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CFA Level 1 > 2: Quantitative Methods > Flashcards

2: Quantitative Methods Flashcards

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CFA flashcards
1
Q

keystrokes for compounding

A

either adjust the interest rate (i/y) OR adjust the periods per year (P/y). But NOT both.

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2
Q

calculating EAR

A

determine the “periodic rate” (interest/compounding period). add 1, then multiply by $1, to get growth of the $1, but then “raise” that value by the amount of compounding periods. this will give EAR PLUS 1, so subtract 1.

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3
Q

EAR with continuous compounding

A

use 365. Interest as a decimal, divide by 365, to get periodic rate. add 1, multiply by $1. “raise” by 365, subtract 1 to get EAR.

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4
Q

annuity (as a series of cash flows)

A

a finite set of LEVEL SEQUENTIAL cash flows

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5
Q

ordinary annuity (as a series of cash flows)

A

has a first cash flow that occurs one period from now (indexed at t=1)

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6
Q

annuity due (as a series of cash flows)

A

has a first cash flow that occurs immediately (indexed as t=0). Change to BGN on calculator.

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7
Q

perpetuity (as a series of cash flows)

A

a perpetual annuity, or a set of level never-ending sequential cash flows, with the first cash flow occurring one period from now. END on calculator

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8
Q

computing PV or FV of unequal cash flows

A

Use CF function for uneven cash flows. enter interest rate, then CPT NPV. this is the PV.
To find FV: Do previous steps first, then use PV above to find FV, using same periods and interest rate.

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9
Q

calculating the projected present value of an annuity

A

solve for PV first. then use PV to find FV for period of time in the future

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10
Q

if an annuity begins today, t=0, then…

A

choose BGN on calculator

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11
Q

calculating PV of perpetuities

A

use 500 for N

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12
Q

Rule of 72

A

divide 72 by the stated interest rate to get the approximate number of years it would take to double an investment at the interest rate.

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13
Q

EAR equation

A

(1+Periodic Rate)^m - 1

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14
Q

steps for calculating Perpetuity PV (as it relates to stocks)

A
  1. PV=A/r, give value at t=1.

2. change P/y, then solve for PV where N=1

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15
Q

2 things to remember on unequal cash flows/annuities…

A

make note of timeline… and CLEAR WORK before advancing in the math

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16
Q

annuity calculations t=x

A

adjust the timeline or N if annuity payment is 1 year away, ordinary annuity

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17
Q

college planning with inflation steps

A
  1. inflate each year to FV
  2. discount each year back to ordinary annuity time frame using RoR
  3. add each year for total cost at ordinary annuity timeframe
  4. solve for PMT, total in step 3 is FV
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18
Q

nominal risk-free rate

A

sum of the real risk-free rate and inflation premium

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19
Q

mutually exclusive projects

A

an investor has two candidates for investment but can only invest in one

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20
Q

money-weighted rate of return

A

aka IRR, aka dollar-weighted return. it accounts for the timing and amount of all cash flows into and out of the portfolio.

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21
Q

time-weighted rate of return

A

does not take into account cash inflows/outflows. better measurement for investment management performance.

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22
Q

HPR (holding period return) equation

A

(ending-beginning)/beginning

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23
Q

time-weighted return calculation considers…

A

dividend payments as cash flows

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24
Q

bank discount yield (T-bills)

A

r=(D/F)(360/t); where D=the dollar discount, which is equal to the difference between the face and the purchase price, F=face value, t=actual number of days remaining to maturity

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25
Q

effective annual yield (EAY)

A

takes the quantity 1 plus the holding period yield and compounds it forward to one year, then subtracts 1 to recover an annualized return that accounts for the effect of interest on interest.

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26
Q

the bank discount yield is always…

A

less than the effective annual yield.

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27
Q

EAY formula

A

think EAR…
(1+periodic rate or HPY)^m or 365/t - 1.
just like EAR, except m=365/t

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28
Q

money market yield

A

aka CD equivalent yield.
makes the quoted yield on a T-bill comparable to yield quotations on interest-bearing money-market instruments that pay interest on a 360-day basis.

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29
Q

in general, the money market yield is equal to…

A

the annualized holding period yield; assuming a 360-day year. Compared to the bank discount yield, the mm yield is computed on the purchase price.

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30
Q

money market yield formula

A

(360rBD)/360-(t)(rBD)

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31
Q

HPY formula

A

(P1-P0+D1)/P0

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32
Q

bond equivalent yield

A

doubling the semiannual YTM, ignoring compounding

33
Q

the money market yield is equal to the…

A

annualized HPY, assuming a 360 day year.
rMM=(HPY)(360/t).
No need to know the rBD.

