than those under which WFE hold
• Set of Environmental Circumstances

All Circumstances
WFE
SFE
SSFE
10
10Economics of IE

• Information feeds into prices, and prices give
  signals for the allocation of resources. High
  commodity/security prices imply that someone has
  made a lot of money. Profit seekers then
  investigate why these prices are high, and how
  they also can attain profits.
• In this way, prices direct resources towards
  their best uses. As a result, well-informed
  prices facilitate in improving the overall
  welfare in an economy.
• Thus, the more informationally efficient a market
  is the better off an economy should be (in
  general).

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11Issues in Information Efficiency

• Define A ? B to mean that an economy with
  property A has higher welfare than an economy
  with property B.
• Efficiencies from resource allocation suggests
  that SFE ? SSFE ? WFE.
• But hold on a minute. Often information on a
  company/ market first becomes available to agents
  who are not allowed to use it. They have
  privileged access (company auditors, bankers,
  market functionaries).
• SFE requires that prices reflect that
  information. Should such insider trading be
  legal?

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12Issues in Information Efficiency, Contd

• Some economists say yes because it enhances the
  efficiency of resource allocation in an economy.
• Others believe that it is more important to
  maintain a belief in the integrity of investment
  markets. The reasoning is that people are less
  inclined to invest in a security if they believe
  that others have more info. Investors move
  prices, and in doing so they impart
  informativeness into prices.
• If investors pull out of a rigged market, the
  quality of information embedded in the market
  price falls. Then resources are not allocated as
  efficiently.
• Paradox of return on gathering information
  (Grossman).

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13 Meaning of Information

• Information refines ones set of beliefs. It
  alters an agents distribution of subjective
  probabilities.

More informed p.d.f.
p.d.f.
Initial p.d.f.
Random variable
14
14Value of Information

• From an economic perspective, information has
  value to the extent that it can alter actions.
  You may benefit from a specific realization of a
  random variable even if you cannot alter actions
  as a result of knowing the realized value.
• But you would benefit from that realization
  anyway whether you learned about it earlier or
  later. Thus, the information has no value. But
  altering actions based on information can
  increase profits over not knowing information
  earlier.

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15Statistical Analysis of IE

• See Handout.

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16Sub- and Supermartingales

• a

Set of all Fair Games
submartingale fair game
supermartingale farir game
martingale fair game
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17A Trading Rule

• a

z off new top
x off top
y off bottom
Time
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18Your Lucky Day?

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Mass density
Mass density axis
Axis for index of profitability (past 5 years)
Search to find one in here
Mass density (possibly same shape)
Axis for index of profitability (next 5 years)
Drawing of your rules profitability over new
time span
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19Patterns in Spot Markets

• a

Cattle Price
January
January
Time
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20CAAR in Event Study

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21Another Study (Bonds when Fed Surprisingly
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22Event Study Anticipated Event

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23Event Study Inefficient Use of Information
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• Long Soybeans

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24Event Study Release of Quarterly Earnings
Reports
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25Event Study SFE Violation for Takeover

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26Event Study SFE Nonviolation for Takeover

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