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CHAPTER 3: THE DECISION USEFULNESS APPROACH TO FINANCIAL REPORTING Francis Moniz, Catherine Koene, Josh Proksch, James Wells, Pamela Feldkamp, Lorcan Duffy The Decision Usefulness Approach Contrasted by stewardship Two questions: Identifying constituencies Decision problems Single-person theory of decision Theory of investment Single-Person Decision Theory Theory viewpoint Payoff Ethical issues Expected Utility Bayes’ Theorem The Information System Predict future investment returns Conditional Probabilities Transparent, Precise, High Quality Trade off between relevance and Reliability Example A student has $1000 to invest. With two possible investment possibilities: government bonds yielding 10% or share of Company A. Company A has two states of nature: State 1: future performance is high Probability State 60% P(H) = 0.60 2: future performance is low Probability 40% P(L) = 0.40 Example Cont’d State 1: P(H) = 0.60 State 2: P(L)=0.40 Act High Low A. Buy Shares 225 0 B. Buy Bonds 100 100 Utility Function: EU(X)=√(X) EU(A)= (0.6)√(225)+(0.4)√(0)=0.6(15)+0.4(0)=9 EU(B)=1.00√(100)=1.00(10)=10 Example Cont’d Alternative: Wait and obtain more information Student’s research find that if Company A is a HighState firm There is a 65% chance of good news (GN) and 35% of bad news (BN) If Company A is a low state firm then there is a 5% chance of GN and 95% of BN Example Cont’d P(GN|H)=0.65 P(BN|H)=0.35 P(GN|L)=0.05 P(BN|L)=0.95 Posterior Probabilities of high performance state: P(H|GN)= P(H)*P(GN|H) = 0.60(0.65) P(H)*P(GN|H) + P(L)*P(GN|L) 0.60(0.65)+0.40(0.05) 0.39 = 0.95122 0.41 P(H|GN)=0.951 . P(L|GN)=1-0.951=0.049 EU(A)=15(0.951)+0(0.049)=14.265 EU(B)=10(1.00)=10 EU(A)>EU(B), annual report has changed the decision and the student will buy shares. The Rational, Risk Averse Investor According to decision theory Rational Investors make their decisions based on the act that yields the highest expected utility. In reality not all investors may make their decisions according to this “rational” basis but the theory suggests that this is the general behaviour of investors who want to make good investments. The Rational, Risk Averse Investor With rational investors, another assumption is that they are risk averse What is meant by risk averse? One definition is: Being risk averse means that an individual will want to minimize risks even when the potential benefit of an action is large. As risk decreases, a risk averse person is willing to accept a situation or make a decision with a higher expected return. There is a trade off between expected return and risk. Risk aversion is the reluctance of a person to accept a bargain with an uncertain payoff rather than another bargain with a more certain, but possibly lower, expected payoff The Rational, Risk Averse Investor -modeling risk aversion To model risk aversion one must use a utility function which shows an individual’s payoff amounts as it relates to the individuals utility for those amounts. Consider the example were an investor has the option to either invest their money in shares of a company or buy bonds. The following table shows the payoff table of the above options and the probabilities of these outcomes. Act State Probability of Payoffs High Low High Low A (buy shares) $225 $0 60% 40% B (buy bonds) $100 $100 100% The Rational, Risk Averse Investor -modeling risk aversionU(x) B 15 10 9 A For this example the rational investor’s utility function is: U(x) = x , x≥0 D C 100 135 A: (0.6 X $225)+ (0.4 X $0) = $135 U(x) = ( 225 X 0.6) + ( 0 X 0.4) = (15*0.6) = 9 225 X (payoff) B: (1.00 X $100) = $100 U(x) = 100 =10 The Principle of Portfolio Diversification Typical investors: risk-averse Risk adverted by investment strategy Mean-variance utility function (𝑈𝑖 𝑎 ) 𝑈𝑖 𝑎 = 𝑓𝑖 𝑥𝑎 , 𝜎𝑎2 a = the investment act i = the investor 𝑥𝑎 = the expected rate of return 𝜎𝑎 = the variance of risk Portfolio Diversification: Example A risk-averse investor has $400 to invest and is considering investing all of it in the share of firm A, currently trading for $25. Assume that the investor assesses a 0.65 probability that these shares will increase in market value to $29 over the coming period and a 0.35 probability that they will decrease to $21. Assume also that A will pay a dividend of $2 per share at the end of the period. Example cont’d $400 divided by $25 = 16 shares If shares increase: $29 x 16 shares + $32 dividend = $496 If shares decrease: $21 x 16 shares +$32 dividend = $368 Payoff Rate of Return Probability Expected Rate of Return Variance $496 (496-400) / 400 = 0.24 0.65 0.156 (0.24 – 0.128) 2x 0.65 = 0.0082 $368 (368-400) / 400 = -0.08 0.35 -0.028 (-0.08 – 0.128) 2x 0.35 = 0.0151 𝑥𝑎 = 0.128 𝜎𝑎2 = 0.0971 Example Cont’d Assume the investor’s utility function (𝑈𝑖 𝑎 ) can be represented by: 𝑈𝑖 𝑎 = 𝑥𝑎 − 2𝜎𝑎2 Therefor, their utility for this investment is: 0.128 – (2 x 0.0971) = -0.0662 The investor now has to decide whether to take this investment or not. Optimal Investment Strategy Assumes no transaction fees or brokerage fees Invest in every single security on market then Cancels market security risk Risk not eliminated still Systemic Risk Economy wide factors that cause unavoidable risk Risk Free Asset Ensures diversification yet lowers risk (treasury bonds, or T-bills) Sell a little of each security in portfolio invest in risk free asset Risk free investment with treasury bonds Probability of 0.8 for 10% increase and 0.2probaility of 2.5% increase xm =(0.10*0.8)+(0.0250*0.2)=0.0850 σm2=[(0.10-0.0850)2*0.8]+[(0.0250-0.0850)2*0.2 =0.0002 + 0.0007 =0.0009 Utility of 2xM – σM2=0.1700 – 0.0009 = 0.1691 Risk Free with Market Risk Toni borrows $100 at 0.04 and buys additional $100 in market share $300 in market portfolio Return of 0.0850 and owes $100 at 4% interest Xa = (300/200 * 0.0850) –(100/200 *0.0400) = (0.1275 – 0.0200) = 0.1075 Variance σa2 =(300/200)2 *0.0009 = 0.0020 Utility = (2*0.1075) -0.0020 = 0.2130 Optimal Investment Graph Beta Measures changes in the price of a security and changes in the market value of market portfolio Β= Cov (A,M) Var (M) Cov A,M is covariance of returns on A to returns on market portfolio M Dividing by Var (M) is done to express Cov (A,M) in units of market variance High beta security undergoes wide swings when market conditions change. Beta Results Transaction costs not ignored when using Beta Buy relatively few securities instead of market securities Important to know expected returns and betas Assess expected return and risk of portfolios Reaction of Professional Accounting Bodies to the Decision Usefulness Approach The objective of the financial statements: To provide financial information that is “useful to present and potential equity investors, lenders, and other creditors in making decisions in their capacity as capital providers.” Primary user group