Slide 1
ACCOUNTING THEORY & CONTEMPORARY ISSUES
(AT I)
MODULE TWO
THE DECISION-USEFULNESS APPROACH TO FINANCIAL
REPORTING
Slide 2
PART 1
- Decision-usefulness and Single Person Decision Theory
PART 2
- The Rational Risk-averse Investor
PART 3
- Portfolio Diversification
PART 4
- The Optimal Investment Decision
PART 5
- The Conceptual Framework
Lecture by:
Dr. A. L. Dartnell, FCGA
Year 2007 – 2008
2
Slide 3
MODULE TWO
PART 1
Decision-Usefulness Approach to Financial Reporting
Handout
Objective
Decision Usefulness (2 Sections)
Theories
The Information System
Main Diagonal
Slide 4
Objective
It should be noted that the first five modules relate to assisting investors to make good
investment decisions, while the second five relate to motivating managers to perform responsibly
by providing a measure of their success in running the firm.
It would be difficult to get a full set of statements based on present value.
The decision-usefulness approach takes the view that if we cannot prepare theoretically correct
financial statements, we can try to make historical cost-based statements more useful.
Slide 5
How do we tackle historical cost accounting? It produces reliable information but does not
always equate with market value nor, for that matter, present value. Thus, it is not always
relevant. Income is an artificial concept.
Slide 6
Section I
Decision-Usefulness
We have a number of people who deal with financial statements, referred to as constituencies
in the course. - investors, lenders, managers, unions, standard setters, government, education
participants, and the general public at large, many of whom may not be direct investors -
3
We cannot tailor statements to the needs of each group. It would be difficult to precisely
tailor our statements to the needs of each group.
Accounting bodies have adopted a decision-usefulness approach to financial reporting with the
main focus on investors and creditors.
Slide 7
Further, finance, economics, accounting, investment and statistics are intertwined.
Thus, some economic and finance theories have been brought forward to aid in determining
what to include in the financial presentation to the various constituencies.
Slide 8
Theories
We use two modern up-to-date theories: the Theory of Decision and the Theory of Investment.
First, the theory of Decision
Single Person Decision Theory
Utility
Bayes’ Theorem
Slide 9
Single Person Decision Theory
Single-person decision theory assumes one must make a decision under uncertainty.
This theory gives a procedure for a person to choose the best of alternatives given the
uncertainty existing.
It also includes the possibility of gaining additional information to add to the decision process.
Decision theory is based on probability or chance. The probability of something happening or
not happening. For example, the probability of 50% chance it will rain and 50% chance it will
not .
4
Future situations are based on "chance", that is, we will get one outcome or another outcome.
Thus, we should take the one with the highest probability of outcome.
Slide 10
Utility
We want to deal with utility? What is it? It is the satisfaction one receives from the acquisition
of a good, service or other situation.
It is difficult for anyone but oneself to determine.
But to understand it we will try to attach a numerical value to it.
Slide 11
Example
Judy has $10,000 to invest.
She can buy shares yielding $2,500 net a year if future profits are good and zero is profits are not
good, a1, or she can buy a risk-free government bond yielding $625, or 6.25%, as a2.
Slide 12
Judy assesses the probability of high profit P(H) as .30 and low (no) profit as P(L).70.
These are prior probabilities, say, based on previous accounting information.
Dollars to be paid are payoffs.
Judy is risk-averse and the utility or satisfaction she receives is the square root of the payoff.
5
Slide 13
Decision tree for Judy’s Choice
Future Profits High (.30)
-- $2,500
Utility - 50 utils
Future Profits Low (.70)
-
Utility - 0 utils
a1
Invest $10,000
a2
Future profits Low or High (1.00) - $625 Utility – 25 utils
Slide 14
Probabilities .30 and .70 and utilities 50, 0 and 25 utils
What are the expected utilities as of now?
EUa1 - 0.30 x 50 + .70 x 0 = 15 utils
EUa2 - 1.00 x 25
= 25 utils
Judy should buy the bonds as the utility is higher than the shares.
Slide 15
Bayes' Theorem:
Now Judy has just received the statements (posterior information) for the past year and the
profitability is high, there is Good News. She knows if the future profitability of the firm is high
there is an 0.80 probability that the statements of the current year will be high or show Good
News. She also thinks that there is a probability of 0.20 that the news could be bad.
Judy also knows that if it is thought the future profitability will be low, there is a 0.90 chance
there will be Bad News and a 0.10 chance there will be good news.
