Chapter 7
Sources of Risks and Their
Determination
By
Cheng Few Lee
Joseph Finnerty
John Lee
Alice C Lee
Donald Wort
Chapter Outline
•
•
•
•
•
2
7.1 RISK CLASSIFICATION AND MEASUREMENT
• 7.1.1 Call Risk
• 7.1.2 Convertible Risk
• 7.1.3 Default Risk
• 7.1.4 Interest-Rate Risk
• 7.1.5 Management Risk
• 7.1.6 Marketability (Liquidity) Risk
• 7.1.7 Political Risk
• 7.1.8 Purchasing-Power Risk
• 7.1.9 Systematic and Unsystematic Risk
7.2 PORTFOLIO ANALYSIS AND APPLICATION
• 7.2.1Expected Return on a Portfolio
• 7.2.2Variance and Standard Deviation of a Portfolio
• 7.2.3The Two-Asset Case
• 7.2.4 Asset Allocation among Risk-Free Asset, Corporate Bond, and Equity
7.3 THE EFFICIENT PORTFOLIO AND RISK DIVERSIFICATION
• 7.3.1 The efficient Portfolio
• 7.3.2 Corporate Application of Diversification
• 7.3.3 The Dominance Principle
• 7.3.4 Three Performance Measures
• 7.3.5 Interrelationship among Three Performance Measure
7.4 DETERMINATION OF COMMERCIAL LENDING RATE
7.5 THE MARKET RATE OF RETURN AND MARKET RISK PREMIUM
7.1 RISK CLASSIFICATION AND
MEASUREMENT
•
•
•
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•
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•
3
Call Risk
Convertible Risk
Default Risk
Interest-Rate Risk
Management Risk
Marketability (Liquidity) Risk
Political Risk
Purchasing-Power Risk
Systematic and Unsystematic Risk
Figure 7-1
Probability Distributions
Between Securities A and B
4
（ Convertible Risk ）
TABLE 7-1 Types of Risk
Risk Type
Description
Call risk
The variability of return caused by the repurchase of the security before its stated maturity.
Convertible risk
The variability of return caused when one type of security is converted into another type of
security.
Default risk
The probability of a return of zero when the issuer of the security is unable to make interest
and principal payments—or for equities, the probability that the market price of the
stock will go to zero when the firm goes bankrupt.
Interest-rate risk
The variability of return caused by the movement of interest rates.
Management risk
The variability of return caused by bad management decisions; this is usually a part of the
unsystematic risk of a stock, although it can affect the amount of systematic risk.
Marketability risk
(Liquidity risk)
The variability of return caused by the commissions and price concessions associated with
selling an illiquid asset.
Political risk
The variability of return caused by changes in laws, taxes, or other government actions.
Purchasing-power risk
The variability of return caused by inflation, which erodes the real value of the return.
Systematic risk
The variability of a single security’s return caused by the general rise or fall of the entire
market.
Unsystematic risk
The variability of return caused by factors unique to the individual security.
5
Types of Risk (Continued)
•
•
6
Business risk refers to the degree of fluctuation of net income
associated with different types of business operations. This kind
of risk is related to different types of business and operating
strategies.
Financial risk refers to the variability of returns associated with
leverage decisions. The question then arises as to how much of
the firm should be financed with equity and how much should be
financed with debt.
7.2 PORTFOLIO ANALYSIS AND
APPLICATION
• Expected
Return on a Portfolio
• Variance and Standard Deviation of a
Portfolio
• The Two-Asset Case
• Asset Allocation among Risk-Free Asset,
Corporate Bond, and Equity
7
7.2.1 Expected Return on a Portfolio
Portfolio analysis is used to determine the return and
risk for these combinations of assets.
• The rate of return on a portfolio is simply the
weighted average of the returns of individual
securities in the portfolio.
•
R p  Wa Ra  Wb Rc  Wc Rc
 (0.4)(0.1)  (0.3)(0.5)  (0.3)(0.12)
 0.091
in which Wa ,Wb , andWc are the percentages of the
portfolio invested in securities A, B, and C,
respectively.
8
7.2.1 Expected Return on a Portfolio
n
R p   RiWi
(7.1)
i 1
where:
n
W
i 1
i
1
W i  the proportion of the individual's investment allocated to security i;and
R i  the expected rate of return for security i.
9
7.2.2 Variance and Standard Deviation
of a Portfolio
N
Cov (W1 R1 , W2 R2 )  
t 1
(W1 R1t  W1 R1 )(W2 R2t  W2 R2 )
N 1
( R1t  R1 )(R2t  R2 )
 W1W2 
N 1
t 1
 W1W2 Cov ( R1 , R2 )
N
where:
(7.2)
R1t  t he rat eof ret urnfor t hefirst securit yin periodt ;
R2t  t he rat eof ret urnfor t hesecondsecurit yin periodt ;
R1 and R2  averagerat esof ret urnfor t hedirst securit yand t he
secondsecurit y,respect ively; and
Cov ( R1 , R2 )  t hecovariancebet ween R1 and R2 .
10
7.2.2 Variance and Standard Deviation
of a Portfolio
The covariance as indicated in Equation (7.2) can be used to
measure the covariability between two securities (or assets) when
they are used to formulate a portfolio. With this measure the
variance for a portfolio with two securities can be derived:
N
Var (W1 R1t  W2 R2t )  
t 1
11
[(W1 R1t  W2 R2t )  (W1 R1  W2 R2 )]2
N 1
(7.3)
7.2.2 Variance and Standard Deviation
of a Portfolio
• The
general formula for determining the
number of terms that must be computed (NTC)
to determine the variance of a portfolio with N
securities is
N2  N
NTC  N variances +
covariances
2
12
Sample Problem 7.1
Security 1
Security 2
W1  40%
W2  60%
t 1
R1t  10%
t 1
R2t  5%
2
15%
2
10%
3
20%
3
15%
R1  10%
R1  15%
N
Var (W1 R1t  W2 R2t )  
t 1
[(W1 R1t  W2 R2t )  (W1 R1  W2 R2 )]2
N 1
 [(0.4)(0.1)  (0.6)(0.05)  (0.4)(0.15)  (0.6)(0.1)]2 / 2
 [(0.4)(0.1
5)  (0.6)(0.1) (0.4)(0.15
)  (0.6)(0.1)
]2 / 2
 [(0.4)(0.2
)  (0.6)(0.15
)  (0.4)(0.15
)  (0.6)(0.1)
]2 / 2
(0.07  0.12) 2 (0.12  0.12) 2 (0.17  0.12) 2