34
Q

the EAY is…

A

365

35
Q

central tendency

A

where the returns are centered

36
Q

dispersion

A

how far returns are dispersed from their center

37
Q

skew-ness

A

whether the distribution of returns is symmetrically shaped or lopsided

38
Q

kurtosis

A

whether extreme outcomes are likely

39
Q

nominal scales

A

represent the weakest level of measurement: they categorize data but do not rank them

40
Q

ordinal scales

A

stronger level of measurement with regard to nominal scales. they sort data into categories that are ordered with respect to some characteristic

41
Q

interval scales

A

provide not only ranking, but also assurance that the differences between scale values are equal. as a consequence of the absence of a true zero point, we cannot meaningfully form ratios on interval scales.

42
Q

ratio scales

A

represent the strongest level of measurement. they have all the characteristics of interval measurement scales as well as a true zero point as the origin.

43
Q

measurement scales, listed worst to best

A

nominal, ordinal, interval, ratio

44
Q

measurement scales:

credit ratings for bond issues

A

ordinal scale. a rating places a bond issue in a category, and the categories are ordered with respect to the expected probability of default. but the difference in the expected probability of default between ratings is not equal. letter credit ratings are not measured on an interval scale

45
Q

measurement scales:

cash dividends per share

A

measured on a ratio scale. for this variable, 0 represents the complete absence of dividends; it is a true zero point.

46
Q

measurement scales:

hedge fund classification types

A

nominal scale. each type groups together hedge funds with similar investment strategies. hedge fund classification schemes do not involve a ranking.

47
Q

measurement scales:

bond maturity in years

A

ratio scale. true zero point.

48
Q

cross-sectional data

A

examining the characteristics of some units at a specific point in time. the mean of these observations is called a cross-sectional mean

49
Q

time-series data

A

if our sample consists of historical returns. the mean of these observations is called a time-series mean

50
Q

the geometric mean is always…

A

less than or equal to the arithmetic mean

51
Q

the only time geometric and arithmetic mean will be equal is when…

A

there is no variability in the observations- when all the observations in the series are the same

52
Q

the difference between the arithmetic and geometric means increases with…

A

the variability in the period-by-period observations

53
Q

the geometric mean represents…

A

the growth rate or compound rate of return on an investment.

54
Q

geometric mean formula and key strokes

A

value=(1+R1)(1+R2)(1+R3)…
=value [y^x] number of returns Rn’s above [1/x] [=]
then subtract 1

55
Q

locating the position of a percentile formula

A

=(n+1)(y/100)

56
Q

harmonic mean is appropriate…

A

when averaging ratios (amount per unit) when the ratios are repeatedly applied to a fixed quantity to yield a variable number of units. Ex. cost averaging

57
Q

mathematical fact concerning harmonic, geometric, and arithmetic means is…

A

unless all the observations in a data set have the same value, the harmonic mean is less than the geometric mean, which in turn is less than the arithmetic mean

58
Q

the lower the quantile…

A

the lower the value in ranking

59
Q

coefficient of variation formula

A

sd/mean

60
Q

sharpe ratio formula

A

(rP-rF)/sdP; where rP is portfolio return, rF is risk free rate, and sdP is standard deviation of portfolio

61
Q

positive skewness

A

has frequent small losses and a few extreme gains

62
Q

negative skewness

A

has frequent small gains and a few extreme losses

63
Q

normal distribution

A

68 percent within 1 standard deviation, 95 percent within 2 standard deviations, 98 percent within 3 standard deviations

64
Q

for the continuous positively skewed distribution…

A

the mode is less than the median, which is less than the mean

65
Q

for the continuous negatively skewed distribution…

A

the mean is less than the median, which is less than the mode

66
Q

leptokurtic

A

distribution that has fatter tails than the normal distribution. has excess kurtosis greater than 0

67
Q

platykurtic

A

distribution that has thinner tails than the normal distribution. has excess kurtosis less than 0.

68
Q

mesokurtic

A

distribution that is identical to the normal distribution as it relates to the weight of the tails. has excess kurtosis equal to 0.

69
Q

if we want to estimate the average return over a one-period horizon, use

A

arithmetic mean because it is the average of one-period returns

70
Q

if we want to estimate the average returns over more than one period, use

A

geometric mean because it captures how the total returns are linked over time

71
Q

a priori probability

A

one based on logical analysis rather than on observation or personal judgment

72
Q

pairs arbitrage trade

A

a trade in two closely related stocks involving the short sale of one and the purchase of the other

73
Q

multiplication rule for probability

A

P(AB)=P(A/B)*P(B)
probability of both happening (joint probability)=conditional probability (probability of a, given b) multiplied by unconditional probability (probability of b)

74
Q

addition rule for probability

A

P(A or B)=P(A)+P(B)-P(AB)

75
Q

multiplication rule for independent events

A

P(AB)=P(A)*P(B)

76
Q

total probability rule

A

explains the unconditional probability of the event in terms of probabilities conditional on the scenarios

77
Q

total probability rule formula

A

P(A)=P(A/S)P(S)+P(A/Sc)P(Sc)

78
Q

covariance matrix formula

A

variance(A+B)=(weightA)^2(varianceA)+(weightB)^2(varianceB)+2(weightA)(weightB)[covariance(A,B)]

CFA Level 1 (2 decks)

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