CFA Level 1 - Quantitative Methods EXAM (2026) UPDATE Verified
Questions And Answers | Latest Already Graded A+ UPDATE |2026
Required rate of return - (answer)The market rate of return is the return that investors and savers
require to get them to willingly lend their funds
discount rates - (answer)Interchangeable with Interest Rates
real risk-free rate - (answer)theoretical nominal risk-free rate ≅ real risk-free rate + expected inflation
ratete on a single-period loan that contains no expectation of inflation and zero probability of default
Nominal Risk Free Rate or T-Bill Formula - (answer)nominal risk-free rate ≅ real risk-free rate + expected
inflation rate
3 types of risk faced for securities - (answer)Default risk: Risk that a borrower will not make the
promissed amounts in a timely manner
Liquidity Risk: Risk of receiving less than fair value for an investment if it must be sold quickly for cash
Maturity Risk: Longer maturity bonds have more maturity risk than shorter term bonds and require a
maturity risk premium.
Holding Period Return (HPR) - (answer)The percentage increase in the value of an investment over a
given period:
Arithmetic Mean Return - (answer)The simple average of a series of periodic returns. It has the
statistical property of being an unbiased estimator of the true mean of the underlying distribution of
returns
geometric mean return - (answer)When periodic rates of return vary from period to period, the
geometric mean return will have a value less than the arithmetic mean return
Harmonic mean - (answer)Used for certain computations, such as the average cost of shares purchased
over time.
,CFA Level 1 - Quantitative Methods EXAM (2026) UPDATE Verified
Questions And Answers | Latest Already Graded A+ UPDATE |2026
e.g. An investor purchases $1,000 of mutual fund shares each month, and over the last three months,
the prices paid per share were $8, $9, and $10. What is the average cost per share?
= 3/(1/8 + 1/9 +1/10)
= $8.926 per share
Relationship between arithmetic mean, harmonic mean and geometric mean - (answer)
Internal Rate of Return (IRR) - (answer)An IRR is the interest rate at which a series of cash inflows and
outflows sum to zero when discounted to their present value
Money Weighted Rate of Return - (answer)Defined as the IRR
Calculated by
- making the beginning value of the account an inflow and all deposits into the account.
- make all withdrawals from the account outflows as is the ending value
- Then equal them to find 'r'
PV(Inflows) = PV(Outflows
Time Weighted Rate of Return - (answer)measures compound growth and is the rate at which $1
compounds over a specified performance horizon.
The time-weighted rate of return is not affected by the timing of cash inflows and outflows.
Time weighted Rate of Return vs Money Weighted Rate of Return - (answer)In the investment
management industry, time-weighted return is the preferred method of performance measurement
because portfolio managers typically do not control the timing of deposits to and withdrawals from the
accounts they manage.
The use of the time-weighted return removes potential investment time distortions, and thus provides a
better measure of a manager's ability to select investments over the period.
, CFA Level 1 - Quantitative Methods EXAM (2026) UPDATE Verified
Questions And Answers | Latest Already Graded A+ UPDATE |2026
Annualized returns - (answer)The same as interest rates or market returns, regardless of the time period
over which they occur
Annualised Return = (1 + HPR)^(365 / days) -1
Present Value of a future cash flow - (answer)
Continuously Compounded Return - (answer)Given an HPR, we can use the natural logarithm
Gross Return vs Net Return - (answer)Gross return refers to the total return on a security portfolio
before deducting fees for the management and administration of the investment account.
Net return refers to the return after these fees have been deducted.
Commissions on trades and other costs that are necessary to generate the investment returns are
deducted in both gross and net return measures.
Pretax nominal return vs after-tax nominal return - (answer)Pretax nominal return refers to the return
before paying taxes. Dividend income, interest income, short-term capital gains, and long-term capital
gains may all be taxed at different rates. After-tax nominal return refers to the return after the tax
liability is deducted.
Real Return - (answer)Real return is nominal return adjusted for inflation
Leveraged Return - (answer)A leveraged return refers to a return to an investor that is a multiple of the
return on the underlying asset..
An investment in a derivative security, such as a futures contract, produces a leveraged return because
the cash deposited is only a fraction of the value of the assets underlying the futures contract.
