Question
In: Finance
Assume the correlation between the two stocks equals 1 exactly.Graph the investment opportunity set. Now assume...
Assume the correlation between the two stocks equals 1 exactly.Graph the investment opportunity set.
Now assume the correlation between the two stocks equals exactly –1. Again, graph the investment opportunity set.
If you would like, you can perform on the same graph.
Solutions
Expert Solution
Let Wa, Wb be the weights of two stocks A & B respectively in the portfolio. Let expected return of A and B be Ra and Rb respectively and the standard deviation be σa and σb. Let Rp and σp be the expected return and standard deviation of the retun of the portfolio.
Rp = WaRa + WbRb
σp2 = (Waσa)2 + (Wbσb)2 + 2ρ(WaσaWbσb)
When ρ = coefficient of correlation = 1 then
σp2 = (Waσa)2 + (Wbσb)2 + 2(WaσaWbσb) = (Waσa + Wbσb)2
Hence, σp = Waσa + Wbσb
Please see the table below:
| Wa | Wb | Ra | Rb | σa | σb | σp | Rp |
| 0% | 100% | 10% | 20% | 15% | 25% | 25.00% | 20.0% |
| 10.0% | 90% | 10% | 20% | 15% | 25% | 24.00% | 19.0% |
| 20.0% | 80% | 10% | 20% | 15% | 25% | 23.00% | 18.0% |
| 30.0% | 70% | 10% | 20% | 15% | 25% | 22.00% | 17.0% |
| 40.0% | 60% | 10% | 20% | 15% | 25% | 21.00% | 16.0% |
| 50.0% | 50% | 10% | 20% | 15% | 25% | 20.00% | 15.0% |
| 60.0% | 40% | 10% | 20% | 15% | 25% | 19.00% | 14.0% |
| 70.0% | 30% | 10% | 20% | 15% | 25% | 18.00% | 13.0% |
| 80.0% | 20% | 10% | 20% | 15% | 25% | 17.00% | 12.0% |
| 90.0% | 10% | 10% | 20% | 15% | 25% | 16.00% | 11.0% |
| 100.0% | 0% | 10% | 20% | 15% | 25% | 15.00% | 10.0% |
And the plot of the investment opportunity set is :
When ρ = coefficient of correlation = -1 then
σp2 = (Waσa)2 + (Wbσb)2 - 2(WaσaWbσb) = (Waσa - Wbσb)2
Hence, σp = |Waσa - Wbσb|
Please see the table below:
| Wa | Wb | Ra | Rb | σa | σb | σp | Rp |
| 0% | 100% | 10% | 20% | 15% | 25% | 25.00% | 20.0% |
| 10.0% | 90% | 10% | 20% | 15% | 25% | 21.00% | 19.0% |
| 20.0% | 80% | 10% | 20% | 15% | 25% | 17.00% | 18.0% |
| 30.0% | 70% | 10% | 20% | 15% | 25% | 13.00% | 17.0% |
| 40.0% | 60% | 10% | 20% | 15% | 25% | 9.00% | 16.0% |
| 50.0% | 50% | 10% | 20% | 15% | 25% | 5.00% | 15.0% |
| 60.0% | 40% | 10% | 20% | 15% | 25% | 1.00% | 14.0% |
| 70.0% | 30% | 10% | 20% | 15% | 25% | 3.00% | 13.0% |
| 80.0% | 20% | 10% | 20% | 15% | 25% | 7.00% | 12.0% |
| 90.0% | 10% | 10% | 20% | 15% | 25% | 11.00% | 11.0% |
| 100.0% | 0% | 10% | 20% | 15% | 25% | 15.00% | 10.0% |
And the investment opportunity frontier is as shown below:
jeff jeffy answered 7 months agoRelated Solutions
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