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CFA L1 Master > Equations > Flashcards

Equations Flashcards

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1
Q

Find: Nominal Risk-Free Rate
Given: Risk-Free Rate + Inflation

A

(1 + nominal risk-free rate) = (1 + real risk-free rate)(1 + inflation premium).

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2
Q

Find: Yield
Given:
(1) Real Risk-Free Rate
(2) Inflation Premium
(3) Default Risk
(4) Liquidity Premium
(5) Maturity Premium

A

r = Real risk-free interest rate + Inflation premium + Default risk premium + Liquidity premium + Maturity premium.

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3
Q

Find: Holding Period Return (1 Period)
Given: Price of Asset at T = 0; T = 1; Dividends

A

The return earned from holding an asset for a single specified period of time. The period may be one day, one week, one month, five years, or any specified period.

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4
Q

Find: Holding Period Return (Multiple Periods)

A
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5
Q

Find: Arithmetic Return

A

The simplest way to compute a summary measure for returns across multiple periods is to take a simple arithmetic average of the holding period returns.

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6
Q

Find: Geometric Mean Return

A

A geometric mean return provides a more accurate representation of the growth in portfolio value over a given time period than the arithmetic mean return

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7
Q

Find: Money-Weighted Return

A

The money-weighted return accounts for the money invested and provides the investor with information on the actual return she earns on her investment.

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8
Q

Find: Time-Weighted Return

A

The time-weighted rate of return measures the compound rate of growth of USD1 initially invested in the portfolio over a stated measurement period.

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9
Q

Find: Annualized Returns
Given: Rate R for Period C

A

To annualize any return for a period shorter than one year, the return for the period must be compounded by the number of periods in a year.

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10
Q

Find: Continuously Compounded Return from T to T + 1
Given: P(t = 0) ; P(t = 1)

A
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11
Q

Find: Real Return
Given:
(1) Real Risk-Free Rate
(2) Risk Premium
(3) Inflation Premium

A
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12
Q

Find: Nominal Risk Free Rate
Given:
(1) Real Risk-Free Rate
(2) Inflation Premium

A
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13
Q

Find: Leveraged Return
Given:
(1) Portfolio Return
(2) Portfolio Equity

A

RP = Portfolio
VB = Borrowings of portfolio
VE = Equity of portfolio
rD = Cost of Debt

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14
Q

Find: Future Value (Continuously Compounded Interest)
Given:
(1) Present Value (PV)
(2) Rate ‘R’
(3) Time ‘T’

A
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15
Q

Find: Present Value of Stock @ T
Given:
(1) Dividend @ T
(2) Growth rate ‘g’
(3) Discount ‘r’

A
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16
Q

Find: MAD
Given:
Dataset

A
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17
Q

Sample Variance Formula

A
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18
Q

Sample Standard Deviation

A
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19
Q

Coefficient of Variation

A
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20
Q

Bayes’ Formula

A
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21
Q

Find: Correlation
Given:
Covariance; Stdevs

A
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22
Q

Safety First Ratio

A

The quantity E(RP) − RL is the distance from the mean return to the shortfall level. Dividing this distance by σP gives the distance in units of standard deviation.

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23
Q

Roy’s safety-first criterion

A

states that the optimal portfolio minimizes the probability that portfolio return, RP, will fall below the threshold level, RL.

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24
Q

Covariance

A

Covariance indicates the direction of the linear relationship between variables

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25
Q

Correlation

A

Correlation measures both the strength and direction of the linear relationship between two variables

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26
Q

Correlation to Covariance

A
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27
Q

Covariance to Correlation

A
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28
Q

Portfolio of Two Assets:
Standard Deviation

A
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29
Q

Utility Function of an Investment

A
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30
Q

GP’s rate of return
(standard)

A
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31
Q

GP’s rate of return
(catch-up clause)

A
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32
Q

MOIC

A
33
Q

Relationship between Forward and Spot Prices

A
34
Q

Herfindahl–Hirschman Index

A
35
Q

N-Firm Concentration Ratio

A
36
Q

Fiscal Multiplier

A
37
Q

Neutral Rate

A

Neutral rate = Trend growth + Inflation target

38
Q

Real Exchange Rate

A
39
Q

Direct Quote

A

Rate = Domestic Currency / Foreign Currency

A direct quote is a foreign exchange rate that shows how much domestic currency is required to buy one unit of foreign currency.

40
Q

Indirect Quote

A

Rate = 1 / Direct Quote

41
Q

Forward Rate
(Full Period)

A
42
Q

Forward Rate
(Fractional Period)

A
43
Q

Current Ratio

A
44
Q

Quick Ratio

A
45
Q

Cash Ratio

A
46
Q

ROIC

A
47
Q

WACC

A
48
Q

Cost of Debt

A

nominal cost of debt * (1 – Tax rate)

49
Q

MM Proposition:
Cost of Equity W/o Taxes

A
50
Q

MM Proposition:
Cost of Equity W Taxes

A
51
Q

MM Proposition:
Value of a Levered Firm

A
52
Q

Static Trade-Off Theory:
Optimal Capital Structure

A
53
Q

Leverage Ratio
(Portfolio)

A
54
Q

Margin Math: Initial Investment

A

Number of Shares x Purchase Price x Initial Margin Requirement

55
Q

Margin Math: Loan Amount

A

Loan Amount = Number of Shares x Purchase Price x (1 - Margin Requirement)

56
Q

Margin Math: Interest on Loan

A

Interest on Loan=Loan Amount×Call Money Rate

57
Q

Margin Math: Commission Costs

A

Commission Costs=Number of Shares×Commission per Share×2

58
Q

Margin Math: Equity @ End

A

Equity at End=Total Sale Proceeds+Dividend Received−Loan Amount−Interest on Loan−Commission Costs

59
Q

Margin Math: Total Return

A

Total Return=Initial InvestmentEquity at End−Initial Investment​

60
Q

Margin Math: Price @ Margin Call

A
61
Q

Margin Math:
maintenance margin requirement

A

25 percent of the current value of the position

62
Q

Return on equity (ROE)

A
63
Q

Degree of Operating Leverage

A

DOL = % Δ Operating Profit/% Δ Sales

64
Q

Degree of Financial Leverage

A

DFL = % Δ Net income/% Δ Operating income

65
Q

Free Cash Flow to Equity

A

FCFE = CFO – FCInv + Net borrowing  

66
Q

DCF to Value Company (Using Equity)

A
67
Q

Estimating a long-term growth rate

A
68
Q

Current Yield

A
69
Q

Yield-to-Maturity

A

The internal rate of return (IRR) on the bond if held until maturity, assuming all payments are made as scheduled.

70
Q

Flat Price

A

The full price of a bond minus accrued interest. Flat prices are usually quoted by bond dealers.

71
Q

bond’s accrued interest

A
72
Q

Full Price

A

PVFull = PVFlat + AI. 

73
Q

duration gap

A

Duration gap = Macaulay duration – Investment horizon

74
Q

Macaulay Duration

A
75
Q

Modified Duration

A
76
Q

forward points

A

The number of forward points equals the forward rate minus the spot rate x 10000

77
Q

Find: Spot Rate
Given:
(1) Forward Points as a %
(2) Forward Rate

A

Spot rate × (1 + Forward points as a percentage) = Forward rate

78
Q

Annualized Holding Return

A
79
Q

Forward premium

A

Forward Premium = Forward Rate - Spot Rate

CFA L1 Master (11 decks)

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