Quantitative Methods - Quantitative Methods Section 2

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71. The outcomes of rolling a dice can be best represented by which of the following types of probability distributions?

  • Option : B
  • Explanation : When a dice is rolled, since there are a finite number of outcomes, it is an example of a discrete probability distribution. The continuous uniform distribution is defined over a range from a lower limit ‘a’ to an upper limit ‘b’. A normal distribution is symmetrical and bell-shaped.
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72. The notation "F (x) = P (X < x)" best describes which of the following?

  • Option : A
  • Explanation : The cumulative distribution function gives the probability that a random variable X is less than or equal to a particular value x, P (X < x). Probability function specifies probability that random variable takes on a specific value. Probability density function is used for continuous random variables.
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73. Discrete uniform probability distribution of net profits for a currency option on EURO (€) is as follows:

Net Profit (€) Probability
Net profit of 0 0.25
Net profit of 2 or less 0.50
Net profit of 4 or less0.75
Net profit of 6 or less1.00

  • Option : C
  • Explanation : P(X ≤ 6) = 1.0 and P(X ≤ 2) = 0.50. Therefore, P (2 ≤ X ≤ 6) = 1.0 – 0.50 = 0.50.
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74. The probability that a stock’s price will change is 0.6 versus a probability of 0.4 that the stock price will not change. If there is a change, the probability of a price increase is 0.4 and the probability of a price decrease is 0.6. The unconditional probability of a price decrease is:

  • Option : B
  • Explanation : Consider the tree diagram below: The probability of a price decrease is equal to the probability of a price change times the probability of a decrease given a change = 0.6 * 0.6 = 0.36.
    Simply Easy Learning
    The probability of a price decrease is equal to the probability of a price change times the probability of a decrease given a change = 0.6 * 0.6 = 0.36.
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75. Ali, a CFA candidate, is evaluating a portfolio, which is composed of Fund A and Fund B. He has collected the following information:

 Fund A Fund B
Portfolio weights (%) 4555
Expected returns (%)2313
Standard deviations (%)  146
Correlation between the returns of
Fund X and Fund Y
0.7 

The portfolio standard deviation of the returns is closest to:

  • Option : B
  • Explanation : The portfolio standard deviation of the returns is calculated through following formula:
    Simply Easy Learning
    And covariance is calculated through following formula: Cov(RARB)=ρ (RARB) σ (RA)σ(RB)
    First calculate the covariance, Cov= 0.7 ∗ .14 ∗ .06 = 0.00588, then enter values in the formula 1 for calculating portfolio standard deviation, you should get portfolio standard deviation = 8.90%.
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