CFA Level 1 Dec. 3rd 2016
Which of the following economic indicators is classified as a leading indicator for the United States economy?
Index of consumer expectations.
Quantitative Methods Rule 3:
Multiplying or dividing an inequality by a negative number changes the direction of the inequality.
Bill Jones is creating a charitable trust to provide six annual payments of $20,000 each, beginning next year. How much must Jones set aside now at 10% interest compounded annually to meet the required disbursements?
N = 6, PMT = -$20,000, I/Y = 10%, FV = 0, Compute PV → $87,105.21.
Expected Holding Period Return on a Stock
Return = [dividend + (end − begin)] / beginning price
An analyst announces that an increase in the discount rate next quarter will double her earnings forecast for a firm. This is an example of a:
This is a conditional expectation. The analyst indicates how an expected value will change given another event.
In the process of hypothesis testing, what is the proper order for these steps?
State the hypotheses. Specify the level of significance. Collect the sample and calculate the test statistics. Make a decision.
"A branch of mathematics dealing with the collection, analysis, interpretation, and presentation of numerical data." is the definition of...
Statistics
A Treasury bill (T-bill) with a face value of $10,000 and 137 days until maturity is selling for 98.125% of face value. Which of the following is closest to the bank discount yield on the T-bill?
The formula for bank discount yield is: (D / F) × (360 / t). Actual discount is 1 − 0.98125 = 0.01875. Annualized is: 0.01875 × (360 / 137) = 0.04927
Default risk is the risk that...
a borrower will not make the promised payments in a timely manner.
The geometric mean return is...
a compound annual growth rate for an investment.
A "time line" is simply...
a diagram of the cash flows associated with a TVM (Time Value Money) problem
A "histogram" is...
a graph of a frequency distribution.
A perpetuity is...
a series of equal cash flows occurring at fixed intervals of equal length forever.
A lump sum is...
a single cash flow. Lump sum cash flows are one-time events and therefore are not recurring
The "mode" is the observation that...
appears most often.
The geometric mean will always be less than or equal to the...
arithmetic mean.
The most common measure of central tendency is the...
arithmetic mean.
The future value of an annuity due deposits are made...
at the beginning of the year.
The future value of an ordinary annuity deposits are made...
at the end of the year.
A cash flow that occurs in the present (today) is put...
at time 0
A qualitative variable measures...
attributes such as gender, religious preference, eye color, type of running shoe preferred, and place of birth. In other words qualitative variables do bot use numbers.
A "continuous" variable can have values...
between any two numbers. For example, a continuous variable can take on values in between 3-4 (e.g., 3.0000001, 3.01, 3.00001 etc) Taking on infinite values between 3 and 4
The center point of the data is known as the...
central tendency of the distribution.
A budget constraint or budget line represents the combinations
combinations of two goods that exhaust a consumer's income.
A "discrete" variable can only have a...
countable number of easily identified values. Taking on whole numbers.
Interest rates are often referred to as...
discount rates and in fact the terms are often used interchangeably.
Quantitative variables can be categorized as...
discrete or continuous variables.
The "range" is simply the...
distance between the lowest and the highest observed values. The larger the range, the wider the dispersion of observations, and the smaller the range, the narrower the dispersion of the data.
The Marshall-Lerner condition suggests that a country's ability to narrow a trade deficit by devaluing its currency depends on:
elasticity of demand for imports and exports.
An annuity is a...
finite number of equal cash flows occurring at fixed intervals of equal length over a defined period of time (e.g., monthly payment of $100 for three years).
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Each of these risk factors is associated with a risk premium that we add to the nominal risk-free rate to adjust for...
greater default risk, less liquidity, and longer maturity relative to a very liquid, short-term, default risk-free rate such as that on T-bills.
A distribution with positive excess kurtosis has a...
higher percentage of small deviations from the mean than normal. So it is more "peaked" than a normal distribution. A distribution with positive skew has a mean > mode.
Which one of the following best characterizes the alternative hypothesis? The alternative hypothesis is usually the:
hoped-for outcome.
Remember we always state effective returns...
in annual terms.
The farthest point on the left side of the lognormal distribution:
is bounded by 0
A firm should continue to accept capital projects until the marginal revenue product of capital (the value added) is
is equal to the cost of capital. Prior to this point, the firm gains from each unit of capital added.
