Equations

Question 1

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

Answer 1

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

Question 2

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

Answer 2

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

Question 3

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

Answer 3

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.

Question 4

Find: Holding Period Return (Multiple Periods)

Answer 4

Question 5

Find: Arithmetic Return

Answer 5

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.

Question 6

Find: Geometric Mean Return

Answer 6

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

Question 7

Find: Money-Weighted Return

Answer 7

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

Question 8

Find: Time-Weighted Return

Answer 8

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

Question 9

Find: Annualized Returns
Given: Rate R for Period C

Answer 9

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.

Question 10

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

Answer 10

Question 11

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

Answer 11

Question 12

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

Answer 12

Question 13

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

Answer 13

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

Question 14

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

Answer 14

Question 15

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

Answer 15

Question 16

Find: MAD
Given:
Dataset

Answer 16

Question 17

Sample Variance Formula

Answer 17

Question 18

Sample Standard Deviation

Answer 18

Question 19

Coefficient of Variation

Answer 19

Question 20

Bayes’ Formula

Answer 20

Question 21

Find: Correlation
Given:
Covariance; Stdevs

Answer 21

Question 22

Safety First Ratio

Answer 22

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.

Question 23

Roy’s safety-first criterion

Answer 23

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

Question 24

Covariance

Answer 24

Covariance indicates the direction of the linear relationship between variables

Question 25

Correlation

Answer 25

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

Question 26

Correlation to Covariance

Answer 26

Question 27

Covariance to Correlation

Answer 27

Question 28

Portfolio of Two Assets: Standard Deviation

Question 29

Utility Function of an Investment

Answer 29

Question 30

GP’s rate of return (standard)

Answer 30

Question 31

GP’s rate of return (catch-up clause)

Answer 31

Question 32

MOIC

Answer 32

Question 33

Relationship between Forward and Spot Prices

Answer 33

Question 34

Herfindahl–Hirschman Index

Answer 34

Question 35

N-Firm Concentration Ratio

Answer 35

Question 36

Fiscal Multiplier

Answer 36

Question 37

Neutral Rate

Answer 37

Neutral rate = Trend growth + Inflation target

Question 38

Real Exchange Rate

Answer 38

Question 39

Direct Quote

Answer 39

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.

Question 40

Indirect Quote

Answer 40

Rate = 1 / Direct Quote

Question 41

Forward Rate (Full Period)

Answer 41

Question 42

Forward Rate (Fractional Period)

Answer 42

Question 43

Current Ratio

Answer 43

Question 44

Quick Ratio

Answer 44

Question 45

Cash Ratio

Answer 45

Question 46

ROIC

Answer 46

Question 47

WACC

Answer 47

Question 48

Cost of Debt

Answer 48

nominal cost of debt * (1 – Tax rate)

Question 49

MM Proposition: Cost of Equity W/o Taxes

Answer 49

Question 50

MM Proposition: Cost of Equity W Taxes

Answer 50

Question 51

MM Proposition: Value of a Levered Firm

Answer 51

Question 52

Static Trade-Off Theory: Optimal Capital Structure

Answer 52

Question 53

Leverage Ratio (Portfolio)

Answer 53

Question 54

Margin Math: Initial Investment

Answer 54

Number of Shares x Purchase Price x Initial Margin Requirement

Question 55

Margin Math: Loan Amount

Answer 55

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

Question 56

Margin Math: Interest on Loan

Answer 56

Interest on Loan=Loan Amount×Call Money Rate

Question 57

Margin Math: Commission Costs

Answer 57

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

Question 58

Margin Math: Equity @ End

Answer 58

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

Question 59

Margin Math: Total Return

Answer 59

Total Return=Initial InvestmentEquity at End−Initial Investment​

Question 60

Margin Math: Price @ Margin Call

Answer 60

Question 61

Margin Math: maintenance margin requirement

Answer 61

25 percent of the current value of the position

Question 62

Return on equity (ROE)

Answer 62

Question 63

Degree of Operating Leverage

Answer 63

DOL = % Δ Operating Profit/% Δ Sales

Question 64

Degree of Financial Leverage

Answer 64

DFL = % Δ Net income/% Δ Operating income

Question 65

Free Cash Flow to Equity

Answer 65

FCFE = CFO – FCInv + Net borrowing  

Question 66

DCF to Value Company (Using Equity)

Answer 66

Question 67

Estimating a long-term growth rate

Answer 67

Question 68

Current Yield

Answer 68

Question 69

Yield-to-Maturity

Answer 69

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

Question 70

Flat Price

Answer 70

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

Question 71

bond's accrued interest

Answer 71

Question 72

Full Price

Answer 72

PVFull = PVFlat + AI. 

Question 73

duration gap

Answer 73

Duration gap = Macaulay duration – Investment horizon

Question 74

Macaulay Duration

Answer 74

Question 75

Modified Duration

Answer 75

Question 76

forward points

Answer 76

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

Question 77

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

Answer 77

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

Question 78

Annualized Holding Return

Answer 78

Question 79

Forward premium

Answer 79

Forward Premium = Forward Rate - Spot Rate