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 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 Low

A. Buy Shares 225 0

B. 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=0.049

0.41

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: 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.

ActState

Probability of Payoffs

High 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 = $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

= 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 asset

Risk free investment with treasury bondsProbability 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

= 0.0020Utility

= (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