Yup, this is a bread and butter calculation in terms of CFA exams...everyone should make sure they know how to calculate this, and also why it is calculated this way. Knowing why, as well as how will stand you in good stead.
I passed level 1 last year and still remember these formulas. I had this index card stock to my monitor at work. I had other cards stuck in the bathroom, on my desk for when I got up in the morning, etc. Hopefully this will help some of you too
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The portfolio standard deviation formula is:
(sigma_p)^2 = (w_1)^2 * (sigma_1)^2 + (w_2)^2 * (sigma_2)^2 + 2(w_1)(w_2) * Cov(R_1, R_2)
We have:
w_1 = 15,000 / 20,000 = 0.75
w_2 = 5,000 / 20,000 = 0.25
sigma_1 = 0.3
sigma_2 = 0.1
Cov(R_1, R_2) = 0.05
Therefore,
(sigma_p)^2 = (0.75^2)(0.3^2) + (0.25^2)(0.1^2) + 2(0.75)(0.25)(0.05) = 0.07
sigma_p = (0.07)^0.5 = 0.2645
correlation (p) = Cov1,2 / (sigma_1) (sigma_2)
Beta (b) = Cov1,2 / Variance_market
Beta (b) = (p) (sigma_1) / Sigma_market
The above mentioned formula: (sigma_p)^2 = (w_1)^2 * (sigma_1)^2 + (w_2)^2 * (sigma_2)^2 + 2(w_1)(w_2) * Cov(R_1, R_2)
I passed level 1 last year and still remember these formulas. I had this index card stock to my monitor at work. I had other cards stuck in the bathroom, on my desk for when I got up in the morning, etc. Hopefully this will help some of you too