Quantitative Methods MCQ - Quantitative Methods Section 2

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

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.

72 The notation "F (x) = P (X < x)" best describes which of the following?

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.

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 less	0.75
Net profit of 6 or less	1.00

The probability of a net profit greater than €2 and less than or equal to €6 is closest to:

P(X ≤ 6) = 1.0 and P(X ≤ 2) = 0.50. Therefore, P (2 ≤ X ≤ 6) = 1.0 – 0.50 = 0.50.

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:

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.

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 (%)	45	55
Expected returns (%)	23	13
Standard deviations (%)	14	6
Correlation between the returns of Fund X and Fund Y	0.7

The portfolio standard deviation of the returns is closest to:

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%.