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 )  .

3175 © 2006 Pearson Education Canada Inc.

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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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