Alex is examining a portfolio that contains 100 stocks that are either value or Growth. Out of these 100 stocks 40% are value stock. The previous portfolio manager had selected 70% of the value stocks and 80% of the growth stocks. What is the probability of selecting a stock at random that is either a value stock or was selected by previous portfolio manager? A) 28% B) 76% C) 88% can anyone help me to understand this?

Probability of selecting a stock at random that is either a value stock or was selected by previous portfolio manager = Pvalue + Pgrowth by previous PM = 0.4 + (1-0.4) * (0.8) = 0.4 + 0.48 = 88%

Because if the selected stock was a value stock, that scenario is already covered by my first parameter (Pvalue). If I included it again I would be double counting. Hope that helps!

A CFA Level 1 Discussion About Quant, Probability

Add A Reply

Topic Resolution: Not Resolved

This topic has 3 replies, 3 voices, and was last updated Jan-229:06 am by Zee Tan.

Author

Posts
- Rabia55
  Participant
  - CFA Level 1
  24 Dec 2021 at 8:29 am
  Up
  7
  Down
  ::
  Alex is examining a portfolio that contains 100 stocks that are either value or Growth. Out of these 100 stocks 40% are value stock. The previous portfolio manager had selected 70% of the value stocks and 80% of the growth stocks. What is the probability of selecting a stock at random that is either a value stock or was selected by previous portfolio manager?
  
  A) 28%
  B) 76%
  C) 88%
  
  can anyone help me to understand this?
- Zee Tan
  Keymaster
  - CFA Charterholder
  31 Dec 2021 at 9:10 pm
  Up
  2
  Down
  ::
  Probability of selecting a stock at random that is either a value stock or was selected by previous portfolio manager
  
  = P_value + P_{growth by previous PM}
  
  = 0.4 + (1-0.4) * (0.8)
  
  = 0.4 + 0.48
  
  = 88%
- genesisx38
  Participant
  - CFA Level 1
  23 Jan 2022 at 2:13 pm
  Up
  0
  Down
  ::
  Hi Zee,
  
  Why is it assumed that the stock selected by the previous portfolio manager must be a growth stock?
  
  Shouldn’t it be a combination of Pgrowth by previous PM + Pvalue by previous PM?
  
  So would be Pvalue + (Pgrowth by previous PM + Pvalue by previous PM) – Intersection of the two (being value stock?)
  
  0.4 + [(1-0.4) * 0.8 + (0.6) * 0.7] – (0.7*0.6) = 0.88? (Same answer but diff. logic)
  - Zee Tan
    Keymaster
    
    CFA Charterholder
    30 Jan 2022 at 9:06 am
    Up
    1
    Down
    ::
    Because if the selected stock was a value stock, that scenario is already covered by my first parameter (P_value). If I included it again I would be double counting. Hope that helps!
Author

Posts

Viewing 2 reply threads

You must be logged in to reply to this topic.