2
2
2
Var port folio 0.0025
13
Sample Problem 7.1
14
Sample Problem 7.1
•
The riskiness of a portfolio can be measured by
the standard deviation of returns as:
N
p 
2
(
R

R
)
 pt p
t 1
(7.6)
N 1
where  p is the standard deviation of the
portfolio’s return and Rp is the expected return of
the n possible returns.
15
7.2.3 The Two-Asset Case
• To
explain the fundamental aspect of the riskdiversification process in a portfolio, consider the
two-asset case:
(7.7)
 (R  R )
N
2
p 
t 1
pt
N 1
N

p
 [W
t 1
2
1
( R1t  R1 ) 2  W22 ( R2t  R2 ) 2  2W1W2 ( R1t  R1 )(R2t  R2 )]
N 1
 W12 Var( R1t )  W22 Var ( R2t )  2W1W2 Cov( R1 , R2 )
where W1  W2  1
16
7.2.3 The Two-Asset Case
By the definitions of correlation coefficients
between R1 and R2 , ( 12 ), the Cov( R1 , R2 ) can be
rewritten:
Cov( R1 , R2 )  12 1 2
(7.8)
Where  1 and  2 are the standard deviations of
the first and second security, respectively.
• From Equations (7.7) and (7.8), the standard
deviation of a two-security portfolio can be defined
as
•
 p  Var (W1 R1t  W2 R2t )
 W   (1  W1 )   2W1 (1  W1 ) 12 1 2
2
1
17
2
1
2
2
2
(7.9)
Sample Problem 7.2
For securities 1 and 2 used in the previous example,
applying Equation (7.9), we get:
Security 1
Security 2
 12  0.0025
W1  0.4
12  1
 22  0.0025
W2  0.6
 p  (0.4) 2 (0.0025)  (0.6) 2 (0.0025)  2(0.4)(0.6)(1)(0.05)(0.05)
 0.0025
 p  0.05 or Var portfolio = 0.0025, the same answer as for
Sample Problem 7.1.
18
Sample Problem 7.2
If 12 = 1.0, Equation (7.6) can be simplified to the linear
expression:
 p  W1 1  W2 2
whereW2  (1  W1 ). Since Equation (7.9) is a quadratic
equation, some value of W1 minimizes  p .
To obtain this value, differentiate Equation (7.9) with
respect to W1 and set this derivative equal to zero. Then we
get:
 2 ( 2  12 1 )
W1  2
 1   22  2 12 1 2
19
(7.10a)
Sample Problem 7.2
If 12  1, Equation (7.10a) reduces from:
 p
W1
 [W12 12  (1  W1 ) 2  22  2W1 (1  W1 ) 12 1 2 ] 1 / 2
 [2W1 12  2(1  W1 ) 22  2(1  2W1 ) 12 1 2 ]
W1 [ 12 22  2  12  1 2 ]  [ 12  12 1 2 ]

