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Financial planning sometimes requires investigation into the expected profitability of undertaking a specific project. An appropriate rate of return for a project is one that adds cash flows to the firm, helps diversify risk of a portfolio and has taken into account the risk associated with the market that is non-diversifiable. To do this, the analysis requires use of the capital asset pricing model (CAPM).
The equation requires information about systematic risk (market risk), and is represented in quantitative terms as beta (β) in the financial industry. The analysis also needs to be made aware of the expected return of the market and the expected return of a theoretical risk-free asset.
CAPM starts by relating the expected return on an asset to its systematic risk. First draw the Security Market Line (SML). The SML equation is expressed as follows:
where
- E[Ri] = the expected return on asset i,
- Rf = the risk-free rate, (bonds at the bank for eg. 10 years)
- E[Rm] = the expected return on the market portfolio,
- bi = the Beta on asset i, and
- E[Rm] - Rf = the market risk premium.
|
|
|
risk |
Market |
Security |
Mrkt |
Security |
|
Nr. |
Period |
free rate |
Return |
Return |
Premium |
Premium |
|
1 |
01.26.09 |
11% |
-2% |
1% |
-13% |
-10% |
|
2 |
02.28.09 |
14% |
0% |
-2% |
-14% |
-16% |
|
3 |
03.31.09 |
15% |
1% |
4% |
-14% |
-11% |
|
4 |
04.30.09 |
16% |
3% |
-1% |
-13% |
-17% |
|
5 |
05.31.09 |
17% |
6% |
6% |
-11% |
-11% |
|
6 |
06.30.09 |
15% |
8% |
4% |
-7% |
-11% |
|
7 |
07.31.09 |
14% |
9% |
5% |
-5% |
-9% |
|
8 |
08.31.09 |
13% |
11% |
14% |
-3% |
1% |
|
9 |
09.30.09 |
13% |
12% |
6% |
-1% |
-7% |
|
10 |
10.31.09 |
12% |
14% |
15% |
2% |
3% |
|
11 |
11.30.09 |
12% |
15% |
16% |
3% |
4% |
|
12 |
12.31.09 |
11% |
16% |
11% |
5% |
0% |
|
13 |
01.31.10 |
10% |
13% |
13% |
3% |
3% |
|
14 |
02.28.10 |
9% |
14% |
16% |
5% |
7% |
|
15 |
03.31.10 |
10% |
15% |
17% |
5% |
7% |
|
16 |
04.30.10 |
8% |
15% |
18% |
7% |
10% |
|
17 |
06.01.10 |
8% |
16% |
20% |
8% |
12% |
|
18 |
07.01.10 |
9% |
17% |
21% |
8% |
12% |
|
19 |
08.01.10 |
9% |
16% |
20% |
7% |
11% |
|
20 |
09.01.10 |
8% |
15% |
22% |
7% |
14% |
|
21 |
10.01.10 |
8% |
15% |
23% |
7% |
15% |
|
22 |
11.01.10 |
9% |
14% |
24% |
5% |
15% |
|
23 |
12.01.10 |
9% |
14% |
26% |
5% |
17% |
|
24 |
01.01.11 |
8% |
16% |
28% |
8% |
20% |
|
25 |
02.01.11 |
10% |
16% |
29% |
6% |
19% |
|
26 |
03.01.11 |
11% |
17% |
31% |
6% |
20% |
|
27 |
04.01.11 |
12% |
18% |
33% |
6% |
21% |
|
28 |
05.01.11 |
11% |
16% |
32% |
5% |
21% |
|
29 |
06.01.11 |
10% |
17% |
31% |
7% |
21% |
|
30 |
07.01.11 |
9% |
16% |
31% |
7% |
22% |
|
31 |
08.01.11 |
10% |
16% |
29% |
6% |
19% |
|
32 |
09.01.11 |
11% |
17% |
27% |
6% |
16% |
|
33 |
10.01.11 |
10% |
16% |
28% |
6% |
18% |
|
34 |
11.01.11 |
9% |
15% |
26% |
6% |
17% |
|
35 |
12.01.11 |
8% |
16% |
26% |
8% |
18% |
|
36 |
01.01.12 |
8% |
16% |
25% |
8% |
17% |
|
37 |
02.01.12 |
9% |
17% |
24% |
8% |
15% |
|
38 |
02.29.12 |
9% |
17% |
23% |
8% |
14% |
|
39 |
03.31.12 |
8% |
16% |
26% |
8% |
18% |
|
40 |
04.30.12 |
7% |
16% |
27% |
9% |
20% |
|
41 |
05.31.12 |
7% |
15% |
28% |
8% |
21% |
|
42 |
06.30.12 |
7% |
15% |
27% |
8% |
20% |
|
43 |
07.31.12 |
9% |
16% |
27% |
7% |
18% |
|
44 |
08.31.12 |
10% |
17% |
26% |
7% |
16% |
|
45 |
09.30.12 |
10% |
16% |
23% |
6% |
13% |
|
46 |
10.31.12 |
9% |
17% |
24% |
8% |
15% |
|
47 |
11.30.12 |
9% |
18% |
21% |
9% |
12% |
|
48 |
01.01.14 |
8% |
16% |
20% |
8% |
12% |
|
49 |
01.31.13 |
9% |
17% |
19% |
8% |
10% |
|
50 |
02.28.13 |
8% |
15% |
18% |
7% |
10% |
|
51 |
04.01.13 |
7% |
14% |
16% |
7% |
9% |
|
52 |
05.01.13 |
6% |
16% |
14% |
10% |
8% |
|
53 |
06.01.13 |
5% |
15% |
14% |
10% |
9% |
|
54 |
07.01.13 |
4% |
14% |
13% |
10% |
9% |
|
55 |
08.01.13 |
4% |
15% |
12% |
11% |
8% |
|
56 |
09.01.13 |
3% |
14% |
13% |
11% |
10% |
|
57 |
10.01.13 |
5% |
16% |
15% |
11% |
10% |
|
58 |
11.01.13 |
4% |
15% |
14% |
11% |
10% |
|
59 |
12.01.13 |
3% |
14% |
16% |
11% |
13% |
|
60 |
01.01.14 |
4% |
15% |
16% |
11% |
12% |
|
SUMMARY OUTPUT |
|||||||
|
Regression Statistics |
|||||||
|
Multiple R |
0,823400164 |
||||||
|
R Square |
0,67798783 |
||||||
|
Adjusted R Square |
0,672435896 |
||||||
|
Standard Error |
0,057513844 |
||||||
|
Observations |
60 |
||||||
|
ANOVA |
|||||||
|
|
df |
SS |
MS |
F |
Significance F |
||
|
Regression |
1 |
0,4039 |
0,403945 |
122,12 |
6,725E-16 |
||
|
Residual |
58 |
0,1919 |
0,003308 |
||||
|
Total |
59 |
0,5958 |
|
|
|
||
|
|
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
|
Intercept |
0,037400126 |
0,0093 |
4,004639 |
0,0002 |
0,0187057 |
0,05609 |
0,018705698 |
|
X Variable 1 |
1,279724851 |
0,1158 |
11,05067 |
7E-16 |
1,0479159 |
1,51153 |
1,047915871 |