CFA Level 1 Exam - Quantitative
Methods Test || With 100% Accurate
Solutions
Yield Conversion - ANSWER-Bank discount yield is primarily used for quoting Treasury
bills. It annualizes the discount on the instrument as a percentage of par over 360-day
period. Do not hold meaning because investors want returns based on amount invested
and BDY is based on par, returns are not based on 365, and BDY assumes simple
interest which ignores interest on interest of compounding.
Bond equivalent yeilds is the semiannual discount rate multiplied by two - from the US
where bonds are quoted at twice the semiannual rate because coupons are paid
semiannually.
Statistics (Defined) - ANSWER-Statistics - Refers to data and methods that we use to
analyze data.
Descriptive Statistics - how large volumes of data are converted into useful, readily
understood information by summarizing their input characteristics.
Inference Statistics - methods used to make forecasts, estimates, or draw conclusions
about a larger set of data based on a smaller, representative set.
Measurement Scales - ANSWER-Nominal Scale - weakest form of measurements.
Counted with no particular order. Ex: Municipal Bond Fund = 1, Corporate Bond Fund =
2, etc
Ordinal Scale - Observation are sorted into several categories, then ordered with
respect to a characteristic. Ex: Assigning 1 to first 100, 2 to second 100, etc. Tells us
nothing about magnitude of difference between categories
Interval Scale - rank observations such that the differences between scale values are
equal so that values can be added and subtracted meaningfully. Ex: Temperature.
Ratios are meaningless
Ratio Scales - strongest form of measurement. Have all values of interval scale and
have a true zero point as the origin, so ratios have meaning. Ex. money
Population and Samples - ANSWER-Population - All members of a specfic group
Parameter - Descriptive measure of the population
Sample - A subset of the population
,Samples statistic - A quantity computer from or used to describe a sample
Frequency Distribution - ANSWER-A tabular illustration of data categorized into a
relatively small number of intervals or classes, such that each observation may fall into
only one interval and the set of intervals must cover the entire range of values for the
data.
Relative frequency = portion of total observations that lie in that interval
Cumulative frequency = number of observations that are less than the upper bound of
the interval (absolute), or the portion of total observations that is less than the upper
bound of the interval (relative)
Frequency => Periodic Interest Rate (I/Y) => N compounding periods
Annual => r/1 => 1
Semiannual => r/2 => 2
Quarterly => r/4 => 4
Monthly => r/12 => 12
Daily => r/365 => 365
Continuous Compounding (Value) - ANSWER-1. Multiply rate by time periods
2. Multiple answer by e (Second LN)
3. Multiply by PV
Present Value of Perpetuity - ANSWER-Financial instrument that pays a fixed amount
of money at set intervals over an infinite period of time
NPV - ANSWER-Present Value of expected cash inflows (+) minus the present value of
the expected outflows (-), discounted at the appropriate cost of capital, which reflects
the opportunity cost of undertaking the investment and compensates investors for
various risks in the investment. Assumes interim cash flows from the project will be
reinvested at the required rate of return.
Use the Calculator (Cash Flow):
Set CF0 = 0 (for profit)
Set CF0 = Initial negative outflow (for total NPV)
∑CF(t) / (1+r)^t
NPV Decision Rule - ANSWER-If the investments NPV is positive, shareholder wealth is
increased and the project should be accepted.
If the investments NPV is negative, shareholder wealth is decreased and the project
should be declined.
For mutually exclusive projects (where only one project may be accepted), the project
with the highest positive NPV should be chosen and would add the most value to the
firm.
, IRR - ANSWER-The discount rate that equates the project's NPV to zero. Effectively, it
is the discount rate that equates the present value of all inflows from a project to the
present value of all project-related outflows. IRR assumes all cash flows from the
project will be reinvested at the IRR.
Function of amount and timing of cash flows. Independent of cost of capital
Interest Rates - ANSWER-Are determined by the demand (borrowers)and supply
(investors) of funds and can be thought of in three ways:
1) The minimum rate of return that you require to accept a payment at a later date.
2) The discount rate that must be applied to future cash flow in order to determine the
present value.
3) The opportunity cost of spending the money today as opposed to saving it for a
certain period and earning a return on it.
Interest Rates - Composition - ANSWER-r = Real risk-free rate + Inflation premium +
Default risk premium + Liquidity premium + Maturity premium
-real risk-free rate - the single-period interest rate for a completely risk-free security if no
inflation were expected; individual preference for current versus future consumption
-inflation premium - added to the real risk-free rate to reflect the expected loss in
purchasing power over the term of the loan (real rf + inflation premium = NOMINAL rf)
-default risk premium - compensates investors for the risk that the borrower might fail to
make promised payments in full in a timely manner
-liquidity risk premium - compensates investors for any difficulty they might face in
converting their holdings readily into cash at their face value (infrequent trading or low
liquidity => high liquidity premium)
-maturity premium - compensates investors for the higher sensitivity of the market value
of longer term debt instruments to changes in interest rates
PV and FV rules - ANSWER-For a given interest rate,
-the FV increases as N increases
-the FV increases as the interest rate increases
For a given discount rate,
-the PV decreases as N increases
-the PV decreases as the discount rate increases
Annuity Due conversion - ANSWER-Annuity payments at the beginning of the period.
Set calculator in BGN mode and insert data per usual.