[W12 12  (1  W1 ) 2  22  2W1 (1  W1 ) 12 1 2 ]
To
 2 ( 2   1 )
2
W1 

( 2   1 )( 2   1 )  2   1
20
(7.10b)
Sample Problem 7.2
• If12
 1 , Equation (7.10a) reduces to:
W1 
•
 2 ( 2   1 )
2

( 1   2 )( 1   2 ) ( 2   1 )
However, if the correlation coefficient between 1 and 2 is –1, then
the minimum-variance portfolio must be divided equally between
security 1 and security 2—that is:
0.05
W1 
0.05  0.05
 0.5
21
(7.10c)
Sample Problem 7.2
As an expanded form of Equation (7.9), a portfolio can be written:

 p  W12 12  2
i 1
 i 1
n 1
n

 
 j 1
n
where:
n

i 1

WiW j  ij i j 

j i 1

n

WiW j Cov( Rit , R jt ) |

1/ 2
(7.11)
1/ 2
Wi andW j  theinvestor's investmentallocatedto securityi and security j , respectively;
 ij  thecorrelation coefficient between securityi and security j ; and
n  the number of securitiesincluded in theportfolio.
22
Sample Problem 7.3
Consider two stocks, A and B:RA  10%, RB  15%,  A  4, and  B  6.
(1) If a riskless portfolio could be formed from A and B, what would
be the expected return of R p ? (2) What would the expected return
be if  AB  0 ?
Solution
2 2
2
2
1/ 2


(
W


(
1

W
)


2
W
(
1

W
)



)
1. p
A A
A
B
A
A
AB A B
If we let  AB  1
 p  [WA A  (1  WA ) B ],  p  0  4WA  6(1  WA ) RB
WA  3 / 5
So
23
3
2
R p  WA RA  (1  WA ) RB    (10%)    (15%)  12%
5
5
Sample Problem 7.3
Solution
2. If we let AB  0
 p  [WA2 A2  (1  WA ) 2  B2 ]1/2
 p
1
 [2WA A2  2(1  WA ) B2 (1)][WA2 A2  (1  WA ) 2  B2 ]1/2  0
WA 2
Then,
WA A2  (1  WA ) B2  0
WA   B2 / ( A2   B2 )  62 / (42  62 )  9 /13
9
4
RP  (10%)  (15%)  11.54%
13
13
24
7.2.4 Asset Allocation among Risk-Free
Asset, Corporate Bond, and Equity
25
•
The most straightforward way to control the risk of the
portfolio is through the fraction of the portfolio invested
in Treasury bills and other safe money market securities
versus risky assets.
•
The capital allocation decision is an example of an asset
allocation choice — a choice among broad investment
classes, rather than among the specific securities within
each asset class.
•
Most investment professionals consider asset allocation
as the most important part of portfolio construction.
Sample Problem 7.4
• Private
fund $500,000 investing in a risk-free
asset $100,000, risky equities (E) $240,000, and
long-term bonds (B) $160,000.
• Current
risky portfolio consists 60% of E and
40% of B, and the weight of the risky portfolio
in the mutual fund is 80%.
26
Sample Problem 7.4
27
•
Suppose the fund manager wishes to decrease risk
portfolio from 80% to 70%, then should sell
$400,000-0.7 ($500,000)=$50,000 of risky
holdings, with the proceed used to purchase more
shares in risk-free asset.
•
To keep the same weights of E and B (60% and
40%)in the risky portfolio, the fund manager
should sell
• 0.6×50,000=$30,000 in E
• 0.4×50,000=$20,000 in B
7.3 THE EFFICIENT PORTFOLIO
AND RISK DIVERSIFICATION
• The
efficient Portfolio
• Corporate Application of Diversification
• The Dominance Principle
• Three Performance Measures
• Interrelationship among Three Performance
Measure
28
7.3.1 The Efficient Portfolio
•
Definition: A portfolio is efficient, if there exists no
other portfolio having the same expected return at a lower
variance of returns, or, if no other portfolio has a higher
expected return as the same risk of returns.
•
This suggests that given two investments, A and B,
investment A will be preferred to B if:
E (A)  E (B) and Var  A   Var  B 
or
E (A)  E (B) and Var  A   Var  B 
Where E(A) and E(B) = the expected returns of A and B,
Var(A) and Var(B) = their respective variances or risk.
29
7.3.1 The efficient Portfolio
30
Sample Problem 7.5
•
Monthly rates of return for April, 2001 to April, 2010 for
Johnson & Johnson (JNJ) and IBM are used as examples. The
basic statistical estimates for these two firms are average
monthly rates of return and the variance-covariance matrix.in
Table 7.3:
Variance-Covariance Matrix
31
JNJ
IBM
JNJ
0.0025
0.0007
IBM
0.0007
0.0071
Sample Problem 7.5
From Equation (7.10), we have:
0.0071  .0007
0.0064

