Math Problem Statement
Mr. Thomson is considering investing in all the companies. However, he is concerned that Equifax experienced major cyber breach in 2017. He believes it’s best to hold a portfolio comprising investment in ‘Koppers’ and ‘Adtran’ only. Compute his portfolio standard deviation if invest in all three companies equally. Comment on what advise you will give Mr. Thomson from diversification context given his concern.
Solution
To compute Mr. Thomson's portfolio standard deviation if he invests equally in Koppers, Adtran, and Equifax, we need the following dataTo compute Mr. Thomson's portfolio standard deviation if he invests equally in Koppers, Adtran, and Equifax, we need the following
- Standard deviation (risk) of each company’s stock returns.
- Correlation coefficients between each pair of companies' returns.
The general formula for the standard deviation of a portfolio with three assets is:
Where:
- , , and are the weights of the investments in Koppers, Adtran, and Equifax respectively (in this case, each weight since the investment is equally distributed).
- (\sigma
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Math Problem Analysis
Mathematical Concepts
Portfolio Theory
Standard Deviation
Risk Management
Correlation Coefficients
Formulas
σ_p = √(w_A^2 σ_A^2 + w_B^2 σ_B^2 + w_C^2 σ_C^2 + 2w_A w_B ρ_AB σ_A σ_B + 2w_A w_C ρ_AC σ_A σ_C + 2w_B w_C ρ_BC σ_B σ_C)
Theorems
Portfolio Standard Deviation Formula
Suitable Grade Level
Undergraduate Finance or Advanced High School Economics
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