Practice Questions Flashcards
Solve for bank discount yield, r(BD), using:
r(BD) = (D/F) x (360/t)
The probability (P) that A or B occurs, or both occur, is closest to:
P(A or B) = P(A) + P(B) − P(AB)
If there is variability in the data, compared with the arithmetic mean, the geometric mean will most likely be:
smaller
How do you calculate the Geometric Mean?
Add one to each of the given returns, then multiply them together and take the nth root of the resulting product
The net present value (NPV) of an investment is equal to the sum of the expected cash flows discounted at:
the discount rate or opportunity cost of capital
According to the NPV rule, shareholder wealth is maximized by selecting a project with the
highest NPV
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.
C. the discount rate that makes the net present value equal to zero.
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.
C. greater than the opportunity cost of capital.
The IRR investment decision rule states
“Accept projects or investments for which the IRR is greater than the opportunity cost of capital.”
What does the money-weighted rate of return consider?
Both the timing and amounts of investments into the fund.
Three Commonly Used Yield Measures
- Holding Period Yield (HPY)
- Effective Annual Yield (EAY)
- Money Market Yield (CD Equivalent Yield)
What are the types of measurement scales and describe them?
- Nominal scales - categorizes data but does not rank them. It contains the least information.
- Ordinal scales - sorts data into categories that are ordered (ranked) with respect to some characteristic or performance
- Interval scales - scale that not only ranks data but also gives assurance that the differences between scale values are equal
- 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.
Definition of Population
all members of a specified group
Definition of Sample
A sample is a subset of a population.
Any descriptive measure of a population characteristic is called a
parameter e.g. median of a population
Definition of Sample Statistic
A sample statistic (or statistic) is a quantity computed from or used to describe a sample.
Harmonic Mean Formula
n / sum(1/x)
The harmonic mean is appropriate for
determining the average price per unit.
The formula for the position of a percentile in an array with n entries sorted in ascending order is
Ly = (n + 1)(y/100)
The formula for mean absolute deviation (MAD) is
sum of (x-mean) / n
Chebyshev’s inequality
the proportion of the observations within k standard deviations of the arithmetic mean is at least 1 – 1/k^2 for all k > 1.
The coefficient of variation (CV) is
the ratio of the standard deviation to the mean, where a higher CV implies greater risk per unit of return.
The Sharpe ratio (S) is
the mean excess portfolio return per unit of risk, where a higher Sharpe ratio indicates better performance.
S = (Rp - Rf) / s
When analyzing investment returns, the geometric mean measures:
an investment’s compound rate of growth over multiple periods.
Distinguish between unconditional and conditional probabilities
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.
Explain the multiplication, addition, and total probability rules
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)
In probability theory, exhaustive events are best described as events:
that include all potential outcomes
Distinguish among empirical, subjective, and a priori probabilities
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.
The multiplication rule for independent events states that
the joint probability of both A and B occurring is P(AB) = P(A)P(B).
Properties of Correlation.
- Correlation is a number between −1 and +1 for two random variables, X and Y:
−1 ≤ ρ(X, Y) ≤ +1 - 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).
Which formula provides the number of possible portfolios?
Combination formula
Define the Combination formula
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
Combination formula
n! / (n-r)!r!
Define the Permutation Formula
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
Permutation Formula
n! / (n-r)!
