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Chapter 10: Return and Risk: The Capital Asset Pricing Model (CAPM)
10.1
a.
Expected Return
= (0.1)(0.045) + (.2)(0.044) + (0.5)(0.12) + (0.2)(0.207)
= 0.1057
=
10.57%
The expected return on Qmart’s stock is 10.57%.
b.
Variance (
σ
2
)
= (0.1)(0.045 – 0.1057)
2
+ (0.2)(0.044 – 0.1057)
2
+ (0.5)(0.12 – 0.1057)
2
+
(0.2)(0.207 – 0.1057)
2
= 0.005187
Standard Deviation (
σ
) = (0.005187)
1/2
= 0.0720
=
7.20%
The standard deviation of Qmart’s returns is 7.20%.
10.2
a.
Expected Return
A
= (1/3)(0.063) + (1/3)(0.105) + (1/3)(0.156)
= 0.1080
=
10.80%
The expected return on Stock A is 10.80%.
Expected Return
B
= (1/3)(0.037) + (1/3)(0.064) + (1/3)(0.253)
= 0.933
=
9.33%
The expected return on Stock B is 9.33%.
b.
Variance
A
(
σ
A
2
)
= (1/3)(0.063 – 0.108)
2
+ (1/3)(0.105 – 0.108)
2
+ (1/3)(0.156 – 0.108)
2
= 0.001446
Standard Deviation
A
(
σ
A
)
= (0.001446)
1/2
= 0.0380
=
3.80%
The standard deviation of Stock A’s returns is 3.80%.
Variance
B
(
σ
B
2
)
= (1/3)(0.037 – 0.0933)
2
+ (1/3)(0.064 – 0.0933)
2
+ (1/3)(0.253 – 0.0933)
2
= 0.014447
Standard Deviation
B
(
σ
B
)
= (0.014447)
1/2
= 0.1202
=
12.02%
The standard deviation of Stock B’s returns is 12.02%.
c.
Covariance(R
A
, R
B
) = (1/3)(0.063 – 0.108)(0.037 – 0.0933) + (1/3)(0.105 – 0.108)(0.064 – 0.933)
+ (1/3)(0.156 – 0.108)(0.253 – 0.0933)
=
0.004539
The covariance between the returns of Stock A and Stock B is 0.004539.
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View Full DocumentCorrelation(R
A
,R
B
) = Covariance(R
A
, R
B
) / (
σ
A
*
σ
B
)
= 0.004539 / (0.0380 * 0.1202)
=
0.9937
The correlation between the returns on Stock A and Stock B is 0.9937.
10.3
a.
Expected Return
HB
= (0.25)(0.02) + (0.60)(0.092) + (0.15)(0.154)
= 0.0733
=
7.33%
The expected return on Highbull’s stock is 7.33%.
Expected Return
SB
= (0.25)(0.05) + (0.60)(0.062) + (0.15)(0.074)
= 0.0608
=
6.08%
The expected return on Slowbear’s stock is 6.08%.
b.
Variance
A
(
σ
HB
2
) = (0.25)(0.02 – 0.0733)
2
+ (0.60)(0.092 – 0.0733)
2
+ (0.15)(0.154 – 0.0733)
2
= 0.003363
Standard Deviation
A
(
σ
HB
) = (0.003363)
1/2
= 0.0580
=
5.80%
The standard deviation of Highbear’s stock returns is 5.80%.
Variance
B
(
σ
SB
2
)
= (0.25)(0.05 – 0.0608)
2
+ (0.60)(0.062 – 0.0608)
2
+ (0.15)(0.074 – 0.0608)
2
= 0.000056
Standard Deviation
B
(
σ
B
)
= (0.000056)
1/2
= 0.0075
=
0.75%
The standard deviation of Slowbear’s stock returns is 0.75%.
c.
Covariance(R
HB
, R
SB
) = (0.25)(0.02 – 0.0733)(0.05 – 0.0608) + (0.60)(0.092 – 0.0733)(0.062 –
(0.0608) + (0.15)(0.154 – 0.0733)(0.074 – 0.0608)
=
0.000425
The covariance between the returns on Highbull’s stock and Slowbear’s stock is 0.000425.
Correlation(R
A
,R
B
) = Covariance(R
A
, R
B
) / (
σ
A
*
σ
B
)
= 0.000425 / (0.0580 * 0.0075)
=
0.9770
The correlation between the returns on Highbull’s stock and Slowbear’s stock is 0.9770.
10.4
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 Summer '06
 TimothyDreyer
 Finance, Capital Asset Pricing Model

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