The Decision Usefulness Approach

The Decision Usefulness Approach to Financial ReportingChapter 3AGENDADecision UsefulnessThe Rational InvestorDiversificationPortfolio RiskConceptual Framework

The Decision Usefulness ApproachIf we cant prepare theoretically correct financial statements, at least we can try to make the financial statements more usefulNon-ideal conditionsContrasted with stewardshipTwo major questions:Who are the users?What decision problems do they face?

Decision UsefulnessPortfolio RiskConceptual FrameworkThe Rational InvestorDiversifica-tion3Single person decision theoryUnderstand 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 Decision UsefulnessPortfolio RiskConceptual FrameworkThe Rational InvestorDiversifica-tion4Example #1Jane has $20,000 to invest in eitherA1 = Shares of ABC Ltd.A2 = 2% Government Bonds

States of nature:

Decision UsefulnessPortfolio RiskConceptual FrameworkThe Rational InvestorDiversifica-tion5Payoff TableDecision UsefulnessPortfolio RiskConceptual FrameworkThe Rational InvestorDiversifica-tionActStateHighLowA1 (buy shares)$1, 600$ 0A2 (buy bonds)$ 225$ 225Prior probabilities P(H) = 0.30P(L) = 0.70Jane is risk-averse Utility = payoff

6Decision TreeDecision UsefulnessPortfolio RiskConceptual FrameworkThe Rational InvestorDiversifica-tion ActState (Probability)Payoff (Utility)Invest $20KA1 A2High performance (0.30) Low performance (0.70) Performance high or low (1.00)$1,600 (40)$0 (0)$225 (15)EU (A1) = (0.3 X 40) + (0.7 X 0) = 12EU (A2) = 1.00 X 15 = 157Conditional Probabilities Decision UsefulnessPortfolio RiskConceptual FrameworkThe Rational InvestorDiversifica-tionP(GN/H) = 0.80Probability of FS showing GN if ABC is a high state firmP(BN/H) = 0.20Probability of FS showing BN if ABC is a high state firmP(GN/L) = 0.10Probability of FS showing GN if ABC is a low state firmP(BN/L) = 0.90Probability of FS showing BN if ABC is a low state firm

8Posterior Probabilities Decision UsefulnessPortfolio RiskConceptual FrameworkThe Rational InvestorDiversifica-tionBayes TheoremP(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) = 0.77P(L/GN) = 1.00 0.77= 0.23 Updated expected utilities EU(A1/GN) = (0.77 x 40) + (0.23 x 0) = 30.8EU(A2/GN) = 1.00 x 15 = 15

9Information DefinedEvidence that has potential to affect an individuals decisionNet of costContinuous process

Decision UsefulnessThe Rational InvestorDiversifica-tionPortfolio RiskConceptual FrameworkThe Information SystemConditional probabilitiesP (GN|H) and P (BN|L)

Decision UsefulnessThe Rational InvestorDiversifica-tionPortfolio RiskConceptual FrameworkInformation System for Decision Theory ExampleCurrent Financial Statement EvidenceGood NewsBad NewsSTATEHIGH 0.80.2LOW0.10.9The Information SystemHighly informative FS exist due to the underlying INFORMATION SYSTEMInformativeness depends on relevance & reliability of the FSExample: 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 estimatesDecision UsefulnessThe Rational InvestorDiversifica-tionPortfolio RiskConceptual FrameworkRational ExpectationsWhen ones assumes the information system probabilities are known Investors are assumed to quickly form accurate estimates of unknown probabilitiesHow do they do this? 2 approaches:Sampling the FSExamining revisions by Value Line analysts of future quarterly earnings forecasts based on current statesDecision UsefulnessThe Rational InvestorDiversifica-tionPortfolio RiskConceptual FrameworkThe Rational, Risk-Averse InvestorRational Investor = typically Risk Averse Risk aversion is important to accountants because it means investors need certain information concerning the risk of future returnsUtility Functions model risk aversionDecision UsefulnessThe Rational InvestorDiversifica-tionPortfolio RiskConceptual FrameworkUtility FunctionsRisk Averse InvestorRisk Neutral InvestorDecision UsefulnessThe Rational InvestorDiversifica-tionPortfolio RiskConceptual Framework

15The principal of portfolio diversification Typical investor is risk averseInvestor will want lowest possible risk; in instances where they bear risk the highest expected payoff will be requiredTradeoff between risk and return greater risk only if expected return is highDiversification lowers riskSome but not all risk can be eliminated by proper investment strategy

General utility function is:Ui (a) = fix - a2 Ui represents utility of investment fi represents the risk factorx represents the expected rate of returnrepresents the varianceA more risk averse person will increase the variance by (for example) a factor of two ultimately lowering the utility