Slide 16
To sum up we can denote:
and
High State - P(GN/H) 0.80 and P(BN/H) 0.20
Low State - P(GN/L) 0.10 and P(BN/L) 0.90
6
With this additional information Judy wishes to recalculate her utilities to see if her decision is
appropriate. So to find out about his probabilities for good news, she uses the formula:
P(H/GN) =
P(H)P(GN/H)
P(H)P(GN/H) + P(L)P(GN/L)
To fill in the terms:
P(H/GN) = 0.30 x 0.80 / (0.30 x 0.80) + (0.70 x 0.10)
= .24 / .24 + .07
= 0.77
Note: the good news is in the numerator and the left side of the denominator. The
bad new is in the right side of the denominator.
Slide 17
The posterior probability of GN is .77 and the P(GN/L) is 1.00 - .77 = 0.23)
With this posterior information we will recalculate Judy's utilities:
EUa1 - 0.77 x 50 + 0.23 x 0 = 38.5
EUa2 - 1.00 x 25
= 25
Thus, the Good News will result in Judy changing her decision to buy the shares.
Slide 18
Another Example re Bayes’ Theorem
Lucy has $1,000 that she wishes to invest for one year. Her choices have been narrowed to a1 –
buy bonds of ABC Ltd., which pay 14.4% interest, unless it goes bankrupt and both principle
and interest will be lost, or buy Canada Savings Bonds, which pay 6.4% interest.
Lucy assesses her prior probability of ABC going bankrupt as 0.40.
Her utility for money is the square root of the amount of her gross payoff.
The Canada Savings Bond payoff is $1,064.
7
Based on her prior probabilities which action should she take?
Slide 19
Comment:
Payoff table for Lucy’s decision is:
State
Act
a1 Buy ABC Ltd.
a2 Buy CSBs
Not bankrupt
Bankrupt
$1,144
1,064
0
$1,064
Slide 20
Based on prior probabilities, the expected utility is:
____
0.6 x √1,144
_____
EU(a2) = 1.00 x √1,064
EU(a1) =
+
___
0.4 √ 0 = 0.6 x 33.82 + 0 = 20.29
= 32.62
(These can be written 0.6 x 1.1441/2)
The utility is greater for the CSBs so Lucy should purchase them.
Slide 21
Before proceeding with her decision, Lucy decides she needs more information.
She examines the debt-to-equity ratio of ABC Ltd. She observes it is low.
With her previous experience in bonds she knows the following:
Slide 22
DEBT – TO – EQUITY RATIO
FUTURE STATE
LO
HI
Not Bankrupt – NB
0.50
0.50
Bankrupt - B
0.05
0.95
8
Which action should she now take?
Slide 23
P(NB|LO)
=
0.60 x 0.50
0.60 x 0.50 + 0.40 x 0.05
P(B|LO)
=
1.00 – 0.94 = 0.06
= 0.30/ 0.32 = 0.94
The expected utility of each act is now:
______
_____
EU(a1|LO) = 0.94 x √1,144 + 0.06 x √ 0
= 0.94 x 33.82 +0
= 31.79
Slide 24
Then, Lucy’s expected utilities for the two would now be:
EUa1 = 31.79 vs EUa2 = 32.62
While the expected utility for the a1 has changed Lucy should not change her decision. Utility
for CSBs is still optimal.
Slide 25
Section II
The Information System – the flow of information
We can see from the above with additional information Judy has made a decision to change her
purchase and Lucy has made no change in her decision. This additional information is part of the
information system.
You are part of the information system. You prepare financial information for investors and this
is a very important part of the course.
But - Historical Cost Statements:
- Do not show future values as do present value statements.
9
Slide 26
- However, they can show good or bad news and suggest whether this will continue into the
future.
We use current information to predict future income and this can predict future returns.
The ultimate interest is to determine market value of shares and future dividends, which is
determined by returns, and the current way of approaching it.
Slide 27
Main Diagonal:
This additional information can be put in a matrix showing what is referred to as the main
diagonal and the off-main diagonal. The probabilities shown are the link between current and
future financial statement information.
This link can be called an information system which can be summarized as follows:
Slide 28
Matrix of Information System
Financial Statements
Future
Profitability
GN
BN
H
0.80
0.20
L
0.10
0.90
Slide 29
The main diagonal is as follows: 0.80 and 0.90; the off-main diagonal is 0.10 and 0.20.
10
Slide 30
We can say this depicts the information system - if the firm is in a high profitability state,
currently, the probability that the current financial statements will show good news in the next
quarter or two is then 0.80. This is linking the past with the future.
Future cash flows are important to the investor and that it what it is about.
Slide 31
Now if we had additional information as indicated by Bayes Theorem, and the good news in
a high situation indicates an increase to 0.85 then the probability of good news in the next
quarter, increases by 5%. The main diagonal increases to 0.85, 0.90, and the off-main
diagonal changes to 0.10 and 0.15. This is an important point.
Slide 32
The link between the previous information and the current information is the posterior
information and the use of Bayes' Theroem.
The lesson to be learned is that with the use of present value or other information,
relevance may be increased but reliability may be decreased, so we must be aware of this.