A distribution with a mean that is less than its median most likely:
is negatively skewed.
Peakedness of a distribution is measured by
kurtosis
Factors of production include
land, labor, capital, and materials. Technology is typically viewed as an exogenous factor that affects the productivity of factors of production.
When demand for a good is inelastic, a higher price will:
lead to an increase in total expenditures for the good.
By convention we put the unknown variable on the...
left side of the equation.
Under perfect competition, a firm will experience economic losses when its selling price is
less than average total cost.
You will notice two very important characteristics of compounding:
1. For the same present value and interest rate, the future value increases as the number of compounding periods per year increases. 2. Each successive increase in future value is less than the preceding increase. (The future value increases at a decreasing rate.)
Perfect symmetry implies:
1. The center point of the distribution is the mean, median, mode. 2. 50% of all possible returns are to the right of (above) the mean 3. 50% of all possible returns are to the left (below) the mean
An analyst wants to determine whether the monthly returns on two stocks over the last year were the same or not. What test should she use if she is willing to assume that the returns are normally distributed?
A paired comparisons test must be used. The difference in means test requires that the samples be independent. Portfolio theory teaches us that returns on two stocks over the same time period are unlikely to be independent since both have some systematic risk.
Which of the following represents the mean, standard deviation, and variance of a standard normal distribution?
By definition, for the standard normal distribution, the mean, standard deviation, and variance are 0, 1, 1.
"Mean" is just another word for....
"average", or the center of the data.
What's the effective rate of return on an investment that generates a return of 12%, compounded quarterly?
(1 + 0.12 / 4)4 − 1 = 1.1255 − 1 = 0.1255.
The holding period yield is the return that the investor will earn if the bill is held until it matures. The holding period yield formula is
(price received at maturity − initial price + interest payments) / (initial price)
Securities may have one or more types of risk, and each added risk increases the required rate of return on the security. These types of risk are:
Default risk, maturity risk, and liquidity risk.
Which of the following is most likely to be considered a characteristic of monopolistic competition?
Differentiated products are a key characteristic of monopolistic competition. Although producers have downward sloping demand curves, they are typically elastic.
formula for the expected return of a portfolio:
E(RP) = w1E(R1) + w2E(R2) + ... + wnE(Rn)
The internal rate of return (IRR) is defined as the rate of return that equates the...
PV of an investment's expected benefits (inflows) with the PV of its costs (outflows). Equivalently the IRR may be defined as the discount rate for which the NPV of an investment is zero.
NPV Decision Rule
The basic idea behind NPV analysis is that if a project has a positive NPV, this amount goes to the firm's shareholders. As such, if a firm undertakes a project with a positive NPV, shareholder wealth is increased.
Given P(X = 20, Y = 0) = 0.4, and P(X = 30, Y = 50) = 0.6, then COV(XY) is:
The expected values are: E(X) = (0.4 × 20) + (0.6 × 30) = 26, and E(Y) = (0.4 × 0) + (0.6 × 50) = 30. The covariance is COV(XY) = (0.4 × ((20 − 26) × (0 − 30))) + ((0.6 × (30 − 26) × (50 − 30))) = 120.
For any random variable that is normally distributed its natural logarithm (ln) will be lognormally distributed.
The opposite is also true: for any random variable that is lognormally distributed its natural logarithm (ln) will be normally distributed. Session 3 > Reading 9 > LOS o
The following data are available on a sample of advertising budgets of 81 U.S. manufacturing companies: The mean budget is $10 million. The sample variance is 36 million. The standard error of the sample mean is:
The sample standard deviation is the square root of the variance: (36,000,000)1/2 = $6,000. The standard error of the sample mean is estimated by dividing the standard deviation of the sample by the square root of the sample size: σmean = s / (n)1/2 = 6,000 / (81)1/2 = $667.
Quantitative Methods Rule 2:
We can add (or subtract) the same letter or number from both sides of an equation without changing the relationship expressed by the equation or the value of the unknown.
Quantitative Methods: Rule 1
We can multiply or divide all terms on both sides of an equation by the same letter or number without changing the relationship expressed by the equation or the value of the unknown variables.
The continuously compounded rate of return =
ln( S1 / S0 )
In a positively skewed distribution, the:
mean is greater than the median.
