These were the slides provided with solutions for Seminar 1, much more in-depth than the seminar solutions provided by the lecturer. Download these if you're struggling to understand the seminar work! (the slides were augmented due to a fault in previous version)
Problem 1(c): Solution
The minimum-variance portfolio of Expected return on the portfolio:
2 assets requires the weight as follows:
𝐸𝑅𝑃 = 𝑊𝐴∗ 𝐸𝑅𝐴 + 𝑊𝐵∗ 𝐸𝑅𝐵
2
𝑆𝐷𝐵 −𝐶𝑜𝑣(𝐴,𝐵)
𝑊𝐴∗ = 2 +𝑆𝐷 2 −2𝐶𝑜𝑣(𝐴,𝐵) Variance of the portfolio:
𝑆𝐷𝐴 𝐵
𝑉𝑎𝑟𝑃 = (𝑊𝐴∗ )2 𝑆𝐷𝐴2 + (𝑊𝐵∗ )2 𝑆𝐷𝐵2 + 2𝑊𝐴∗ 𝑊𝐵∗ 𝐶
𝑊𝐵∗ = 1 − 𝑊𝐴∗
or Standard deviation of the portfolio:
2
𝑆𝐷𝐴 −𝐶𝑜𝑣(𝐴,𝐵) 𝑆𝐷𝑃 = 𝑉𝑎𝑟𝑃
𝑊𝐵∗ = 2 +𝑆𝐷 2 −2𝐶𝑜𝑣(𝐴,𝐵)
𝑆𝐷𝐴 𝐵
𝑊𝐴∗ = 1 − 𝑊𝐵∗
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