CHAPTER 6: RISK, RETURN and CAPITAL ASSET PRICING
MODEL
I.
Expected Rate of Return Based on Historical Data
1/ Historical data
Year/risk
2013
2014
2015
2016
Stock A
15%
5%
-5%
9%
Stock b
13%
4%
-2%
5%
2/ The expected return of stock A & Stock B in 2017:
Since we don’t have a probability distribution, the expected return for 2017 is
simply the mean of all the returns.
E(R
A2017
) = R
A
=
∑
T
=
1
n
RAT
/
n
E(R
A2017
)
=
(0.15+0.05-0.05+0.09)/4
=
6%
E(R
B2017
)= R
B
=
∑
T
=
1
n
RAT
/
n
E(R
B2017
)=
(0.13+0.04-0.02+0.05)/4
=
5%
3/ The variance of stock A and stock B retunes
(This measures how the return
differs from the expected return)
:
E(R
A
)
=
∑
T
=
1
n
(
RAt
−
RA
)
2
(
n
−
1
)
E(R
A
)
=
(
0.15
−
0.06
)
2
+(
0.05
−
0.06
)
2
+(−
0.05
−
0.06
)
2
+(
0.09
−
0.06
)
2
4
−
1
=
0.00707
E(R
B
)
=
(
0.13
−
0.05
)
2
+(
0.04
−
0.05
)
2
+(−
0.02
−
0.05
)
2
+(
0.05
−
0.05
)
2
4
−
1
=
0.00380
4/ The standard deviation
(Measures the Risk/Divarication level):
σ
(R
A
) =
√
(
R A
)
=
√
0.0071
=8.4%
σ
(R
B
) =
√
(
RB
)
=
√
0.0038
=0.06164 = 6.16%
5/Coefficient of variation
(Standard Deviation on the expected return/Risk per unit of
return)
1

CV
=
σ
(
R A
)
E
(
R A
)
CV
A
=
0.084
0.06
=
1.4
For each 1% of return is stock A the risk is equal to 1.4%. Meaning this stock is relatively
risky.
CV
=
σ
(
RB
)
E
(
RB
)
CV
B
=
0.0616
0.05
=
1.23
For each 1% of return in stock B the risk is equal to 1.23%.
6/ The covariance between stock A and stock B
(It measures the quantity of association
between A & B, either associated positively or negatively, if the calculated number is positive then we
have a positive association and if it’s negative vice versa)
:
Cov(R
A
,R
B
)=
∑
t
=
1
n
(
R At
−
R A
) (
R Bt
−
R B
)
(
n
−
1
)
Cov (R
A
,R
B
)
=
(
0.15
−
0.06
)(
0.13
−
0.05
)+(
0.05
−
0.06
)(
0.04
−
0.05
)+(−
0.05
−
0.06
)(−
0.02
−
0.05
)+(
0.09
−
0.06
)(
0.05
−
0
4
−
1
=
-0.05/0.025
0.01500
7/ Correlation Coefficient
(Measures the intensity (not quantity) of correlation between two
variables):
r
AB
=
Cor
(
R A ,R B
)
σ
(
R A
)
σ
(
R B
)
-1
≤r AB≤
+
1
It should be between -1 and +1, Meaning if:
r
AB
=+1, if both R
A
& R
B
are positive they are positively and perfectly correlated
r
AB
= -1, if both R
A
& R
B
are negative they’re negatively correlated
r
AB
= 0, No correlation between R
A
& R
B
8/ Calculating the Stock return
(Not the expected):
Q:
Assume you bought a stock for 12 and sold it for 16 and you received 1 riyal
as dividends.
R
t
=
(
Pt
−
Pt
1
)+
Dt
(
Pt
1
)
2

II.Data based on probability Distribution:We predict the future by hypothesizing the following: State of the worldProbability of OccurrenceRAKRBKExpansion0. 3%30%16%Stagnation0. 4%20%2%Rescission0.3%-5%-18%What changes here is that formula here is based in k. 1.1
2%
3

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