1. The Decision Usefulness Approach to Financial Reporting
Chapter 3

2. AGENDA Decision Usefulness The Rational Investor Diversification
Portfolio Risk
Conceptual Framework

3. The Decision Usefulness Approach
The Rational Investor
Diversifica-tion
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:
Who are the users?
What decision problems do they face?

4. Single person decision theory
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
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

5. State 1 State 2 Example #1 Jane has $20,000 to invest in either
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
Example #1
Jane has $20,000 to invest in either
A1 = Shares of ABC Ltd.
A2 = 2% Government Bonds
States of nature:
ABC future performance high
State 1
ABC future performance low
State 2

6. Payoff Table Jane is risk-averse Utility = √payoff Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
Payoff Table
Act
State
High
Low
A1 (buy shares)
$1, 600
$ 0
A2 (buy bonds)
$ 225
Prior probabilities
P(H) = 0.30
P(L) = 0.70
Jane is risk-averse
Utility = √payoff

7. Decision Tree Act State (Probability) Payoff (Utility)
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
Decision Tree
Act State (Probability) Payoff (Utility)
High performance (0.30)
$1,600 (40) A1
Low performance (0.70)
$0 (0)
Invest $20K A2
Performance high or low (1.00)
$225 (15)
EU (A1) = (0.3 X 40) + (0.7 X 0) = 12
EU (A2) = 1.00 X 15 = 15

8. Conditional Probabilities
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
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

9. Posterior Probabilities
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
Posterior Probabilities
Bayes’ Theorem
P(H/GN) = P(H)P(GN/H)
P(H) P(GN/H)+ P(L) P(GN/L)
= 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

10. Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
Information Defined
Evidence that has potential to affect an individual’s decision
Net of cost
Continuous process

11. The Information System
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
The Information System
Conditional probabilities
P (GN|H) and P (BN|L)
Information System for Decision Theory Example
Current Financial Statement Evidence
Good News
Bad News
STATE
HIGH
0.8
0.2
LOW
0.1
0.9

12. The Information System
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
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

13. Rational Expectations
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
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:
Sampling the FS
Examining revisions by Value Line analysts of future quarterly earnings forecasts based on current states

14. The Rational, Risk-Averse Investor
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
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

15. Utility Functions Risk Averse Investor Risk Neutral Investor
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
Utility Functions
Risk Averse Investor
Risk Neutral Investor

16. The principal of portfolio diversification
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
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
Diversification  lowers risk
Some but not all risk can be eliminated by proper investment strategy
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
A more risk averse person will increase the variance by (for example) a factor of two ultimately lowering the utility

17. Application of Portfolio Diversification
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
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 $ 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

18. Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
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

19. Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
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

20. The optimal investment decision
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
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

21. Portfolio Risk Calculating & Interpreting Beta:
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
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

22. Calculating Beta The beta of shares of firm A is calculated by: Where;
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
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

23. Some Examples Decision Usefulness The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
Some Examples
Company
Beta
Apple
1.26
McDonalds
0.41
Johnson & Johnson
0.52
AIG
3.44

24. Calculating covariance
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
Calculating covariance
Returns
Joint Probabilities A M
High
( )( ) x 0.72=
Low
(0.15 – )( – ) x 0.02=
(-0.10 – )( – ) x 0.08=
(-0.10 – )( – ) x 0.18=
Cov (A,M)=

25. BETA Given that, We obtain: Low Beta = Low Risk Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
BETA
Given that,
We obtain:
Low Beta = Low Risk

26. Portfolio Expected Value and Variance
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
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

27. Portfolio Variance The variance of a portfolio with two securities is:
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
Portfolio Variance
The variance of a portfolio with two securities is:
Variance of a portfolio is determined by the variance of each securities and the covariance between securities
Firm-Specific Risk
Firm-Specific Risk
Systematic Risk

28. Portfolio Risk as the Number of Securities Increases
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
Portfolio Risk as the Number of Securities Increases
Number of Securities
Variance Terms
Covariance Terms
Firm-Specific Risk*
Systematic Risk* 1
100% 0% 2
50% 10 45
10%
90% N
N(N – 1)/2
*assuming each security is an equal portion of the portfolio

29. Firm-Specific risk Decision Usefulness The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
Firm-Specific risk

30. Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
IASB & CICA
IAS 1: “The objective of financial statements is to provide information about the 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”

31. What is useful information?
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
What is useful information?
Help investors assess the amounts, timing, and uncertainty of future cash flows
Enhance relevance and reliability of accounting information

32. Relevance and Reliability
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
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 shall adopt accounting policies 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

33. How is historical information useful?
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
How is historical information useful?
Helps form expectations
Under non-ideal conditions:
Relevant Information  allows investors to form their own expectations

34. Predicting future performance
Decision Usefulness
The Rational Investor
Diversifica-tion
Portfolio Risk
Conceptual Framework
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

35. Summary & Questions?