### The Decision Usefulness Approach

```THE DECISION USEFULNESS APPROACH
TO FINANCIAL REPORTING
Chapter 3
AGENDA
1.
2.
3.
4.
5.
DECISION USEFULNESS
THE RATIONAL INVESTOR
DIVERSIFICATION
PORTFOLIO RISK
CONCEPTUAL FRAMEWORK
THE DECISION USEFULNESS APPROACH
“If we can’t prepare theoretically correct financial
statements, at least we can try to make the financial
statements more useful”
Non-ideal conditions
Contrasted with stewardship
Two major questions:
1.
Who are the users?
2.
What decision problems do they face?
SINGLE PERSON DECISION THEORY
Understand how individuals make rational decisions
under uncertainty
Appreciate the concept of information
 Allows decision makers to update their subjective beliefs
Financial statements are a source of information
EXAMPLE #1
Jane has \$20,000 to invest in either
A1 = Shares of ABC Ltd.
A2 = 2% Government Bonds
States of nature:
State 1
• ABC future performance
high
State 2
• ABC future performance
low
PAYOFF TABLE
Act
State
High
Low
\$1, 600
\$0
\$ 225
\$ 225
Prior probabilities
P(H) = 0.30
P(L) = 0.70
 Jane is risk-averse
 Utility = √payoff
DECISION TREE
Act
State (Probability)
High performance (0.30)
A1
Low performance (0.70)
Payoff (Utility)
\$1,600 (40)
\$0 (0)
Invest
\$20K
A2
Performance high or low (1.00)
EU (A1) = (0.3 X 40) + (0.7 X 0) = 12
EU (A2) = 1.00 X 15 = 15
\$225 (15)
CONDITIONAL PROBABILITIES
 P(GN/H) = 0.80
 Probability of FS showing GN if ABC is a high state firm
 P(BN/H) = 0.20
 Probability of FS showing BN if ABC is a high state firm
 P(GN/L) = 0.10
 Probability of FS showing GN if ABC is a low state firm
 P(BN/L) = 0.90
 Probability of FS showing BN if ABC is a low state firm
POSTERIOR PROBABILITIES
 Bayes’ Theorem
P(H/GN) =
P(H)P(GN/H)
.
P(H) P(GN/H)+ P(L) P(GN/L)
=
0.3 x 0.8
(0.3 x 0.8) + (0.7 x 0.1)
= 0.77
P(L/GN) = 1.00 – 0.77
= 0.23
 Updated expected utilities
EU(A1/GN) = (0.77 x 40) + (0.23 x 0) = 30.8
EU(A2/GN) = 1.00 x 15 = 15
INFORMATION DEFINED
Evidence that has potential to affect an individual’s
decision
 Net of cost
 Continuous process
THE INFORMATION SYSTEM
Conditional probabilities
 P (GN|H) and P (BN|L)
Information System for Decision Theory Example
Current Financial Statement Evidence
STATE
Good News
HIGH
0.8
0.2
LOW
0.1
0.9
THE INFORMATION SYSTEM
Highly informative FS exist due to the underlying
INFORMATION SYSTEM
Informativeness depends on relevance & reliability
of the FS
Example: a new standard requires a company to
switch methods of valuing capital assets.
 RESULT= increased relevance since it is a better predicator of future
firm performance but decreased reliability due to the need for
estimates
RATIONAL EXPECTATIONS
When ones assumes the information system
probabilities are known
Investors are assumed to quickly form accurate
estimates of unknown probabilities
 How do they do this? 2 approaches:
1. Sampling the FS
2. Examining revisions by Value Line analysts of future quarterly
earnings forecasts based on current states
THE RATIONAL, RISK-AVERSE INVESTOR
 Rational Investor = typically Risk Averse
 Risk aversion is important to accountants because it
means investors need certain information concerning
the risk of future returns
 Utility Functions model risk aversion
UTILITY FUNCTIONS
Risk Averse Investor
Risk Neutral Investor
THE PRINCIPAL OF PORTFOLIO
DIVERSIFICATION
 Typical investor is risk averse
 Investor will want lowest
possible risk; in instances where
they bear risk the highest
expected payoff will be required
 Tradeoff between risk and return
 greater risk only if expected
return is high
 General utility function is:
 Ui (a) = fix̅ - σa2
 Ui represents utility of investment

fi represents the risk factor
 x̅ represents the expected rate of
return
 σrepresents the variance
 Diversification  lowers risk
 A more risk averse person will
 Some but not all risk can be
increase the variance by (for
example) a factor of two
ultimately lowering the utility
eliminated by proper
investment strategy
APPLICATION OF PORTFOLIO
DIVERSIFICATION
Assume a client wishes to purchase the following:
 8 shares of firm I valued at \$10 per share paying a dividend of \$1
per share with a 67.50% chance of the share increasing to \$10.50
and a 32.50% chance of the share decreasing to \$8.50
 6 shares of firm II at \$20 per share paying a dividend of \$1 per share
with a 74% chance of the share increasing to \$22 dollars and a 26%
chance of the share decreasing to \$17
 With each different potential outcome the probability with independence is