OR
PV annuity due = PV ordinary annuity * (1+r)
FV annuity due = FV ordinary annuity * (1+r)
Methods Test || With 100% Accurate
Solutions
Yield Conversion - ANSWER-Bank discount yield is primarily used for quoting Treasury
bills. It annualizes the discount on the instrument as a percentage of par over 360-day
period. Do not hold meaning because investors want returns based on amount invested
and BDY is based on par, returns are not based on 365, and BDY assumes simple
interest which ignores interest on interest of compounding.
Bond equivalent yeilds is the semiannual discount rate multiplied by two - from the US
where bonds are quoted at twice the semiannual rate because coupons are paid
semiannually.
Statistics (Defined) - ANSWER-Statistics - Refers to data and methods that we use to
analyze data.
Descriptive Statistics - how large volumes of data are converted into useful, readily
understood information by summarizing their input characteristics.
Inference Statistics - methods used to make forecasts, estimates, or draw conclusions
about a larger set of data based on a smaller, representative set.
Measurement Scales - ANSWER-Nominal Scale - weakest form of measurements.
Counted with no particular order. Ex: Municipal Bond Fund = 1, Corporate Bond Fund =
2, etc
Ordinal Scale - Observation are sorted into several categories, then ordered with
respect to a characteristic. Ex: Assigning 1 to first 100, 2 to second 100, etc. Tells us
nothing about magnitude of difference between categories
Interval Scale - rank observations such that the differences between scale values are
equal so that values can be added and subtracted meaningfully. Ex: Temperature.
Ratios are meaningless
Ratio Scales - strongest form of measurement. Have all values of interval scale and
have a true zero point as the origin, so ratios have meaning. Ex. money
Population and Samples - ANSWER-Population - All members of a specfic group
Parameter - Descriptive measure of the population
Sample - A subset of the population
,Samples statistic - A quantity computer from or used to describe a sample
Frequency Distribution - ANSWER-A tabular illustration of data categorized into a
relatively small number of intervals or classes, such that each observation may fall into
only one interval and the set of intervals must cover the entire range of values for the
data.
Relative frequency = portion of total observations that lie in that interval
Cumulative frequency = number of observations that are less than the upper bound of
the interval (absolute), or the portion of total observations that is less than the upper
bound of the interval (relative)
Frequency => Periodic Interest Rate (I/Y) => N compounding periods
Annual => r/1 => 1
Semiannual => r/2 => 2
Quarterly => r/4 => 4
Monthly => r/12 => 12
Daily => r/365 => 365
Continuous Compounding (Value) - ANSWER-1. Multiply rate by time periods
2. Multiple answer by e (Second LN)
3. Multiply by PV
Present Value of Perpetuity - ANSWER-Financial instrument that pays a fixed amount
of money at set intervals over an infinite period of time
NPV - ANSWER-Present Value of expected cash inflows (+) minus the present value of
the expected outflows (-), discounted at the appropriate cost of capital, which reflects
the opportunity cost of undertaking the investment and compensates investors for
various risks in the investment. Assumes interim cash flows from the project will be
reinvested at the required rate of return.
Use the Calculator (Cash Flow):
Set CF0 = 0 (for profit)
Set CF0 = Initial negative outflow (for total NPV)
∑CF(t) / (1+r)^t
NPV Decision Rule - ANSWER-If the investments NPV is positive, shareholder wealth is
increased and the project should be accepted.
If the investments NPV is negative, shareholder wealth is decreased and the project
should be declined.
For mutually exclusive projects (where only one project may be accepted), the project
with the highest positive NPV should be chosen and would add the most value to the
firm.
, IRR - ANSWER-The discount rate that equates the project's NPV to zero. Effectively, it
is the discount rate that equates the present value of all inflows from a project to the
present value of all project-related outflows. IRR assumes all cash flows from the
project will be reinvested at the IRR.
Function of amount and timing of cash flows. Independent of cost of capital
Interest Rates - ANSWER-Are determined by the demand (borrowers)and supply
(investors) of funds and can be thought of in three ways:
1) The minimum rate of return that you require to accept a payment at a later date.
2) The discount rate that must be applied to future cash flow in order to determine the
present value.
3) The opportunity cost of spending the money today as opposed to saving it for a
certain period and earning a return on it.
Interest Rates - Composition - ANSWER-r = Real risk-free rate + Inflation premium +
Default risk premium + Liquidity premium + Maturity premium
-real risk-free rate - the single-period interest rate for a completely risk-free security if no
inflation were expected; individual preference for current versus future consumption
-inflation premium - added to the real risk-free rate to reflect the expected loss in
purchasing power over the term of the loan (real rf + inflation premium = NOMINAL rf)
-default risk premium - compensates investors for the risk that the borrower might fail to
make promised payments in full in a timely manner
-liquidity risk premium - compensates investors for any difficulty they might face in
converting their holdings readily into cash at their face value (infrequent trading or low
liquidity => high liquidity premium)
-maturity premium - compensates investors for the higher sensitivity of the market value
of longer term debt instruments to changes in interest rates
PV and FV rules - ANSWER-For a given interest rate,
-the FV increases as N increases
-the FV increases as the interest rate increases
For a given discount rate,
-the PV decreases as N increases
-the PV decreases as the discount rate increases
Annuity Due conversion - ANSWER-Annuity payments at the beginning of the period.
Set calculator in BGN mode and insert data per usual.
OR
PV annuity due = PV ordinary annuity * (1+r)
FV annuity due = FV ordinary annuity * (1+r)
