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Question of the Week - Portfolio Management

Des Moines, IA, USAPosts: 211 Sr Associate
edited March 2016

You are given the following portfolio:

Company Name | Amount Invested | Standard Deviation

Isotics | 15,000 | 0.3

Ambiss | 5,000 | 0.1

The portfolio's standard deviation, if the covariance is 0.05, is closest to:

20%
0%
23%
41%
7 votes
26%
58%
10 votes

Comments

• Des Moines, IA, USAPosts: 211 Sr Associate
26%

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

• LondonPosts: 155 Jr Portfolio Manager
26%
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.
• MA, USAPosts: 222 Jr Portfolio Manager
23%
Darn haha. Tried doing the math in my head. I'll stick to the BA2 going forward lol.
• London, United KingdomPosts: 2 Associate
23%
Stupidly misread 'covariance' as 'correlation' and multiplied it by the standard deviations.
• limaPosts: 2 Associate
I got confused...  anyone, could tell the general formula of portfolio standard deviation ??? thanks
• MelbournePosts: 80 Sr Associate
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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