The "mean absolute deviation" is a...
measure of the dispersion of the sample observations around the center of the distribution. It measures the average deviation from the mathematical mean. A deviation is measured as the distance from the mean to each observation.
The "median" is the...
middle observation of the ranked data.
Once the cash flows are assigned to a time line, they may be...
moved to the beginning of the investment period to calculate the PV through a process called discounting or to the end of the period to calculate the FV using a process called compounding.
Cash outflows (payments) are given a...
negative sign, and cash inflows (receipts) are given a positive sign.
Quantitative variables are expressed...
numerically and could include the average number of children in the typical household, average height of American females, the percentage of people in the population with false teeth, or the average number of computers sold daily.
An "observation" is...
one member of a sample. A sample of size 30 has 30 observations.
Computing Present Value (PV) works in the...
opposite direction and it brings the cash flows from an investment back to the beginning of the investment's live based on an appropriate compound rate of return.
A "sample" is a...
portion or subset of a population that is used to estimate charateristics of (i.e., make inferences about) the population.
The Cash Flow Additivity Principle refers to the fact that...
present value of any stream of cash flows equals the sum of the present values of the cash flows.
The net present value (NPV) of an investment project is the...
present value of expected cash inflows associated with the project less the present value of the project's expected cash outflows, discounted at the appropriate cost of capital.
In the long-run, after all firms in a perfectly competitive industry have adopted new technology, the:
price will equal minimum average total cost.
Computing Future Value (FV) involves...
projecting the cash flows forward, on the basis of an appropriate compound interest rate, to the end of the investment's life.
The two main categories of variables are...
qualitative and quantitative.
An example of a continuous variable is the amount of...
rainfall during July in a city.
The most common "measures of dispersion" are...
range, mean absolute deviation, and standard deviation.
The neutral rate of interest is
real trend rate of economic growth plus the inflation target.
Liquidity risk is the risk of...
receiving less than fair value for an investment if it must be sold for cash quickly.
Price discrimination:
reduces the allocative inefficiency that exists when prices are greater than marginal cost by increasing output toward the quantity where price equals marginal cost.
Given a choice between consuming oranges and beans, a consumer's equilibrium bundle of goods is most likely to:
represent the most preferred affordable combination of oranges and beans.
Equilibrium interest rates are the...
required rate of return for a particular investment in the sense that the market rate of return is the return that investors and savers require to get them to willingly lend their funds.
Interpret interest rates as...
required rates of return, discount rates, or opportunity costs.
Population is...
the collection of all possible individuals, objects, measurements, or other items; (e.g., the population of the U.S. is all people who call the U.S. their home country).
The "normal distribution" is the...
the famous "bell-shaped curve", where the mean, median, and mode are equal. `
If a distribution is skewed:
the magnitude of positive deviations from the mean is different from the magnitude of negative deviations from the mean.
The most popular statistical measures of central tendency are...
the mean, median, and mode.
Finally, we can also view interest rates as...
the opportunity cost of current consumption. If the market rate of interest on 1 year securities is 5%, earning an additional 5% is the opportunity forgone when current consumption is chosen rather than saving (postponing consumption).
Maturity risk is in regards to...
the prices of longer-term bonds are more volatile than those of shorter-term bonds. Longer maturity bonds have more maturity risk than shorter-term bonds and require a maturity risk premium.
An example of a discrete variable is the outcome of...
the roll of a die. (1,2,3,4,5, or 6)
The standard error of the sample mean equals
the standard deviation of the population divided by the square root of the sample size, 4 = 20 / n1/2
Explain an interest rate as...
the sum of a real risk-free rate and premiums that compensate investors for bearing distinct types of risk.
The "frequency distribution" of data is...
the tally of observations falling in equally spaced intervals.
Interest rates are our measure of....
the time value of money, although risk differences in the financial securities lead to differences in their equilibrium interest rates.
Future value is...
the value in the future of a cash flow received or paid today. On a timeline, future values occur after (to the right of) their relevant cash flows.
Present value is...
the value today of a cash flow to be received or paid on the future. On a timeline, present values occur before (to the left of) their relevant cash flows.
Descriptive statistics are used mainly to
to summarize important characteristics of large data sets.
Consumer surplus is most accurately defined as the difference between the:
total value consumers place on the quantity of a good purchased, and the total amount they must pay for that quantity.
A "variable" is an...
unknown quantity (measurement) that can have different values.