Question

question 12:

The risk of a portfolio can be lower than the risk of the two individual components that make up the portfolio when

	a.	the return of the two components are negatively related.
	b.	the return of the two components are positively related.
	c.	the risk of one of the components is much lower than the risk of the other.
	d.	the risk of one of the components is much higher than the risk of the other.
	e.	the expected return of one of the components is much higher than the expected return of the other.
	f.	the expected return of one of the components is much lower than the expected return of the other.

Question 1:
From past experience, we know that there are 14% of freshmen, 25% of sophomores, 32% of juniors and the remaining are seniors at NAU. We also know that 21% of the freshmen, 22% of the sophomore and 11% of the juniors have taken BA 201. Also 86% of the general student population at NAU have not taken BA 201. If we randomly ask a student from NAU and find out that she has NOT taken BA201, what is the probability (in percentage) that she is a freshman? Use Excel to solve. Hint: (1) Use Excel to setup the joint probability table; (2) Notice that 21%, 22% and 11% are the conditional probabilities NOT joint probabilities; (3) just enter the value without the % sign in the answer box.

Question 2:

When two events are collectively exhaustive and mutually exclusive, which of the following are always true? (2 correct answers)

	a.	P(A or B) = 0
	b.	P(A or B) = 1
	c.	P(A and B) = 0
	d.	P(A and B) = 1
	e.	P(A|B) = P(A)
	f.	P(A|B)= P(A) * P(B)

Question 4:

When there are only two possible events A and B that are mutually exclusive, which of the following is(are) always true? (2 correct answers)

	a.	P(A or B) = 0
	b.	P(A or B) = 1
	c.	P(A and B) = 0
	d.	P(A and B) = 1
	e.	P(A|B) = P(A)
	f.	P(A|B) = P(B)
	g.	P(A and B) = P(A) * P(B)

Question 5:

When there are more than two events and they are statistically independent, which of the following is(are) always true? (2 correct answers)

	a.	P(A or B) = 0
	b.	P(A or B) = 1
	c.	P(A and B) = 0
	d.	P(A and B) = 1
	e.	P(A|B) = P(A)
	f.	P(A and B) = P(A) * P(B)

Answer 1

Multiple questions. Hence answering the top most one:

The risk of a portfolio can be lower than the risk of the two individual components that make up the portfolio when

	a.	the return of the two components are negatively related.
	b.	the return of the two components are positively related.
	c.	the risk of one of the components is much lower than the risk of the other.
	d.	the risk of one of the components is much higher than the risk of the other.
	e.	the expected return of one of the components is much higher than the expected return of the other.
	f.	the expected return of one of the components is much lower than the expected return of the other.

Correct answer is-

a.	the return of the two components are negatively related.

Reason: Due to negative relation, first stock's return will increase if second stock's return reduces and vice versa. Thus portfolio risk is reduced.