The increase in probability will make it more relevant but will make it less reliable than if we
stayed with the historical cost original estimate. Example, to use market values may increase
relevance but may decrease reliability because of the volatility.
If we can increase relevance, without sacrificing reliability, we could increase financial statement
usefulness to investors.
In summary the information system is very important in decision-making and the more relevant
it is the greater will be the main diagonal probabilities.
Slide 33
An Exam Question:
HH is a risk-averse investor. He has $10,000 and he will invest in Share A or Share B. Payoffs
and probabilities are shown below:
11
Slide 34
Share A
High future profitability (0.30)
Low future profitability (0.70)
$4,100)
400) Payoff
Share B
High future profitability (0.60)
Low future profitability (0.40)
$1,225)
625) Payoff
HH is a rational decision maker and has a square root utility for money
Slide 35
a) Based on the above information which is the more risky investment? Do not calculate at this
point.
Answer
Based on the fact that the range of the payoffs is wider for Share A than Share B, it would be
expected that there would be more risk. Also the probabilities are more widely separated both
features of which would make it a more risky investment.
b) What are the calculations?
Slide 36
Answer
Ea1 = (0.30 x 4,1001/2 + 0.70 x 4001/2) = 33.21
Ea2 = (0.60 x 1,2251/2 + 0.40 x 6251/2 = 31.00
Slide 37
c) Discuss the risk-averse tradeoff between investing in Share A and investing in Share B.
Which should he invest in?
Answer
Share A gives the higher utility and while it has the greater risk, it gives the higher return.
The payoff for A is greater and thus it outweighs the greater risk of A.
12
Slide 38
d) You are given the following re the information system for firm A.
Financial Statements
Future Profitability
Good News
Bad News
High
0.65
0.35
Low
0.25
0.75
Slide 39
How will informativeness of the system change if firm A is required to switch
from historical cost accounting to market value accounting for its capital assets. Answer from the
point of view of relevance and reliability.
Answer
Relevance is likely to increase, which would cause the main diagonal probabilities to increase
and off-main diagonals to decrease. The reason is current market values are a better predictor of
future cash flows than historical values. However, reliability is likely to decrease as would the
main diagonal probabilities would decrease as market values would be more volatile and more
subject to managerial bias than historical cost. So we cannot tell which would have the greater
influence – relevance or reliability.
13
Slide 40
PART 2
The Rational, Risk-Averse Investor
We want to discuss the question of risk and the investor.
The Rational, Risk-Averse Investor
Decision theory assumes that the investor is risk-averse, which seems reasonable.
This feeling of risk-aversement grows as the stakes become higher.
As indicated earlier the risk averse mode is measured by what is referred to as a utility function,
"which relates payoff amounts to the decision maker's utility for those amounts."
The utility function is:
_
U(x) = √x, x ≥0; (x is the amount of the payoff and x must be equal or greater than
zero)
14
Slide 41
To indicate what we call a risk-averse utility function we can use the diagram below that is in
your text, page 60.
U(x) |
50
B
30
E
25
D
C
15
0
0
625
750
2,500x (payoff)
D is a government bond which will yield 25 utils.
C is a stock which would have two payoffs - a good one of $2,500 or a bad one of $0. If you
take the probabilities given of 30% for a good payoff and 70% for zero payoff, you arrive at a
return of $750. ($2,500 x .30 + 0 x .70 = 750) - utility – 15 utils.
A risk-averse investor would take the government bond (D) with lower payoff prospect but a
higher utility of 25 utils. There is a higher payoff for C but a lower utility because of risk.
The line at D, shows a more attractive situation to the risk averse investor, as payoff goes up,
utility rises.
Now assume the probabilities change and while the investor still receives $750 for the stock
payoff, the investor's utility may rise to 30, and the stock would be more attractive than the
government bond – see point E.
You will see the kinked utility line rises to the point where the utility reaches a maximum. With
the higher payoff the investor gets the full utility – 50 utils.
15
If a person were risk-neutral, no concern for risk, there would be a 45º line. It would be a straight
line or linear function as shown on page 61 of the text.
Risk aversion is important to accountants because as risk increases investors need to have more
information concerning that risk.
16
Slide 42
PART 3
Portfolio Diversification
We now want to consider the area of portfolios and risk.
Slide 43
Portfolio Diversification
The theory of investment relates to the decisions of an individual as related to portfolio theory
(management).
Its value is that it helps us better understand the needs and risks of investors.
The theory of investment is aimed at or considers the situation where the individual investor
has a certain amount of wealth and he/she must make the decision as to how much to consume
now out of income and how much to invest for consumption in the future.
We can acquire risk-free investments (government bonds - guaranteed return of principal and
interest) and investments which carry risk.