 0.5818
0.0025  0.0071  2(0.0007) 0.011
W2  1.0  0.5818  0.4182
W1 
Using the weight estimates and Equations (7.2) and (7.3):
E ( RP )  (0.5818)(0.0080)  (0.4182)(0.0050)
 0.0067454
 P2  (0.5818)2 (0.0025)  (0.4182) 2 (0.0071)  2(0.5818)(0.4182)(0.0007)
 0.0024
 P  0.0493
When 12 is less than 1.00 it indicates that the combination of the two securities
will result in a total risk less than their added respective risks.
32
7.3.2 Corporate Application of
Diversification
33
•
The effect of diversification is not necessarily limited to
securities but may have wider applications at the corporate
level.
•
Instead of “putting all the eggs in one basket,” the
investment risks are spread out among many lines of
services or products in hope of reducing the overall risks
involved and maximizing returns.
•
The overall goal is to reduce business risk fluctuations of
net income.
7.3.3 The Dominance Principle
• The dominance principle has been developed as a means of
conceptually understanding the risk/return tradeoff.
• As with the efficient-frontier analysis, we must assume an
investor prefers returns and dislikes risks.
34
7.3.4 Three Performance Measures
The Sharpe measure (SP) (Sharpe, 1966) is of immediate concern.
Given two of the portfolios depicted in Figure 7.4, portfolios B and
D, their relative risk-return performance can be compared using the
equations:
SP D 
RD  R f
D
and
SP B 
RB  R f
B
where
SP D , SP B  Sharpe performanc
e measures;
RD , RB  theaveragereturnof each portfolio;
R f  risk - free rate;and
 D ,  B  therespectivestandarddeviationon risk of each portfolio.
35
Sharpe measure (SP)
If a riskless rate exists, then all investors would prefer A to B
because combinations of A and the riskless asset give higher
returns for the same level of risk than combinations of the
riskless asset and B.
36
Sample Problem 7.6
Table 7.4
Smyth Fund
Jones Fund
Average return R (%)
18
16
Standard deviation  (%)
20
15
Risk-free rate  R f (%)  9.5
Using the Sharpe performance measure, the risk-return measurements for these two
firms are:
0.18  0.095
SPSmyth 
 0.425
0.20
0.16  0.095
SP Jones 
 0.433
0.15
Jones fund has better performance based on Sharpe measure.
37
Sample Problem 7.7
The performances of portfolios A-E shown in Table 7.5.
Portfolio
Return (%)
Risk (%)
A
50
50
B
19
15
C
12
9
D
9
5
E
8.5
1
R  Rf
By using Sharpe measure SP  M
, assume risk-free rate is 8%, the rank of
M

portfolios is A>B>E>C>D:
SPA  0.84,SPB  0.73,SPC  0.44,SPD  0.20,SPE  0.50
Protfolio A is the most desirable.
However, for risk-free rate 5%, the order changes to E>B>A>D>C:
SPA  0.90,SPB  0.933,SPC  0.77,SPD  0.80,SPE  0.35
Now E is the best portfolio.
38
Treynor measure (TP)
Treynor measure (TP), developed by Treynor in 1965, examines
differential return when beta is the risk measure.
The Treynor measure can be expressed by the following:
•
TP
Rj  Rf
j
(7.13)
where: R j  average return of jth portfolio;
R f  risk  free rate; and
 j  beta coefficient for jth portfolio.
•
39
The Treynor performance measure uses the beta coefficient (systematic
risk) instead of total risk for the portfolio as a risk measure.
Jensen’s measure (JM)
• Jensen (1968, 1969) has proposed a measure referred to as the
Jensen differential performance index (Jensen’s measure or
JM).
• JM is the differential return which can be viewed as the
difference in return earned by the portfolio compared to the
return that the capital asset pricing line implies should be
earned.
• CAPM:
•
•
40
RP  R f  (RM  R f ) P
JM  RP  [R f  (RM  R f ) p ]
(7.14)
(7.15)
Sample Problem 7.8
Portfolio
Ri
(%)

