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**The Decision Usefulness Approach to Financial Reporting**

Chapter 3

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**AGENDA Decision Usefulness The Rational Investor Diversification**

Portfolio Risk Conceptual Framework

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**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?

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**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

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**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

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**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

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**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

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**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

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**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

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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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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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

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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

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**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

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**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

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**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

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**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

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**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)=

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**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

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**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

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**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

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**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

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**Firm-Specific risk Decision Usefulness The Rational Investor**

Diversifica-tion Portfolio Risk Conceptual Framework Firm-Specific risk

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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”

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**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

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**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

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**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

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**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

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Summary & Questions?

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Chapter 5 Portfolio Risk and Return: Part I

Chapter 5 Portfolio Risk and Return: Part I

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