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

  1. Standard deviation (risk) of each company’s stock returns.
  2. Correlation coefficients between each pair of companies' returns.

The general formula for the standard deviation of a portfolio with three assets is:

σp=wA2σA2+wB2σB2+wC2σC2+2wAwBρABσAσB+2wAwCρACσAσC+2wBwCρBCσBσC\sigma_p = \sqrt{w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + w_C^2 \sigma_C^2 + 2w_A w_B \rho_{AB} \sigma_A \sigma_B + 2w_A w_C \rho_{AC} \sigma_A \sigma_C + 2w_B w_C \rho_{BC} \sigma_B \sigma_C}

Where:

  • wAw_A, wBw_B, and wCw_C are the weights of the investments in Koppers, Adtran, and Equifax respectively (in this case, each weight wA=wB=wC=13w_A = w_B = w_C = \frac{1}{3} 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