CHAPTER 3: THE DECISION USEFULNESS APPROACH TO FINANCIAL REPORTINGFrancis 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 60% P(H) = 0.60 State 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
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
Act High LowA. Buy Shares 225 0B. Buy Bonds 100 100
Example Cont’d Alternative: Wait and obtain more
information Student’s research find that if Company
A is a High-State 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 P(H|GN)=0.951 P(L|GN)=1-0.951=0.0490.41
EU(A)=15(0.951)+0(0.049)=14.265EU(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: 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
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.
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
PayoffsHigh Low High Low
A (buy shares)
$225 $0 60% 40%
B (buy bonds)
$100 $100 100%
For this example the rational investor’s utility function is:U(x) = x , x≥0
B: (1.00 X $100) = $100 U(x) = 100 =10
The Rational, Risk Averse Investor-modeling risk aversion-
A: (0.6 X $225)+ (0.4 X $0) = $135 U(x) = ( 225 X 0.6) + ( 0 X 0.4) = (15*0.6) = 9
9
X (payoff)
U(x)
15
10
A
DC
100 135
B
225
The Principle of Portfolio Diversification
Typical investors: risk-averse Risk adverted by investment strategy Mean-variance utility function ()
a = the investment act i = the investor = the expected rate of return = 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 = $368Payoff
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
= 0.128 = 0.0971
Example Cont’d Assume the investor’s utility function ()
can be represented by:
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 assetRisk free investment with treasury bonds
Probability of 0.8 for 10% increase and 0.2probaility of 2.5% increasexm =(0.10*0.8)+(0.0250*0.2)=0.0850σm
2=[(0.10-0.0850)2*0.8]+[(0.0250-0.0850)2*0.2 =0.0002 + 0.0007 =0.0009Utility of 2xM – σM
2=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
Varianceσa
2 =(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