If there is a risk, there is a risk-return situation. The risk-averse investor requires a higher
return for taking the risk. There is a tradeoff between the two. A premium is paid for the risk
involved. The greater the risk the greater the premium.
For example, a second mortgage will carry a higher risk premium than will a corporation bond.
How does the individual protect himself/herself against risk in choosing a portfolio? It can
be done by diversifying the securities in the portfolio. Risk can be reduced in this way.
Slide 44
Diversification, Mean-Variance Utility and Risk
A word on the utility formula. You had a formula previously for the utility of the investor.
17
A variation of the utility is introduced at this point which represents the investment act:
Slide 45
_
Ui(a) = fi(xa,óa2)
Where: a is the act
i is investor
f is the function of
x bar is the expected return or expected value
σ2 is the variance of the investment
Slide 46
Mean-variance utility is important because it makes investors decisions more explicit.
A specific form for a mean-variance utility function could be
_
_
2
Ui(a) = 2xa - óa , as shown in your notes, or, say, U(a) = x - 1/3(ó2a)
The first formula is 2 times the expected return minus the variance.
The second formula is the expected return minus 1/3 of the variance.
Slide 47
We will illustrate the value of portfolio diversification.
It should be noted that the risk is indicated by the variance. For example, if you take the returns
of two securities, and plot them, normally there would be a normal distribution of those returns
as depicted by the Bell curve or a normal distribution.
If the spread around the mean is greater for one security than the other, that is, if the variance and
standard deviation is greater for the one than the other there is more risk inherent in the greater
spread of the returns around the mean.
Slide 48
Example from the text: (Page 63)
Note: The transaction charges are ignored.
18
Assume share A sells for $20. It could rise to $22. or fall to $17. There is a chance of it going to
$22 is 0.74, and the chance of it going to $17 is 0.26.
Dividends of $1.00 a share will be paid on share A.
Janet has $200 to buy the shares. What will her return be given the above data?
She buys 10 shares of A at $20. Looking forward for a year what return would Janet expect?
Slide 49
(22 x 10 + 10 x 1)0.74 + (17 x 10 + 10 x 1)0.26 = $170.20 + 46.80 / 200 = 1.085 – 1 = 0.085
Expected value of return 0.085 - Note - this is net return
but the gross return can be used also, i.e., $217/200 = 1.085
Lets take the variance and standard deviation and see the risk involved:
End of
Period
value
Rate
of
Return Prob.
Expected
Value
230
230 - 200 = 0.15 ( 0.74) = 0.1110
200
180 180 - 200 = - 0.10 (0.26) = -0.0260
200
EV 0.0850
Assume Janet's utility function is:
U(s) = 2EV - óa2
Her utility for this investment would be:
U(s) = 2EV - ó2 or 2 x 0.0850 - 0.0120 = 0.1580
Variance
(0.15 -0.085)2 0.74 =
0.0031
(-0.10 - 0.0850)2 0.26 = 0.0089
Φ 2 = 0.0120
Φ = 0.1095
19
Slide 50
Now assume the following data for shares bought by Janet:
She has $200 and she can diversify and buy shares of B Company as well as A shares.
Assume A shares are still $20 each and B shares are $10 each.
A $1.00 dividend will be paid on both. Also B shares have 0.6750 chance of rising to $10.50
and a 0.3250 chance of falling to $8.50.
To diversify her portfolio she spends:
$120 on share A, acquiring 6 shares.
80 on share B, acquiring 8 shares.
The gross end value of each will be:
Share A
Share B
H
H
a) (22 x 6) + (10.50 x 8)
b)
132 +
68
c)
102 + 84
d)
102 + 66
L
L
+ 14 dividends =
+ 14
“
=
+ 14
“
=
+ 14 “
=
$230
214
200
184
-
Given
Probability
0.5742
0.1658
0.1008
0.1592
1.0000
Note: these probabilities are given. Independent probability, for example, 0.74 x 0.6750 =
0.4995, results in a lower amount and the writer has increased it to 0.5742. See the text for the
reasons.
20
Combinations:
a+c
a+d
b+c
b+d
230
214
200
184
Given
Prob.
- 200/200 = 0.15 x 0.5742
- 200/200 = 0.07 x 0.1658
- 200/200 = 0.00 x 0.1008
- 200/200 = - 0.08 x 0.1592
Expected value
Variance
(0.15 - 0.0850)2 x 0.5742
(0.07 - 0.0850)2 x 0.1658
(0.00 - 0.0850)2 x 0.1008
(-0.08 - 0.0850)2 x 0.1592
1.0000 Ó2
Ó
Expected
Rate of Ret.
= 0.0861
= 0.0116
= 0.0000
= -0.0127
= 0.0850
= 0.0024
= 0.0000
= 0.0007
= 0.0043
= 0.0074
= 0.0860
Slide 51
We see that the variance and standard deviation are less than the variance and standard deviation
of the purchase of only A shares:
A
B
Ó2 - 0.0120 > 0.0074
Ó - 0.1095 > 0.0860
Slide 52
In summary then diversification can reduce risk.
