Fin management materials / 3 P4AFM-Session04_j08
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SESSION 04 – PORTFOLIO THEORY AND CAPM
EXAMPLE SOLUTION
Solution 1
Investment 1
Probability |
Return |
px |
x − |
|
p(x − |
|
)2 |
x |
x |
px
0.1 |
10% |
1 |
−5 |
2.5 |
0.4 |
30% |
12 |
15 |
90.0 |
0.2 |
40% |
8 |
25 |
125.0 |
0.3 |
−20% |
−6 |
−35 |
367.5 |
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|
|
_____ |
________ |
expected return |
|
|
15 |
585.0 |
x |
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|
_____ |
________ |
Standard deviation |
= |
585 |
||
=24.2
Investment 1 has an expected return of 15% and a standard deviation (risk) of 24.2%
Investment 2
Probability |
Return |
px |
x − |
|
p(x − |
|
)2 |
x |
x |
px
0.3 |
10% |
3 |
- 5 |
7.5 |
0.3 |
20% |
6 |
5 |
7.5 |
0.2 |
30% |
6 |
15 |
45.0 |
0.2 |
0% |
0 |
−15 |
45.0 |
|
|
|
|
___ |
______ |
expected return |
|
|
|
15 |
105.0 |
x |
|
||||
|
|
|
|
___ |
______ |
Standard deviation |
= |
|
105 |
||
|
|
|
= |
10.2 |
|
Investment 2 has an expected return of 15% with a risk of 10.2%
Solution 2
It is likely that investors would prefer investment 2 as they can achieve the same expected return as with investment 1 but with a lower level of risk.
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SESSION 04 – PORTFOLIO THEORY AND CAPM
Solution 3
Return on portfolio |
= (0.6 × 8%) + (0.4 × 16%) |
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= 11.2% |
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|
Risk of portfolio |
|
|
|
|
|
|
|
|
|
(a) |
= |
0.62 ×42 |
+ 0.42 ×82 |
+ 2×0.6 |
×0.4×0.9×4×8 = 5.46% |
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(b) |
= |
0.62 |
×42 |
+0.42 |
×82 |
+2 |
×0.6 |
×0.4 |
×0.5×4×8 = 4.87% |
(c) |
= |
0.62 |
×42 |
+0.42 |
×82 |
+2 |
×0.6 |
×0.4 |
×−0.2×4×8 = 3.80% |
Solution 4
Beta factor |
= |
|
0.72×15 |
|
21 |
||||
|
|
|||
|
= |
0.51 |
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Solution 5
Ke |
= |
7 + 1.2 × (15 − 7) |
|
= |
16.6% |
Solution 6
Using published formula find the asset beta of the computer industry:
Ba |
= |
1.4× |
4 |
4 + 1×0.67 |
|||
Asset beta |
= |
1.2 |
|
As A plc is ungeared then this asset beta is the appropriate beta for use in the CAPM in order to determine the discount rate that A plc should use for a computer manufacturing project:
Required return = |
5 + 1.2 × (12 − 5) |
=13.4%
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SESSION 04 – PORTFOLIO THEORY AND CAPM
Solution 7
Using published formula find the asset beta of the computer industry:
Ba |
= |
1.4× |
4 |
4 + 1×0.67 |
|||
Asset beta |
= |
1.2 |
|
In order to find the discount rate for A plc this asset beta must be converted into an equity beta appropriate to A plc:
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2 |
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|
1.2 |
= |
Be |
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2 + 1×0.67 |
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1.2 |
= |
Be × 0.749 |
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Be |
= |
1.6 |
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Ke of A plc if in computer manufacture |
= |
5 + 1.6 × (12 – 5) |
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|
= |
16.2% |
The discount rate that A plc must use is the WACC that it would have if its Ke were 16.2%. In the absence of any other information assume the pre-tax cost of debt is 5% (risk free rate).
Discount rate |
= |
16.2% × ⅔ + 5 (1 – 0.33) × ⅓ |
|
= |
11.92% |
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SESSION 04 – PORTFOLIO THEORY AND CAPM
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