Practice Questions

Question 1

Solve for bank discount yield, r(BD), using:

Answer 1

r(BD) = (D/F) x (360/t)

Question 2

The probability (P) that A or B occurs, or both occur, is closest to:

Answer 2

P(A or B) = P(A) + P(B) − P(AB)

Question 3

If there is variability in the data, compared with the arithmetic mean, the geometric mean will most likely be:

Answer 3

smaller

Question 4

How do you calculate the Geometric Mean?

Answer 4

Add one to each of the given returns, then multiply them together and take the nth root of the resulting product

Question 5

The net present value (NPV) of an investment is equal to the sum of the expected cash flows discounted at:

Answer 5

the discount rate or opportunity cost of capital

Question 6

According to the NPV rule, shareholder wealth is maximized by selecting a project with the

Answer 6

highest NPV

Question 7

Q. The internal rate of return (IRR) is best described as the:

A. opportunity cost of capital.
B. time-weighted rate of return.
C. discount rate that makes the net present value equal to zero.

Answer 7

C. the discount rate that makes the net present value equal to zero.

Question 8

Q. The internal rate of return (IRR) rule indicates acceptance of a project when the IRR is:

A. greater than zero.
B. less than the opportunity cost of capital.
C. greater than the opportunity cost of capital.

Answer 8

C. greater than the opportunity cost of capital.

Question 9

The IRR investment decision rule states

Answer 9

“Accept projects or investments for which the IRR is greater than the opportunity cost of capital.”

Question 10

What does the money-weighted rate of return consider?

Answer 10

Both the timing and amounts of investments into the fund.

Question 11

Three Commonly Used Yield Measures

Answer 11

1. Holding Period Yield (HPY)
2. Effective Annual Yield (EAY)
3. Money Market Yield (CD Equivalent Yield)

Question 12

What are the types of measurement scales and describe them?

Answer 12

1. Nominal scales - categorizes data but does not rank them. It contains the least information.
2. Ordinal scales - sorts data into categories that are ordered (ranked) with respect to some characteristic or performance
3. Interval scales - scale that not only ranks data but also gives assurance that the differences between scale values are equal
4. Ratio scales - has all the characteristics of the above scales as well as a true zero point as the origin. e.g. purchasing power. $2 has a weaker purchasing power than $4.

Question 13

Definition of Population

Answer 13

all members of a specified group

Question 14

Definition of Sample

Answer 14

A sample is a subset of a population.

Question 15

Any descriptive measure of a population characteristic is called a

Answer 15

parameter e.g. median of a population

Question 16

Definition of Sample Statistic

Answer 16

A sample statistic (or statistic) is a quantity computed from or used to describe a sample.

Question 17

Harmonic Mean Formula

Answer 17

n / sum(1/x)

Question 18

The harmonic mean is appropriate for

Answer 18

determining the average price per unit.

Question 19

The formula for the position of a percentile in an array with n entries sorted in ascending order is

Answer 19

Ly = (n + 1)(y/100)

Question 20

The formula for mean absolute deviation (MAD) is

Answer 20

sum of (x-mean) / n

Question 21

Chebyshev’s inequality

Answer 21

the proportion of the observations within k standard deviations of the arithmetic mean is at least 1 – 1/k^2 for all k > 1.

Question 22

The coefficient of variation (CV) is

Answer 22

the ratio of the standard deviation to the mean, where a higher CV implies greater risk per unit of return.

Question 23

The Sharpe ratio (S) is

Answer 23

the mean excess portfolio return per unit of risk, where a higher Sharpe ratio indicates better performance.

S = (Rp - Rf) / s

Question 24

When analyzing investment returns, the geometric mean measures:

Answer 24

an investment’s compound rate of growth over multiple periods.

Question 25

Distinguish between unconditional and conditional probabilities

Answer 25

Unconditional probability (also known as marginal probability) is simply the probability that an event occurs, without taking into account any other preceding events.

A conditional probability is the probability of an event given that another event has occurred.

Question 26

Explain the multiplication, addition, and total probability rules

Answer 26

Addition Rule - The additional rule determines the probability of at least one of the events occurring.

P(A or B) = P(A) + P(B) – P(AB)

If A and B are mutually exclusive, then P(A and B) = 0, so the rule can be simplified:

P(A or B) = P(A) + P(B) for mutually exclusive events A and B

Multiplication Rule - determines the joint probability of two events.

P(AB) = P(A | B)P(B)

Total Probability Rule - determines the unconditional probability of an event in terms of probabilities conditional on scenarios. It is used to estimate an expected value based on mutually exclusive and exhaustive scenarios.

P(A) = P(A | B1)P(B1) + P(A | B3)P(B3) + … + P(A | Bn)P(Bn)

Question 27

In probability theory, exhaustive events are best described as events:

Answer 27

that include all potential outcomes

Question 28

Distinguish among empirical, subjective, and a priori probabilities

Answer 28

Empirical Probability - the probability that results from analyzing actual past data.

Subjective Probabilities - probabilities usually reflect personal belief or judgment.

A Priori Probabilities - A probability based on logical analysis rather than on observation or personal judgment.

Question 29

The multiplication rule for independent events states that

Answer 29

the joint probability of both A and B occurring is P(AB) = P(A)P(B).

Question 30

Properties of Correlation.

Answer 30

1. Correlation is a number between −1 and +1 for two random variables, X and Y:
   −1 ≤ ρ(X, Y) ≤ +1
2. A correlation of 0 (uncorrelated variables) indicates an absence of any linear (straight-line) relationship between the variables. An increasingly positive correlation indicates an increasingly strong positive linear relationship (up to 1, which indicates a perfect linear relationship). An increasingly negative correlation indicates an increasingly strong negative (inverse) linear relationship (down to −1, which indicates a perfect inverse linear relationship).

Question 31

Which formula provides the number of possible portfolios?

Answer 31

Combination formula

Question 32

Define the Combination formula

Answer 32

The number of ways that we can choose r objects from a total of n objects, when the order in which the r objects are listed does not matter

Question 33

Combination formula

Answer 33

n! / (n-r)!r!

Question 34

Define the Permutation Formula

Answer 34

The number of ways that we can choose r objects from a total of n objects, when the order in which the r objects are listed does matter

Question 35

Permutation Formula

Answer 35

n! / (n-r)!