i
(%)
A
50
50
2.5
B
19
15
2.0
C
12
9
1.5
D
9
5
1.0
E
8.5
1
0.25
Rank portfolios based on JM: JM  ( Ri  R f )  i ( RM  R f )
(1)When RM=10% and Rf=8%,
JM A  37 %,JM B  7 %,JM C  1%,JM D  2 %,JM E  0 %
A>B>C>E>D
(2)When RM=12% and Rf=8%,
JM A  32%,JM B  3 %,JM C   2 %,JM D  3 %,JM E   0.5 %
A>B>E>C>D
41
Sample Problem 7.8
Portfolio
Ri
(%)

i
(%)
A
50
50
2.5
B
19
15
2.0
C
12
9
1.5
D
9
5
1.0
E
8.5
1
0.25
Rank portfolios based on JM: JM  ( Ri  R f )  i ( RM  R f )
(3)When RM=8% and Rf=8%,
JM A  42%,JM B  11 %,JM C  4 %,JM D  1 %,JM E  0.5 %
A>B>C>D>E
(4)When RM=12% and Rf=4%,
JM A  26 %,JM B   1 %,JM C   4 %,JM D   3 %,JM E  2.5 %
A>E>B>D>C
42
Since
7.3.5 Interrelationship among Three
Performance Measure
Since
 p   pm /  m2 and  pm   pm /  p m
The JM must be multiplied by
equivalent SM:
JM
P
1/𝜎𝑃
in order to derive the
[ RP  R f ] [ RM  R f ] ( pm )


P

m
 m p
[ RP  R f ] [ RM  R f ]

 SPP  SPm
P
m
(7.16)
(7.17)
(commom constant)
If the JM divided by 𝛽𝑃 ,it is equivalent to the TM plus some
constant common to all portfolios:
JM [ RP  R f ] [ RM  R f ] P