Decision UsefulnessThe Rational InvestorDiversifica-tionPortfolio RiskConceptual FrameworkApplication 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 $8.506 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

Decision UsefulnessPortfolio RiskConceptual FrameworkThe Rational InvestorDiversifica-tionWith each different potential outcome the probability with independence is distinguished using the probabilities givenDue 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

Decision UsefulnessPortfolio RiskConceptual Framework

The Rational InvestorDiversifica-tionThe 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

Decision UsefulnessPortfolio RiskConceptual Framework

The Rational InvestorDiversifica-tionDecision UsefulnessPortfolio RiskConceptual FrameworkThe more shares your portfolio has the less risky it is; this is known as holding the market portfolioSystematic risk is risk that that cannot be avoided by diversifying as it is the risk inherent to the entire marketIf investor is more risk averse, they may consider purchasing a risk free asset (ex. treasury bills) lowering the risk

The optimal investment decisionThe Rational InvestorDiversifica-tionDecision UsefulnessPortfolio RiskConceptual FrameworkCalculating & Interpreting Beta:Beta: Measures the co-movement between changes in the price of a security and changes in the overall marketUsed to gauge a securitys risk Portfolio RiskThe Rational InvestorDiversifica-tion21Decision UsefulnessPortfolio RiskConceptual FrameworkCalculating BetaThe Rational InvestorDiversifica-tionThe beta of shares of firm A is calculated by:

Where;Cov(A,M) measures how strongly return of security A varies compared to market, andVar(M) expresses the volatility of the market overall

22Decision UsefulnessPortfolio RiskConceptual FrameworkSome ExamplesThe Rational InvestorDiversifica-tionCompanyBetaApple1.26McDonalds0.41Johnson & Johnson0.52AIG3.4423Decision UsefulnessPortfolio RiskConceptual FrameworkCalculating covarianceThe Rational InvestorDiversifica-tion

ReturnsJoint ProbabilitiesAMHighHigh(0.15 - 0.0850)(0.10 - 0.0850) x 0.72= 0.0007HighLow(0.15 0.0850)(0.0250 0.0850) x 0.02= -0.0001LowHigh(-0.10 0.0850)(0.0250 0.0850) x 0.08= -0.0002LowLow(-0.10 0.0850)(0.0250 0.0850) x 0.18= 0.0020Cov (A,M)= 0.002424Decision UsefulnessPortfolio RiskConceptual FrameworkBETAThe Rational InvestorDiversifica-tionGiven that,

We obtain:

Low Beta = Low Risk

25Decision UsefulnessPortfolio RiskConceptual FrameworkPortfolio Expected Value and VarianceThe Rational InvestorDiversifica-tionRecall, 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

26Decision UsefulnessPortfolio RiskConceptual FrameworkPortfolio VarianceThe Rational InvestorDiversifica-tionThe 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 RiskFirm-Specific RiskSystematic Risk27Decision UsefulnessPortfolio RiskConceptual FrameworkPortfolio Risk as the Number of Securities IncreasesThe Rational InvestorDiversifica-tionNumber of SecuritiesVariance TermsCovariance TermsFirm-Specific Risk*Systematic Risk*110100%0%22150%50%10104510%90%NNN(N 1)/2*assuming each security is an equal portion of the portfolio28Decision UsefulnessPortfolio RiskConceptual FrameworkFirm-Specific riskThe Rational InvestorDiversifica-tion29Decision UsefulnessPortfolio RiskConceptual FrameworkIASB & CICAThe Rational InvestorDiversifica-tionIAS 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 shipDecision UsefulnessPortfolio RiskConceptual FrameworkWhat is useful information?The Rational InvestorDiversifica-tionHelp investors assess the amounts, timing, and uncertainty of future cash flowsEnhance relevance and reliability of accounting information

Decision UsefulnessPortfolio RiskConceptual FrameworkRelevance and ReliabilityThe Rational InvestorDiversifica-tionIAS 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) reliableCICA 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 1000Section 1000: outlines relevance and reliabilityDecision UsefulnessPortfolio RiskConceptual FrameworkHow is historical information useful?The Rational InvestorDiversifica-tionHelps form expectationsUnder non-ideal conditions:Relevant Information allows investors to form their own expectations

Decision UsefulnessPortfolio RiskConceptual FrameworkPredicting future performanceThe Rational InvestorDiversifica-tionAccrualsMatch revenue and costsEx. Accounts Receivable predict future sales proceedsEarningsBetter for predicting poor performanceAccruals anticipate unrealized losses future cash flow reductionsSummary & Questions?