Initial investment = V_0
Questions And Answers | Latest Already Graded A+ UPDATE |2026
Required rate of return - (answer)The market rate of return is the return that investors and savers
require to get them to willingly lend their funds
discount rates - (answer)Interchangeable with Interest Rates
real risk-free rate - (answer)theoretical nominal risk-free rate ≅ real risk-free rate + expected inflation
ratete on a single-period loan that contains no expectation of inflation and zero probability of default
Nominal Risk Free Rate or T-Bill Formula - (answer)nominal risk-free rate ≅ real risk-free rate + expected
inflation rate
3 types of risk faced for securities - (answer)Default risk: Risk that a borrower will not make the
promissed amounts in a timely manner
Liquidity Risk: Risk of receiving less than fair value for an investment if it must be sold quickly for cash
Maturity Risk: Longer maturity bonds have more maturity risk than shorter term bonds and require a
maturity risk premium.
Holding Period Return (HPR) - (answer)The percentage increase in the value of an investment over a
given period:
Arithmetic Mean Return - (answer)The simple average of a series of periodic returns. It has the
statistical property of being an unbiased estimator of the true mean of the underlying distribution of
returns
geometric mean return - (answer)When periodic rates of return vary from period to period, the
geometric mean return will have a value less than the arithmetic mean return
Harmonic mean - (answer)Used for certain computations, such as the average cost of shares purchased
over time.
,CFA Level 1 - Quantitative Methods EXAM (2026) UPDATE Verified
Questions And Answers | Latest Already Graded A+ UPDATE |2026
e.g. An investor purchases $1,000 of mutual fund shares each month, and over the last three months,
the prices paid per share were $8, $9, and $10. What is the average cost per share?
= 3/(1/8 + 1/9 +1/10)
= $8.926 per share
Relationship between arithmetic mean, harmonic mean and geometric mean - (answer)
Internal Rate of Return (IRR) - (answer)An IRR is the interest rate at which a series of cash inflows and
outflows sum to zero when discounted to their present value
Money Weighted Rate of Return - (answer)Defined as the IRR
Calculated by
- making the beginning value of the account an inflow and all deposits into the account.
- make all withdrawals from the account outflows as is the ending value
- Then equal them to find 'r'
PV(Inflows) = PV(Outflows
Time Weighted Rate of Return - (answer)measures compound growth and is the rate at which $1
compounds over a specified performance horizon.
The time-weighted rate of return is not affected by the timing of cash inflows and outflows.
Time weighted Rate of Return vs Money Weighted Rate of Return - (answer)In the investment
management industry, time-weighted return is the preferred method of performance measurement
because portfolio managers typically do not control the timing of deposits to and withdrawals from the
accounts they manage.
The use of the time-weighted return removes potential investment time distortions, and thus provides a
better measure of a manager's ability to select investments over the period.
, CFA Level 1 - Quantitative Methods EXAM (2026) UPDATE Verified
Questions And Answers | Latest Already Graded A+ UPDATE |2026
Annualized returns - (answer)The same as interest rates or market returns, regardless of the time period
over which they occur
Annualised Return = (1 + HPR)^(365 / days) -1
Present Value of a future cash flow - (answer)
Continuously Compounded Return - (answer)Given an HPR, we can use the natural logarithm
Gross Return vs Net Return - (answer)Gross return refers to the total return on a security portfolio
before deducting fees for the management and administration of the investment account.
Net return refers to the return after these fees have been deducted.
Commissions on trades and other costs that are necessary to generate the investment returns are
deducted in both gross and net return measures.
Pretax nominal return vs after-tax nominal return - (answer)Pretax nominal return refers to the return
before paying taxes. Dividend income, interest income, short-term capital gains, and long-term capital
gains may all be taxed at different rates. After-tax nominal return refers to the return after the tax
liability is deducted.
Real Return - (answer)Real return is nominal return adjusted for inflation
Leveraged Return - (answer)A leveraged return refers to a return to an investor that is a multiple of the
return on the underlying asset..
An investment in a derivative security, such as a futures contract, produces a leveraged return because
the cash deposited is only a fraction of the value of the assets underlying the futures contract.
Initial investment = V_0