(7.18)
P
P
P
 TM P  [ RM  R f ]  TM P  commom constant
43
Sample Problem 7.9
Continuing with the example used for the Sharpe performance measure in
Sample Problem 7.6, assume that in addition to the information already provided
the market return is 10 percent, the beta of the Smyth Fund is 0.8, and the Jones
Fund beta is 1.1. Then, according to the capital asset pricing line, the implied
return earned should be:
RSmyth  0.095  (0.10  0.095)(0.8)  0.099
RJones  0.095  (0.10  0.095)(1.1)  0.1005
Using the Jensen measure, the risk-return measurements for these two firms are:
JM Smyth  0.18  0.099)  0.081
JM Jones  0.16  0.1005 0.0595
44
7.4 Determination of Commercial Lending Rate
Based upon the mean and variance Equations (7.1) and (7.2) it is possible to
calculate the expected lending rate and its variance. Using the information
provided in Table 7.8, the weighted average and the standard deviation can be
calculated:
(A)
(B)
(C)
(D)
( B D )
(A+C)
Economic
Conditions
Boom
Rf
(%)
12
Probability
0.25
Normal
10
0.50
Poor
8
0.25
Rp
(%)
3.0
5.0
8.0
3.0
5.0
8.0
3.0
5.0
8.0
Probability
0.40
0.30
0.30
0.40
0.30
0.30
0.40
0.30
0.30
Joint
Lending
Probability
Rate
of Occurrence
(%)
0.100
15
0.075
17
0.075
20
0.200
13
0.150
15
0.150
18
0.100
11
0.075
13
0.075
16
R  (0.100)(15%)  (0.075)(17%)  (0.075)(20%)  (0.200)(13%)  (0.150)(15%)
 (0.150)(18%)  (0.100)(11%)  (0.075)(13%)  (0.075)(16%)
 15.1%
  [(0.100)(15  15.1) 2  (0.075)(17  15.1) 2  (0.075)(20  15.1) 2  (0.200)(13  15.1) 2  (0.150)(15  15.1) 2
 (0.150)(18  15.1) 2  (0.100)(11  15.1) 2  (0.075)(13  15.1) 2  (0.075)(16  15.1) 2 ]1/2
 2.51%
45
According to lending rates in Table 7.8
The weighted average and the standard deviation are:
R  15.1%,   2.51%
46
7.5 The Market Rate Of Return And
Market Risk Premium
•
•
The market rate of return is the return that can be expected from
the market portfolio.
The market rate of return can be calculated using one of several
types of market indicator series, such as the Dow-Jones Industrial
Average or the Standard and Poor (S&P) 500 by using the
following equation:
I t  I t 1
 Rmt
I t 1
where: Rmt  marketrateof returnat timet;
I t  marketindex at t; and
I t 1  marketindex at t  1.
47
(7.19)
7.5 The Market Rate Of Return And
Market Risk Premium
48
•
A risk-free investment is one in which the investor is sure
about the timing and amount of income streams arising from
that investment.
•
The reasonable investor dislikes risks and uncertainty and
would, therefore, require an additional return on his investment
to compensate for this uncertainty. This return, called the risk
premium, is added to the nominal risk-free rate.
•
Table 7.9 illustrates the concept of risk premium by using the
market rate of return of S&P 500 index.
7.5 The Market Rate Of Return And
Market Risk Premium
TABLE 7.9 Market Returns and T-bill by Quarters
Quarter
S&P 500
(A)
Market
Return
(percent)
(B)
T-Bill
Rate
(percent)
(A)－(B)
Risk
Premium
(percent)
1980
IV
135.76
1981
49
I
136.00
+ 0.18
13.36
-13.18
II
131.21
- 3.52
14.73
-18.25
III
116.18
-12.94
14.70
-27.64
IV
122.55
+ 5.48
10.85
- 5.37
7.5 The Market Rate Of Return And
Market Risk Premium
TABLE 7.9 Market Returns and T-bill by Quarters (Continued)
S&P 500
(A)
Market
Return
(percent)
(B)
T-Bill
Rate
(percent)
(A)－(B)
Risk
Premium
(percent)
I
152.96
+ 8.76
8.35
0.41
II
168.11
+ 9.90
8.79
1.11
III
166.07
- 1.22
9.00
-10.22
IV
164.93
- 0.69
9.00
- 9.69
I
159.18
- 3.49
9.52
-13.01
II
153.18
- 3.77
9.87
-13.64
III
166.10
+ 8.43
10.37
- 1.94
IV
167.24
+ 0.68
8.06
- 7.37
Quarter
1983
1984
50
7.5 The Market Rate Of Return And
Market Risk Premium
TABLE 7.9 Market Returns and T-bill by Quarters (Continued)
S&P 500
(A)
Market
Return
(percent)
(B)
T-Bill
Rate
(percent)
(A)－(B)
Risk
Premium
(percent)
I
180.66
+ 8.02
8.52
- 0.50
II
188.89
+ 4.55
6.95
- 2.4
III
184.06
- 2.62
7.10
- 9.72
IV
207.26
+12.60
7.07
+ 5.53
I
232.33
+12.09
6.56
+ 5.53
II
245.30
+ 5.58
6.21
- 0.63
III
238.27
- 2.86
5.21
- 8.07
IV
248.61
+ 4.33
5.43
- 1.10
Quarter
1985
1986
51
7.5 The Market Rate Of Return And
Market Risk Premium
TABLE 7.9 Market Returns and T-bill by Quarters (Continued)
S&P 500
(A)
Market
Return
(percent)
(B)
T-Bill
Rate
(percent)
(A)－(B)
Risk
Premium
(percent)
I
292.47
+17.64
5.59
+12.05
II
301.36
+ 3.03
5.69
- 2.66
III
318.66
+ 5.74
6.40
+ 0.05
IV
240.96
-24.38
5.77
-30.10
Quarter
1987
52
7.6 SUMMARY
This chapter has defined the basic concepts of risk and risk
measurement. The efficient-portfolio concept and its
implementation was demonstrated using the relationships of risk
and return. The dominance principle and performance measures
were also discussed and illustrated. Finally, the interest rate and
market rate of return were used as measurements to show how the
commercial lending rate and the market risk premium can be
calculated.
Overall, this chapter has introduced uncertainty analysis assuming
previous exposure to certainty concepts. Further application of the
concepts discussed in this chapter as related to security analysis and
portfolio management are explored in later chapters.
53