distinguished using the probabilities given
 Due to economy wide/market wide factors it generally goes without saying that
“if one stock is going up, there is a better chance that other stocks will also go
up” or “if one stock is going down, there is a better chance that other stocks
are going down”
 This, as a result, explains the diversified probabilities as the UP,UP and DOWN, DOWN
situation both increased their probabilities by the same 7.47% factor under diversified
probability
 The utility according to our earlier equation (assuming a neutral
stance) would then be Ui = 8.50% -0.74% = 7.76%
 If you have invested in either of the stocks single handedly the
utility would have been lower showing that there would have
been more risk associated with investing in 1 particular stock
THE OPTIMAL INVESTMENT DECISION
 The more shares your portfolio has the less risky it is; this
is known as “holding the market portfolio”
 Systematic risk is risk that that cannot be avoided by
diversifying as it is the risk inherent to the entire market
 If investor is more risk averse, they may consider purchasing
a risk free asset (ex. treasury bills) lowering the risk
PORTFOLIO RISK
Calculating & Interpreting Beta:
 Beta: Measures the co-movement between changes in
the price of a security and changes in the overall market
 Used to gauge a security’s risk
CALCULATING BETA
The beta of shares of firm A is calculated by:
Where;
Cov(A,M) measures how strongly return of security A varies compared
to market, and
Var(M) expresses the volatility of the market overall
SOME EXAMPLES
Company
Beta
Apple
1.26
McDonalds
0.41
Johnson & Johnson
0.52
AIG
3.44
CALCULATING COVARIANCE
Returns
A
Joint Probabilities
M
High
High
(0.15 - 0.0850)(0.10 - 0.0850) x 0.72= 0.0007
High
Low
(0.15 – 0.0850)(0.0250 – 0.0850) x 0.02= -0.0001
Low
High
(-0.10 – 0.0850)(0.0250 – 0.0850) x 0.08= -0.0002
Low
Low
(-0.10 – 0.0850)(0.0250 – 0.0850) x 0.18= 0.0020
Cov (A,M)= 0.0024
BETA
 Given that,
 We obtain:

Low Beta = Low Risk
PORTFOLIO EXPECTED VALUE AND VARIANCE
 Recall, that an investors utility function for an investment looks like
 Expected return of portfolio P:
 Where X is the expected return of a given security and K is the
proportion of that security in the overall portfolio
PORTFOLIO VARIANCE
 The variance of a portfolio with two securities is:
Firm-Specific Risk
Firm-Specific Risk
Systematic Risk
 Variance of a portfolio is determined by the variance of each securities
and the covariance between securities
PORTFOLIO RISK AS THE NUMBER OF
SECURITIES INCREASES
Number of
Securities
Variance
Terms
Covariance
Terms
Firm-Specific
Risk*
Systematic
Risk*
1
1
0
100%
0%
2
2
1
50%
50%
10
10
45
10%
90%
N
N
N(N – 1)/2
*assuming each security is an equal portion of the portfolio
FIRM-SPECIFIC RISK
Firm-Specific Risk
120%
100%
80%
60%
40%
20%
0%
1
2
3
4
5
6
7
Number of Securities
8
9
10
IASB & CICA
 IAS 1: “The objective of
financial statements is to
financial position, financial
performance, and cash flows of
an entity that is useful to a wide
range of users in making
economic decisions.”
 CICA section 1000: “The
objective of financial statements
is to communicate information
that is useful to investors,
creditors, and other users in
making their resource allocation
decisions and/or assessing
management steward ship”
WHAT IS USEFUL INFORMATION?
Help investors assess the amounts, timing, and
uncertainty of future cash flows
Enhance relevance and reliability of accounting
information
RELEVANCE AND RELIABILITY
 IAS 8: “In the absence of an
IFRS ...management shall use
judgement in developing and
applying an accounting policy
that results in information
that is: a) relevant to the
economic decision making
needs of users; and b)
reliable”
 CICA Section 1100: “an entity
and disclosures that are a)
consistent with primary
resources of GAAP, and b)
developed through exercise of
professional judgement and
application of concepts
described in Section 1000”
 Section 1000: outlines relevance
and reliability
HOW IS HISTORICAL INFORMATION
USEFUL?
 Helps form expectations
 Under non-ideal conditions:
 Relevant Information  allows investors to form their own
expectations
PREDICTING FUTURE PERFORMANCE
 Accruals
 Match revenue and costs
 Ex. Accounts Receivable  predict future sales proceeds
 Earnings
 Better for predicting poor performance
 Accruals anticipate unrealized losses  future cash flow
reductions
SUMMARY & QUESTIONS?
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