Janet's utility function as assumed above:
Diversified
- U(s) = 2 x 0.0850 - 0.0074 = 0.1626
Not Diversified - U(s) = 2 x 0.0850 - 0.0120 = 0.1580
Once the expected value and the variance are applied to the utility formula you see Janet’s utility
is higher with the diversified portfolio.
21
Slide 53
Diversification and Risk
Diversification is aimed at eliminating as much as possible the risk
inherent in a portfolio of shares.
All shares embody two types of risk – Systematic Risk and Firm-Specific Risk
Slide 54
Systematic risk caused by economy-wide or market-wide factors, that is, interest rates, general
economic conditions, etc., and,
Non-systematic risk or firm-specific factors peculiar to the firm itself, such as management,
technology, strikes, etc.
Slide 55
Diversification can achieve two things:
1. - it can to a great extent nullify the effect of firm specific factors by one firm cancelling out
another's firm-specific risk and, also,
2. - the effect of systematic risk can be a little reduced. The notes indicate that the probabilities
of a correlation of the returns under systematic risk will give a higher return than if the
probabilities of the shares are considered under the independent probability process. Under
independent probability the individual share probabilities are multiplied, but when correlated
they are considered separately. (See page 65 of the text for further explanation).
Slide 56
Note:- If there were only market-wide factors involved, all firms returns would be perfectly
correlated with one another. There would be no variation.
If there were only firm-specific factors, there would be no correlation between firms. The
firms would have their own distinct character.
For the following illustrations both types of risks are assumed.
22
Slide 57
PART 4
The Optimal Investment Decision
In this part we want to discuss the optimal decision in portfolio management.
The Optimal Investment Decision - Without transaction costs.
If holding two types of shares as compared to one type, reduces risk then holding a large number
or all the shares in the market should be better again.
This would be called "holding the market."
The reason for the less risk is that firm-specific risks tend to cancel each other out. One share
realizes a high return and one a low return, resulting in an average return.
There is economy-wide risk mentioned above and this would prevent a complete cancelling out
of risk. This is called systematic risk, as mentioned.
Then diversifiable risk is called non-systematic risk, as indicated in Janet’s example.
Slide 58
What should Janet do? She is thinking of buying all the shares in the market. But she can't do
this. Lets look at the Toronto Stock Exchange Main Index as a substitute for the market.
She and her broker discuss the TSE chances of moving up or down.
They decide that if the economy is:
Slide 59
Good - it will rise 10% - Probability of this is
Bad - it will rise 2.5% "
“ “ “
- 80%
- 20%
23
Expected Value = 0.10 x 0.80 + 0.025 x 0.20 = 0.0850
Variance - Ó2 = (0.10 - 0.0850)2 x 0.80 + (0.0250 - 0.0850)2 x 0.20
= 0.0002 + 0.0017 = 0.0009
Slide 60
U(s) – (2 x 0.085) – 0.0009 = 0.1691 This is greater than her utility of 0.1626 shown earlier
for the two share portfolio.
(Note: we will use this market data later in our calculations.)
Slide 61
Janet and her risk situation
A likely scenario for Janet’s risk could be:
Situation
A
Variance
0
Expected Return
7%
Type of Security
Government Security
B
0.1836
15%
Corporation Bond
C
0.2224
20%
Second Mortgage
Slide 62
Janet would probably consider her optimal investment decision as follows:
if she were: very risk-averse she would likely take A
If she were: moderately risk-averse she may take B
If she were: not very risk-averse she may take C.
Slide 63
The Optimal Investment Decision - With transaction costs.
When transaction costs are considered, a risk-averse investor's optimal investment decision is to
buy relatively few securities rather than the market portfolio. In this way, most of the benefits of
diversification can be attained, at reasonable cost.
24
It is contended that about 10 securities can diversify enough to eliminate most of the
diversifiable or non-systematic risk. Then in a portfolio of ten we would like to know how
much systematic and non-systematic risk exists.
Slide 64
Beta
We need Beta, which is a measure related to the firm. Beta measures the correlation between
the changes in the price of the security of a firm as compared to the changes in the market value
of the market portfolio – it indicates the systematic risk the firm is facing. (Important)
This information can indicate what might be expected in regard to return. A person can choose
the portfolio in regard to risk and return and their transaction costs.
Slide 65
Process
The formula for beta for share A is ßa = Cov(A,M)/Var(M)
Covariance is: a measure of the association of two random variables. To put it another way,
covariance measures how much the two random variables, such as Share A and the Market,
vary with each other, that is, how their returns co-vary. Note: the variance of the market or
the share is the variation, say, in the return, from the expected value or mean.
