CFA CFA Level 1 Question of the Week – Portfolio Management

Question of the Week – Portfolio Management

  • This topic has 6 replies, 6 voices, and was last updated Dec-18 by rsparks.
  • Author
    Posts
    • AdaptPrep
      Participant
      Up
      0
      Down

      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%
    • AdaptPrep
      Participant
      Up
      3
      Down

      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

    • Stuj79
      Participant
      Up
      4
      Down

      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.

    • googs1484
      Participant
      Up
      2
      Down

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

    • aaronpcjb
      Participant
      Up
      0
      Down

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

    • struggler
      Participant
      Up
      5
      Down

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

    • rsparks
      Participant
      Up
      3
      Down

      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 🙂

Viewing 6 reply threads
  • You must be logged in to reply to this topic.