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cfa l1 formulas > Formulas > Flashcards

Formulas Flashcards

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CFA flashcards
1
Q

Real Exchange Rate =?

A

nominal FX rate * (base currency CPI/ price currency CPI)

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2
Q

No-Arbitrage Forward Exchange Rate =?

A

Forward/Spot = 1+price currency IR / 1+base currency IR

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3
Q

Basic EPS =?

A

( net income - pref divs)/ weighted avg no. common shares outs…

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4
Q

Diluted EPS =?

A

Adj income available for common shares/ Weighted average common shares + potential common shares outstanding

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5
Q

Current Ratio =?

A

Current Assets/Current Liabilities

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6
Q

Quick Ratio =?

A

(Cash + Marketable Securities + Receivables)/Current Liabilities

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7
Q

Cash Ratio =?

A

(Cash + Marketable Securities)/Current Liabilities

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8
Q

Defensive Interval =?

A

(Cash + Marketable Securities + Receivables)/Daily Cash Expenditures

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9
Q

Receivables Turnover =?

A

Annual Sales/Average Receivables

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10
Q

Inventory Turnover =?

A

COGS/Average Inventory

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11
Q

Payables Turnover Ratio =?

A

Purchases/Average Trade Payables

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12
Q

Days of Sales Outstanding =?

A

365/Receivable Turnover

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13
Q

Days of Inventory on Hand =?

A

365/Inventory Turnover

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14
Q

Number of Days of Payables =?

A

365/Payables Turnover Ratio

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15
Q

Cash Conversion Cycle =?

A

Days of Inventory on Hand + Days of Sales Outstanding - Number of Days of Payables

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16
Q

Total Asset Turnover =?

A

Revenue/Average Total Assets

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17
Q

Fixed Asset Turnover =?

A

Revenue/Average Fixed Assets

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18
Q

Working Capital Turnover =?

A

Revenue/Average Working Capital

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19
Q

Gross Profit Margin =?

A

Gross Profit/Revenue

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20
Q

Operating Profit Margin =?

A

Operating Profit/Revenue OR EBIT/Net Sales

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21
Q

Net Profit Margin =?

A

Net Income/Revenue

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22
Q

Return on Assets (Total Capital) =?

A

EBIT/Average Total Capital

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23
Q

Debt-to-equity ratio =?

A

Total Debt/Total Equity

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24
Q

Total-Debt-Ratio =?

A

Total Debt/Total Assets

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25
Q

Interest Coverage =?

A

EBIT/Interest

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26
Q

Fixed Charge Coverage =?

A

(EBIT + Lease Payments)/(Interest + Lease Payments)

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27
Q

Growth Rate (g) =?

A

RR * ROE

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28
Q

Retention Rate =?

A

1 - (dividends declared/operating income after tax)

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29
Q

Traditional DuPont Equation, ROE =?

A

(Net Income/Sales)(Sales/Assets)(Assets/ Equity) OR (Net Profit Margin)(Asset Turnover)(Equity Multiplier)

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30
Q

Extended DuPont Equation =?

A

(Net Income/EBT)(EBT/EBIT)(EBIT/Revenue)(Revenue/Avg Total Assets)(Avg Total Assets/Avg Equity) OR:
ROE = tax burden × interest burden ×
EBIT margin × asset turnover × leverage

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31
Q

Return on Invested Capital (ROIC) =?

A

Net Operating Profit After Tax/Average Book Value of Total Capital

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32
Q

WACC =?

A

WACC = (wd)[kd(1 – t)] + (wce)(kce)

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33
Q

CAPM =?

A

= Rf + Beta(Rm-Rf)

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34
Q

Leverage Factor =?

A

1/Margin %

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35
Q

Levered return =?

A

HPR*Leveraged Factor

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36
Q

Margin Call Price =?

A

P(1 - initial margin %)/1 - maintenance margin %

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37
Q

Price Weighted Index =?

A

Sum of Stock Prices/Adjusted Divisor

38
Q

Value-weighted Index =?

A

(∑current prices#shares)/(∑base year prices#base year shares) x base value

39
Q

One Period Valuation Model =?

A

D1/(1+ke) + P1/(1+ke)

40
Q

Supernormal growth model (multi-stage) DDM =?

A

D1/(1+ke) + Dn/(1+ke)^n + Pn/(1+ke)^n where Pn = Dn+1/(ke-gc)

41
Q

Constant growth model: =?

A

D0(1+gc)/(ke-gc) = D1/ke-gc

42
Q

Earnings Multiplier Model

A

P0/E1 = (D1/E1)/k-g = payout ratio/k-g

43
Q

Leading P/E =?

A

Price per share/Forecast EPS over next 12 months

44
Q

Trailing P/E =?

A

Price per share/EPS over previous 12 months

45
Q

P/B =?

A

Price per share/Book value per share

46
Q

P/S =?

A

Price per share/Sales per shares

47
Q

P/CF =?

A

Price per share/Cash flow per share

48
Q

Haircut =?

A

1 - 1/InitialMargin

49
Q

Flat Price of a Bond =

A

Full Price - Accrued Interest

50
Q

Accrued Interest of a Bond =?

