- This topic has 6 replies, 6 voices, and was last updated Dec-183:35 pm by
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Up0
You are given the following
portfolio:Company Name | Amount
Invested | Standard DeviationIsotics | 15,000 | 0.3
Ambiss | 5,000 | 0.1
The portfolio’s standard
deviation, if the covariance is 0.05, is closest to:- 20%
- 23%
- 26%
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Up5
I got confused… anyone, could tell the general formula of portfolio standard deviation ??? thanks 🙂
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Up4
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.
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Up3
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) = 0.07sigma_p = (0.07)^0.5 = 0.2645
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Up3
I would also highlight the interaction between correlation, beta, variance and standard dev. I had the below all on one card:
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 🙂
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Up2
Darn haha. Tried doing the math in my head. I’ll stick to the BA2 going forward lol.
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Up0
Stupidly misread ‘covariance’ as ‘correlation’ and multiplied it by the standard deviations.
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