CFA Level 1: Quant Formulas,
Workings
1. nominal risk free rate = real risk free rate + expected inflation
2. required interest rate on a security = nominal risk free rate + default risk premium
+ liquidity premium + maturity risk premium
3. EAR or APY= (1+periodic rate)^m - 1
always higher than annual percentage rates (not compounded)
4. ordinary annuity: cash flows that occur at the end of each compounding period
5. annuity due: payments or receipts occur at the beginning of each period
6. PV of Perpetuity: Payment/interest rate
7. Effect of increase in the frequency of compounding rates: increases FV,decreases PV
8. amortization schedule: interest component = interest rate * beginning balanceprincipal component
= payment - interest component
ending balance = period's beginning balance (last period's ending balance) - prin-cipal component
9. holding period return: (ending value-beginning value) / beginning value OR(Ending value /
beginning value) - 1
10. time-weighted rate of return: The compound rate of growth of one unit of currency invested in a
portfolio during a stated measurement period; a measure ofinvestment performance that is not sensitive to
the timing and amount of withdrawalsor additions to the portfolio. Also a geometric mean return
11. money weighted return: IRR based on cash inflows and outflows
12. Bank discount yield: RBD = D/F * 360/t Where: D = dollar discount from facevalue, F = face
value, T = days until maturity, 360 = days in a year
US T-Bills are quoted on a bank discount basis
13. holding period yield: Holding Period Return = (ending value/beginning value)
-1
EAY^t/365 - 1
total return an investor earns between the purchase date and the sale or maturitydate
14. effective annual yield: EAY = (1 + HPY)^365/t - 1 where t is days to maturity.Remember that
EAY > bank discount yield, for three reasons: (a) yield is based onpurchase price, not face value, (b) it
is annualized with compound interest (intereston interest), not simple interest, and (c) it is based on a
365-day year rather than 360 days. Be prepared to compare these two measures of yield and use these
threereasons to explain why EAY is preferable.
, CFA Level 1: Quant Formulas,
Workings
15. money market yield (Rmm): = HPR * (360/days until maturity)
16. bond equivalent yield: = Semiannual Yield * 2
semiannual yield needs to be compounded
17. Descriptive statistics: used to summarize the important characteristics of largedata sets
18. Inferential statistics: a sample, pertain to the procedures used to make fore-casts, estimates or
judgement about a large set of data
19. nominal scale / categorical: level of measurement with least information, ob-servations are
classified or counted with no particular order
20. ordinal scale: level of measurement, categorized with respect to specifiedcharacteristic
21. interval scale: provides relative ranking like ordinal scale plus assurance thatthe difference
between the scale values are equal e.g. temperature
however measurement of 0 does not necessarily indicate the total absence of whatwe are measuring -
e.g. 30 c is not three times as hot as 10 c
22. ratio scale: ratio scales provide ranking and equal difference between scalevalues and a true
zero point as the origin e.g. measurement of money
23. difference between parameter and sample statistic: parameter is used forpopulation
sample statistic is used for sample
24. modal interval: For any frequency distribution, the interval with the greatestfrequency
25. relative frequency: dividing the absolute frequency of reach return by the totalnumber of
observations
26. mode: the value that occurs most frequently in a data set
unimodal: one value that happens most frequent
bimodal, trimodal: two or three values happen the most frequent
27. geometric mean: Compounded annual rate of return for an investment, har-monic mean <
geometric mean < arithmetic mean
= (X1 * X2 * X3 * Xn) ^1/n
28. harmonic mean: N/[(1/X1)+(1/X2)+(1/X3)..etc.] *used for computations such asaverage cost of
shares purchased over time--average price per share
harmonic mean < geometric mean < arithmetic mean
29. measures of location: (n+1) * y/100
Workings
1. nominal risk free rate = real risk free rate + expected inflation
2. required interest rate on a security = nominal risk free rate + default risk premium
+ liquidity premium + maturity risk premium
3. EAR or APY= (1+periodic rate)^m - 1
always higher than annual percentage rates (not compounded)
4. ordinary annuity: cash flows that occur at the end of each compounding period
5. annuity due: payments or receipts occur at the beginning of each period
6. PV of Perpetuity: Payment/interest rate
7. Effect of increase in the frequency of compounding rates: increases FV,decreases PV
8. amortization schedule: interest component = interest rate * beginning balanceprincipal component
= payment - interest component
ending balance = period's beginning balance (last period's ending balance) - prin-cipal component
9. holding period return: (ending value-beginning value) / beginning value OR(Ending value /
beginning value) - 1
10. time-weighted rate of return: The compound rate of growth of one unit of currency invested in a
portfolio during a stated measurement period; a measure ofinvestment performance that is not sensitive to
the timing and amount of withdrawalsor additions to the portfolio. Also a geometric mean return
11. money weighted return: IRR based on cash inflows and outflows
12. Bank discount yield: RBD = D/F * 360/t Where: D = dollar discount from facevalue, F = face
value, T = days until maturity, 360 = days in a year
US T-Bills are quoted on a bank discount basis
13. holding period yield: Holding Period Return = (ending value/beginning value)
-1
EAY^t/365 - 1
total return an investor earns between the purchase date and the sale or maturitydate
14. effective annual yield: EAY = (1 + HPY)^365/t - 1 where t is days to maturity.Remember that
EAY > bank discount yield, for three reasons: (a) yield is based onpurchase price, not face value, (b) it
is annualized with compound interest (intereston interest), not simple interest, and (c) it is based on a
365-day year rather than 360 days. Be prepared to compare these two measures of yield and use these
threereasons to explain why EAY is preferable.
, CFA Level 1: Quant Formulas,
Workings
15. money market yield (Rmm): = HPR * (360/days until maturity)
16. bond equivalent yield: = Semiannual Yield * 2
semiannual yield needs to be compounded
17. Descriptive statistics: used to summarize the important characteristics of largedata sets
18. Inferential statistics: a sample, pertain to the procedures used to make fore-casts, estimates or
judgement about a large set of data
19. nominal scale / categorical: level of measurement with least information, ob-servations are
classified or counted with no particular order
20. ordinal scale: level of measurement, categorized with respect to specifiedcharacteristic
21. interval scale: provides relative ranking like ordinal scale plus assurance thatthe difference
between the scale values are equal e.g. temperature
however measurement of 0 does not necessarily indicate the total absence of whatwe are measuring -
e.g. 30 c is not three times as hot as 10 c
22. ratio scale: ratio scales provide ranking and equal difference between scalevalues and a true
zero point as the origin e.g. measurement of money
23. difference between parameter and sample statistic: parameter is used forpopulation
sample statistic is used for sample
24. modal interval: For any frequency distribution, the interval with the greatestfrequency
25. relative frequency: dividing the absolute frequency of reach return by the totalnumber of
observations
26. mode: the value that occurs most frequently in a data set
unimodal: one value that happens most frequent
bimodal, trimodal: two or three values happen the most frequent
27. geometric mean: Compounded annual rate of return for an investment, har-monic mean <
geometric mean < arithmetic mean
= (X1 * X2 * X3 * Xn) ^1/n
28. harmonic mean: N/[(1/X1)+(1/X2)+(1/X3)..etc.] *used for computations such asaverage cost of
shares purchased over time--average price per share
harmonic mean < geometric mean < arithmetic mean
29. measures of location: (n+1) * y/100
