CFA CFA Level 1 Question of the Week – Portfolio Management

# Question of the Week – Portfolio Management

• Author
Posts
Participant
• Undecided
0

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%
• 23%
• 26%
• struggler
Participant
• Undecided
5

I got confused…  anyone, could tell the general formula of portfolio standard deviation ??? thanks ðŸ™‚

• Stuj79
Participant
• CFA Charterholder
4

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.

Participant
• Undecided
3

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

• rsparks
Participant
• CFA Level 2
3

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 ðŸ™‚

• googs1484
Participant
• CFA Level 3
2

Darn haha. Tried doing the math in my head. I’ll stick to the BA2 going forward lol.

• aaronpcjb
Participant
• CFA Level 1
0

Stupidly misread ‘covariance’ as ‘correlation’ and multiplied it by the standard deviations.