Two portfolios on the capital market line have the same slope but different standard deviation.
The Capital allocation line equation is given by
Here, is the slope of the CML and is same for both the portfolios
Lets us consider a case of 2-portfolio on a CML with different portfolio standard deviation
is the expected return on the risky-part of the portfolio
is the risk-free rate = 2%
is the standard deviation on risky-part of the portfolio = 0.4
is the standard deviation of portfolio 1 = 0.2
is the standard deviation of portfolio 2 = 0.25
We use excel, to get different expected return on the portfolios and using the risk-free rate and standard deviations mentioned
E(Rp1) | 0.02+0.2*((E(Ra)-0.02)/0.4) |
E(Rp2) | 0.02+0.25*((E(Ra)-0.02)/0.4) |
E(Ra) | E(Rp1) | E(Rp2) |
1% | 1.500% | 1.37500% |
2% | 2.000% | 2.00000% |
3% | 2.500% | 2.62500% |
4% | 3.000% | 3.25000% |
5% | 3.500% | 3.87500% |
6% | 4.000% | 4.50000% |
7% | 4.500% | 5.12500% |
8% | 5.000% | 5.75000% |
9% | 5.500% | 6.37500% |
10% | 6.000% | 7.00000% |
11% | 6.500% | 7.62500% |
12% | 7.000% | 8.25000% |
13% | 7.500% | 8.87500% |
14% | 8.000% | 9.50000% |
15% | 8.500% | 10.12500% |
16% | 9.000% | 10.75000% |
17% | 9.500% | 11.37500% |
18% | 10.000% | 12.00000% |
19% | 10.500% | 12.62500% |
20% | 11.000% | 13.25000% |
21% | 11.500% | 13.87500% |
22% | 12.000% | 14.50000% |
23% | 12.500% | 15.12500% |
24% | 13.000% | 15.75000% |
25% | 13.500% | 16.37500% |
26% | 14.000% | 17.00000% |
27% | 14.500% | 17.62500% |
28% | 15.000% | 18.25000% |
29% | 15.500% | 18.87500% |
30% | 16.000% | 19.50000% |
31% | 16.500% | 20.12500% |
32% | 17.000% | 20.75000% |
33% | 17.500% | 21.37500% |
34% | 18.000% | 22.00000% |
35% | 18.500% | 22.62500% |
36% | 19.000% | 23.25000% |
37% | 19.500% | 23.87500% |
38% | 20.000% | 24.50000% |
39% | 20.500% | 25.12500% |
40% | 21.000% | 25.75000% |
41% | 21.500% | 26.37500% |
42% | 22.000% | 27.00000% |
43% | 22.500% | 27.62500% |
44% | 23.000% | 28.25000% |
45% | 23.500% | 28.87500% |
Now, we calculated the correlation for both these portfolios using excel => Data => Data Analysis => Correlation
We get the correlation matrix as
E(Rp1) | E(Rp2) | |
E(Rp1) | 1 | |
E(Rp2) | 1 | 1 |
Since, the correlation between the portfolios is 1, we observe that the two portfolios (on the CML) are perfectly correlated.
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