A

coupon payment * (days from last coupon to settlement/days in coupon period)

51
Q

What does a 1y3y mean?

A

A 3 year forward rate, 1 year from now

52
Q

Approximate Modified Duration =?

A

(V-)-(V+)/ (2×V0×ΔYTM)
where:
V0 = the initial price
V− = the price of the bond if YTM is decreased by ΔYTM
V+ = the price of the bond if the YTM is increased by ΔYTM

53
Q

Approximate Convexity =?

A

(V-)+(V+)-(2V0)/ V0×(ΔYTM)^2
where:
V0 = the initial price
V− = the price of the bond if YTM is decreased by ΔYTM
V+ = the price of the bond if the YTM is increased by ΔYTM

54
Q

Percentage Change in full Bond Price =?

A

(−annual modified durationΔYTM)
+(0.5annual
convexity * (ΔYTM)^
2)

55
Q

Money Convexity =?

A

annual convexity × full price of bond position

56
Q

Effective Convexity =?

A

(V-)+(V+)-(2V0)/ V0×(Δcurve)^2

57
Q

Effective Duration =?

A

(V-)-(V+)/(2×V0×Δcurve)

58
Q

With convexity adjustment, what is the change in the full bond price?

A

− (effective duration)(Δcurve) + (1/2)(effective convexity)(Δcurve)^2

59
Q

Forward Contract Value =?

A

Vt(T) = [St + PVt(costs)– PVt(benefits)] – F0(T)*(1 + Rf)^–(T–t)

60
Q

Intrinsic Value of a Call Option?

A

= Max[0, S – X]

61
Q

Intrinsic Value of a Put Option?

A

Max[0, X – S]

62
Q

European Put Call Parity Relationship =?

A

c + X(1 + Rf)^-T = S + p

63
Q

Contango =?

A

Futures Price > Spot Price

64
Q

Backwardation =?

A

Futures Price < Spot Price

65
Q

Annualised return =?

A

(1+HPR)^365/days -1

66
Q

Continuously Compounded Return =?

A

= ln (1+HPR)

67
Q

Nominal Risk Free Rate =?

A

nominal risk-free rate ≈ real risk-free rate + expected inflation rate.

68
Q

Geometric Mean Return =?

A

=n√(1+R1)×(1+R2)×..×(1+Rn)-1

69
Q

Harmonic Mean Return =?

A

number of observations/sum of the reciprocal of each number in the series.
Often used for calculating average cost of shares over time.

70
Q

Coefficient of Variation=?

A

Standard Deviation/Arithmetic Mean

71
Q

Target Downside Deviation =?

A

Starget=⎷n∑alXi–B * (Xi–B)^2/(n–1)

where B = the target

72
Q

Bayes Formula =?

A

P(A|B) = P(B|A)/P(B) × P(A)

73
Q

Correlation (A,B) =?

A

Covariance A,B/(std dev A * std dev B)

74
Q

Variance of a 2 stock portfolio

A

VarP= w^2Aσ^2A+w^2Bσ^2B+ 2wAwBCovA,B

75
Q

How to calculate covariance of two assets in a portfolio?

A

CovA,B = E{[RA − E(RA)][RB − E(RB)]}

76
Q

Roy’s safety first criterion =?

A

SFRatio=(E(Rp)−RL)/σp

77
Q

In a normal distribution, 68% of observations fall within how many s?

A

68% of observations fall within ± 1s

78
Q

In a normal distribution, 90% of observations fall within how many s?

A

90% fall within ± 1.65s.

79
Q

In a normal distribution, 95% of observations fall within how many s?

A

95% fall within ± 1.96s.

80
Q

In a normal distribution, 99% of observations fall within how many s?

A

99% fall within ± 2.58s.

81
Q

How do we calculate a z-score?

A

z = (observation - population mean)/
standard deviation

82
Q

How do we find R^2 =?

A

R^2 = SSR / SST

83
Q

How do we find Mean Squared Error (MSE)?

A

MSE= SSE/n-2

84
Q

How do we find the standard error of estimate? What does it mean for the model fit?

A

SEE= √MSE where a lower SEE means a better model fit

85
Q

How do we calculate the F-statistic, and what is this used for?

A

F = MSR / MSE
we can use to test whether the slope coefficient is statistically significant.

86
Q

When is a z test used?

A

z-test is used to determine whether two population means are different when the variances are known and the sample size is large

87
Q

When is a paired comparisons test used?

A

A paired comparisons test is appropriate to test the mean differences of two samples believed to be dependent

88
Q

When is a chi-squared test used?

A

a chi-square test is used for tests concerning the variance of a single normally distributed population.

89
Q

When is an F-Test used?

A

to test the difference between the variances of two normally distributed populations with random independent samples

90
Q

When is a non-parametric test appropriate?

A

When the samples consist of ranked values, parametric tests are not appropriate. In such cases, nonparametric tests are most appropriate.

91
Q

When would you not use a parametric test?

A

Numerical Values- particularly with a large sample size

92
Q
A

cfa l1 formulas (3 decks)

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