Thus, where Cov(A,M) is referred to, it is the covariance of the returns of A with the returns of
the market portfolio M. The Var(M) is the variance of the market. Dividing by Var(M)
standardizes the Cov(A,M) in terms of market variance - similar to getting a z value in statistics
or the standard deviation.
Slide 66
Follow the Handout
Then, ßeta measures how strongly the return of A varies as the market return varies. To use
the example in the text to explain:
To calculate the beta of A share, assume the payoff probabilities of A as follows:
(Some of these data have been given re share A and the market in the previous parts of the
lesson. Other data are given now. )
25
For Share A:
When economy is good and the market return is high:
Probability return on Share A is high - 0.90
"
" "
Share A " low - 0.10
Return in high state 15%
When economy is low and the market return is low:
Probability return on Share A is high - 0.10
"
" "
Share A " low - 0.90
Return in low state negative 10%
For the Market:
When the economy is good and return is high:
Probability of 0.80, that the market will be 10%
When the economy is bad and return is low:
Probability of 0.20, that the market will be 2.5%
Expected value for both 0.085
Calculation of Covariance
Payoff
A
high
high
low
low
M
high
low
high
low
(1)
Share
Return EV
(0.15 – 0.085)
(0.15 - 0.085)
(-0.10- 0.085)
(-0.10- 0.085)
(2)
(3)
Market
Probabilities
Return EV
[2 highs = (.8 x .9)]
(0.10 - 0.085)
x 0.72 (.8 x .9)
(0.025 - 0.085)
x 0.02 (.2 x .1)
(0.10 - 0.085)
x 0.08 (.8 x .1)
(0.025 –0.085)
x 0.18 (.2 x .9)
= 0.0007
= -0.0001
= -0.0002
= 0.0020
Cov(A,M)
= 0.0024
See below for explanation of terms.
Now to calculate beta for share A we divide the covariance by the market variance.
We calculated market variance on page 67 – which was 0.0009
26
Cov(A,M) /Mar(V)
Beta - ßa = 0.0024/ 0.0009 = 2.6667
Beta of Share A is 2.6667
Slide 67
(Still follow the Handout)
The market is always 1.00, so share A is 2.6667 more volatile than the market. This means that
share A’s volatility or reaction to systematic risk is 2.6667 times that of the market. In other
words, if the market increased 10%, share A will probably increase 26.7%, and vice versa for a
decrease.
Legend:
Column 1 - the high return for Share A is 0.15, and the low return is –0.10; the expected value is
0.085.
Column 2 - the high return for the market is 0.10 and the low return is 0.025; the expected value
is 0.085.
Column 3 - this column relates to the highs and lows of the market and shares. For example, the
high-high probability - for the share the high is 0.9 and the high probability for the market is 0.8,
multiplied we get .72. In the probabilities, the market governs what the share will be.
Assume a market variance - 0.0009 – shown below
For Share B will take from text as a Variance of 0.0088, p 87, and a Beta of 1.5556, p.71.
Slide 68
Portfolio Expected Value and Variance
Now as a portfolio manager we want to find out if we can diversify further or have we
diversified as much as we can? How much systematic risk is there in the portfolio of 10 shares?
Systematic risk in the portfolio is something about which we can do very little or nothing as all
shares face the systematic risk of the economy
We want to measure the systematic risk in the portfolio of 10 shares. A and B are two of the
shares. Assume we have C, D, E. F, G, H, I, J also.
27
We take the covariance between all combinations of the shares: A and B, A and C, A and D, etc.,
B and C, B and D, etc.
To determine how many covariances we would have, use the formula on Page 72 of the text:
n(n - 1)/2, in that this case: 10(10 - 1)/2 = 90/2 - 45.
We will do one covariance between A and B and extrapolate our findings.
The formula for the expected value is:
_
_
_
EVp = k1x1 + k2x2 + knxn
_
x is the expected return and k is the proportion of each share in the portfolio.
In our case we use the two shares: A and B and some of the earlier figures.
Their expected values are 0.085 each and their proportions in the portfolio are .60 and .40
($120 and 80 a division of $200)
EVp = 0.6 x 0.085 + 0.4 x 0.085 = 0.0850
You will note that at the top of page 72 of the text, the formula for the variance of the portfolio is
shown. Further down the page it is more simplified for Covariance of A & B, and it suits our
purpose. It is:
Var(A+B) = k12Var(A) + (1-k1)2Var(B) + 2k1(1-k1)M(Var)ßAßB
Let's complete it: we need the proportion of each share, the variance of A and Variance of
B, the market variance and beta A and beta B. The variance of Share A is 0.012 and of Share B
it is 0.0088.
