Transcript Perfectly Specified Decision Process, Cont.
Chapter 3 The Decision Usefulness Approach to Financial Reporting
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Single-Person Decision Theory
Perfectly Specified Decision Process
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Motivation for Decision Theory Model
• A
model of rational decision making in the face of uncertainty
• Other ways to make decisions? • Captures
average investor behaviour?
• Helps us understand how financial
statement information is useful
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Example
• Perfectly Specified Decision Process – A game against
Nature . “Nature does not think”
– NB: Concept of an “
Information System ”
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Perfectly Specified Decision Process Consider an investor with $10,000 to invest in one of the following mutually exclusive acts: a 1 : buy shares of x Ltd. For $10,000 a 2 : buy Canada Savings Bonds (CSB) for $10,000 Let there be 3 “states of nature”: θ 1 : shares fall 10% in market value θ 2 : shares hold steady θ 3 : shares rise 80%
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Perfectly Specified Decision Process, Cont.
Prior Payoff Table Probabilities Outcome θ 1 θ 2 a 1 a 2 -1000 1000 0 1000 θ 3 8000 1000 P( θ 1 ) = .05
P(θ 2 ) = .70
P(θ 3 ) = .25
1.00
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Perfectly Specified Decision Process, Cont.
Assume the investor uses expected monetary value as a decision criterion (EMV) EMV (a 1 ): (.05)(-1000) + 0 + .25(8000) = 1950 EMV (a 2 ): (.05)(1000) + .70(-1000) +.25 (1000) = 1000 Therefore, if investor acts now, should take a 1 .
But: May be worthwhile to secure additional information.
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Decision Problem
Think of the financial statements of X Ltd. as an information system conveying information about probabilities of θ.
Assume the financial statements will give one of the following 3 mutually exclusive messages:
m
1 :"
poor
"
NI CA
/ /
SE CL
.
05 1 .
9
m
2 :"
fair
"
NI CA
/ /
SE CL
.
12 2 .
0
m
3 :"
good
"
NI
/
SE CA
/
CL
.
18 2 .
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Decision Problem, Cont.
The information system can be characterized by the following table: θ 1 Θ 2 θ 3 P(m 1 /θ) .75
.50
.10
P(m 2 /θ) .20
.30
.20
P(m 3 /θ) .05
.20
.70
These conditional probabilities, or likelihoods, are the probabilities of receiving the various messages conditional on each state being true.
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Decision Problem, Cont.
Now, for any message, the decision maker can revise his/her prior probabilities using
Bayes’ Theorem.
Suppose that
m
1 statements.
was received from the financial Then:
P
1 /
m
1
P
P
1
m
1 /
m
1 /
P
1 (.
05 )(.
75 ) .
4125 .
09 Similarly:
P
( 2 /
m
1 ) =P(
m
1 ) =.85
P
( 3 /
m
1 ) =.06
1.00
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Decision Problem, Cont.
Note the EMV of each act is
EMV
(
a
1 ) (.
09 )( 1000 )
EMV
(
a
2 ) 1000 0 (.
06 )( 8000 ) $ 390 So if
m
1 were received act a 2 would be chosen.
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Decision Problem, Cont.
You should verify that if
m
2 was received:
P
( 1
P
( 2
P
( 3 /
m
2 ) /
m
2 ) /
m
2 ) .
0370 .
7778 .
1852 where
P
(
m
2 )
P
(
m
2 .
2700 / )
P
( ) 1 .
0000 And the optional act is then
a
1 with EMV of $1444.48.
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Decision Problem, Cont.
Similarly, if
m
3 was received:
P
( 1
P
( 2
P
( 3 /
m
3 ) /
m
3 ) /
m
3 ) .
0079 .
4409 .
5512 1 .
0000 where
P
(
m
3 ) .
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The Information System
• One of the Most Important Text
Concepts
• Conditional on Each State of Nature (i.e.,
future firm performance), gives Probability of the GN or BN in the Financial Statements Objective
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The Information System, Cont’d.
• Translation of First Entry in Information
System Example in Table 3.2 of Text:
–
If future firm performance is going to be good, the probability that the current financial statements will show GN is 0.80
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Information Defined
• Information is Evidence that has the
Potential to Affect an Individual’s Decision
– An
ex ante definition
– Individuals receive information all the time – Individual-specific – Are financial statements information? © 2006 Pearson Education Canada Inc.
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Does it Work?
• Problems of Implementing Model – Specify states of nature – Prior probabilities of states (subjective) – Payoffs – Information system s/b objective • Forces Careful Consideration • How Else to Decide? • Captures
Average Behaviour
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The Rational Investor
• Definition – Maximizes expected utility, using the single-
person decision theory model
– May be risk averse • Then, will diversify • Needs information about risk as well as expected
return
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Beta
• Definition – Standardized covariance between return on
share and return on market
• Only Relevant Risk Measure for a
Reasonably Diversified Investor
– Why? Because firm specific risk diversifies
away.
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Decision Theory Model Underlies Concepts Statements
• Rationale for Concepts Statements • Examples – FASB SFAC No. 1 – FASB SFAC No. 2 –
CICA Handbook , Section 1000
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