What is the standard deviation (in percent) of a portfolio invested 50% in Techcity and 50% in Techsio?
The standard deviation of a portfolio invested 50% in Techcity and 50% in Techsio is approximately 0.2201%.
Calculation of Portfolio Standard Deviation
To calculate the standard deviation of a portfolio invested in Techcity and Techsio, we use the following formula:
Portfolio Standard Deviation = √[(Weight of Techcity * Standard Deviation of Techcity)^2 + (Weight of Techsio * Standard Deviation of Techsio)^2 + 2 * (Weight of Techcity) * (Weight of Techsio) * (Correlation Coefficient)]
Given data:
- Weight of Techcity = 50%
- Weight of Techsio = 50%
- Correlation Coefficient = 0.42
- Standard Deviation of Techcity = 1%
- Standard Deviation of Techsio = 16%
Substitute the values into the formula:
Portfolio Standard Deviation = √[(0.5 * 0.01)^2 + (0.5 * 0.16)^2 + 2 * 0.5 * 0.5 * 0.42]
Simplifying the equation:
Portfolio Standard Deviation = √[(0.005)^2 + (0.08)^2 + 0.042]
Portfolio Standard Deviation = √[0.000025 + 0.0064 + 0.042]
Portfolio Standard Deviation = √0.048425
Portfolio Standard Deviation ≈ 0.2201%
Therefore, the standard deviation of the portfolio invested 50% in Techcity and 50% in Techsio is approximately 0.2201%.