Var(A & B) = 0.62 x 0.012 + 0.42 x 0.0088 + 2 x 0.6 x 0.4 x 0.0009 x 2.6667 x 1.5556
= 0.0043 + 0.0014 + 0.0017
= 0.0074
Points:
-
Important to note that the third term is 0.0017 for the variance between A and B. This
represents the systematic risk in the portfolio from Shares A and B – it is about 23% of
the total. Not too bad as the text says as there is a large
number of covariances.
28
Slide 69
You will note in the text it states that most of the risk is systematic risk because for n10 the
coefficient for variance terms is 1/100. Thus we have two variance terms here which would
make 2/100. If you have 45 such situations it will comprehend 90% of the total.
Thus, if 90% of your risk is systematic which you cannot diversify away, your portfolio is
well diversified.
Information about securities' returns and beta enables one to estimate expected returns and risk
involved.
Slide 70
Question: What does a risk-averse investor expect?
Answer: What he is looking for and expects is high returns and low risk.
Another question which is typically examination material:
Question: Beaver, one prominent writer, in one of his articles states that the message which
comes through loud and clear from finance theory is that the investor is concerned with assessing
risk as well as expected return.
a) Explain why the investor is concerned with risk as well as with expected return. What is the
important measure of risk as implied by portfolio theory? Explain why it is important.
Answer: The investor is concerned with risk as well as return because of risk aversion. He/she
is concerned about risk because their capital is at stake. If an investor is risk averse, he/she will
trade off risk and expected return. They will demand a higher return for a higher risk security.
The important measure of risk implied by portfolio theory is beta, which measures the
co-movement between changes in the market price of a security and changes in the market value
of the market portfolio. For a fully diversified portfolio, beta represents the contribution of a
security to the risk of a portfolio. Firm-specific risk is diversified away, leaving beta or
systematic risk as the relevant risk measure.
b) Question: Are financial statement-based measures of risk useful to risk averse investors?
Give an example of a financial statement-based risk measure and explain why or why not it may
be useful.
29
Answer: If one states yes, they could explain that the investor may not be fully diversified. If
so, the firm specific risk becomes relevant. Then financial statement-based risk measures, such
as the debt to equity ratio, are useful measures of firm specific risk since they measure the
likelihood of the firm running into financial and covenant-based problems.
If the investor is well-diversified, beta is the relevant risk measure of a security. Financial
statement-based risk measures may be correlated with beta. For example, higher debt to equity
ratio may be associated with higher beta. Then the investor who wishes to determine the beta of
a security may find financial statement-based risk measure useful.
If one answers no, that financial statement-based measures of risk are not useful to investors
because risk averse investors will be well diversified in which case beta is the relevant risk
measure of a security. Financial statement-based risk measure says little directly about beta.
30
Slide 71
PART 5
The Conceptual Framework
How Have The Rule-Setters (Accounting Bodies) Reacted to Decision Usefulness?
The major professional accounting bodies have adopted the decision-usefulness approach. The
first and most complete statement was set up by the Financial Accounting Standards Board in the
United States. See your Appendix 2-1 in the lesson notes. The Board set up a conceptual
framework for accounting procedures.
Conceptual Framework
.
What is it? One definition is "A theory of accounting to which practical problems can be
referred for solution in a relatively objective manner."
Slide 72
Background
Accounting is an information system by which data are recorded for decision-making purposes.
Because of the wide variety of situations in business and other organizations it is difficult to set
out rules, guidelines and standards to follow for all accounting situations. A voluminous record
would be required.
Also, as times change, accounting is changing, and any framework must accommodate daily
occurrences and it must be viable for the practitioner.
One approach is to sketch out a conceptual framework that is a broad general outline, so that
problems can be solved within the framework, and a base is formed on which generally accepted
accounting principles can be formulated. In other words principles for specific purposes are
established. For example, a general concept would be stated that amortization should be taken on
capital assets. Then principles would be established as to how amortization must be taken for
particular industries.
31
Naturally no framework could be constructed to encompass all known and later discovered realworld activities or phenomena.
A valid framework should be able to encompass unforeseen circumstances and enable new
solutions to be achieved.
Where such general frameworks have been conceived, they have mainly been by academics but
have lacked detailed work rules, which fails to answer the practitioner's requirement.
Slide 73
(Follow the Handout)
Objectives
FASB'S first objective was to have a conceptual framework which would enable accountants to
provide information which would be useful to present and potential investors, creditor grantors
and others in order that they may make rational investment, credit and other business decisions.
"Rational" attaches it to "economic decision theory", which means a maximization of expected
utility.
The second objective is to give information for present and potential investors to assess
amounts, timing and uncertainty of prospective cash receipts from dividends, interest, etc.
This, of course, relates to risk.
Question: Can historical cost-based statements be useful for future revenues?
Answer
To be useful there must be a linkage of the past and the future. Can the investor be helped by
past statements?
Question: What is one of the major problems in preparing historical cost-based statements?
Answer: It is necessary to know the problems of the investors, that is, the investors' needs.
32
Qualitative Characteristics
You will note on Page 2:l-4 of the Appendix in the lesson notes that a number of characteristics
are listed and commented upon in SFAC 2. These characteristics are very important to having
decision-useful material.
COMPARABILITY AND CONSISTENCY - information should be provided which can allow
comparison of firms within the industry and other related situations. The data should be
consistent so that investors and others can compare periods.
MATERIALITY - should be considered. Not only from a quantity point of view but also from a
quality viewpoint. An item may be large or small but quality is important.
COST – BENEFIT - Any provision of material for investors should bear a good cost-benefit
relationship. It would be unwise to have firms prepare
information which was in limited use.
Remember our task is to help a wide variety of investors to estimate cash flow.
RELEVANT AND RELIABLE - these are both mentioned in the FASB appendix.
Relevant accounting information is capable of making a difference in a decision by helping
users to form predictions about the outcomes of past, present and future events or to confirm or
change prior expectations.
If the decision-maker's ability can be enhanced then the financial reporting will be of value.
Relevant information is necessary for to be successful in this respect. However, the decisionusefulness approach can be achieved.
Reliable information is also necessary to achieve the decision-usefulness approach. Reliable
information means that the information is precise and free from bias.
To be reliable information must have representational faithfulness, it must be verifiable and
neutral.
Sometimes it is a problem for a manager to provide unbiased information but if this is not
followed then he/she is not representing the material in a faithful manner.
If one looks back on the reserve recognition accounting of the first module, it was seen that
management was not satisfied with the approach because they could not be sure of the estimates.
They wanted to be correct but found it difficult.
If a firm is to provide information on which an investor will base future cash flows, then that
material must be reliable.
33
Question: What are the qualitative characteristics of financial accounting information as
pronounced in SFAC2 of FASB?
Answer: These are characteristics which make accounting information useful.
CICA Handbook
The decision-usefulness approach has been followed by the Canadian accounting bodies.
CICA in Section 1000 of the Handbook states that the objective of financial information is to
communicate to investors, creditors and others useful information to enable them to make good,
sound decisions.
Such information should enable them to make predictions of cash flows.
While the section recognizes that there is a wide variety of needs among users, the aim should be
to provide information primarily for investors and creditors - this relates primarily to stocks and
debt of various forms.
It also points out that the material should be relevant and reliable which was the focus of the
FASB release. Further, that there has to be a tradeoff, especially between these two
characteristics, in order to achieve the best situation.
One interesting point regarding the CICA release is the absence of any mention of risk. The
McDonald Commission doing a subsequent study on audits recommended that such a study be
undertaken. However, the decision-usefulness approach has been followed.
ASAC
The Accounting Standards Authority of Canada, which was set up by the Certified General
Accountants Association, had as its goal to set up a conceptual framework for standard-setting
which would achieve the objective outlined in the definition above.
The ASAC was based on the FASB study but with a Canadian viewpoint.
The objective was that financial reporting should provide information for managers, investors,
credit grantors and others information on which to make sound decisions.
The approach should be that information would be provided which would enable one to make
predictions regarding the probability, the amounts and the timing of future cash flows.
It was pointed out that relevant material is that material which can make a difference in the
decision one might take. It is meaningful material. It may result in one changing his/her beliefs.
34
In summary it is the approach of all three bodies to provide quality information for
investors, creditors and others.
A typical examination question:
Question:
The decision usefulness approach to financial reporting suggests that accountants should
understand the decision problems of financial statement users.
a) Explain why accountants need to understand the decision-problems of financial statement
users if they are to prepare useful financial statements.
Answer: Accountants need to understand the decision problems of users so that they will know
what information is needed for good investment decisions.
b) What two aspects of future firm performance does the theory of the portfolio investment
decision tell us that rational, risk averse investors need help with?
Answer: They need help with assessing the expected returns and the risk of their portfolio
investments. To embellish the answer one could add that the shares' betas are the relevant risk
measures for assessing portfolio risk, as firm-specific risk can be largely diversified away.
c) Explain how accounting information can help in assessing the two aspects of future
performance - risk and return.
Answer: It can help in assessing a share's expected return by providing an information system
that enables investors to use current accounting information to revise their subjective beliefs
about future firm performance.
This could also be answered by using the formula for the expected return on a portfolio as
indicated in the notes:
xp = k2x1 + k2x2 + ... + knxn
Financial statement information can help in assessing portfolio risk by providing ratios that
measure risk and which are correlated with the share's beta, such as, leverage, earnings
variability, etc. This topic will be covered in lesson 4.
Ethical Issues Read ERH Units A1 and A3, also, Unit C4. Two cases - A request by
a client is made to fudge the statements, and one on auditor responsibility.
35