Equations Flashcards
Find: Nominal Risk-Free Rate
Given: Risk-Free Rate + Inflation
(1 + nominal risk-free rate) = (1 + real risk-free rate)(1 + inflation premium).
Find: Yield
Given:
(1) Real Risk-Free Rate
(2) Inflation Premium
(3) Default Risk
(4) Liquidity Premium
(5) Maturity Premium
r = Real risk-free interest rate + Inflation premium + Default risk premium + Liquidity premium + Maturity premium.
Find: Holding Period Return (1 Period)
Given: Price of Asset at T = 0; T = 1; Dividends
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.
Find: Holding Period Return (Multiple Periods)
Find: Arithmetic Return
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.
Find: Geometric Mean Return
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
Find: Money-Weighted Return
The money-weighted return accounts for the money invested and provides the investor with information on the actual return she earns on her investment.
Find: Time-Weighted Return
The time-weighted rate of return measures the compound rate of growth of USD1 initially invested in the portfolio over a stated measurement period.
Find: Annualized Returns
Given: Rate R for Period C
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.
Find: Continuously Compounded Return from T to T + 1
Given: P(t = 0) ; P(t = 1)
Find: Real Return
Given:
(1) Real Risk-Free Rate
(2) Risk Premium
(3) Inflation Premium
Find: Nominal Risk Free Rate
Given:
(1) Real Risk-Free Rate
(2) Inflation Premium
Find: Leveraged Return
Given:
(1) Portfolio Return
(2) Portfolio Equity
RP = Portfolio
VB = Borrowings of portfolio
VE = Equity of portfolio
rD = Cost of Debt
Find: Future Value (Continuously Compounded Interest)
Given:
(1) Present Value (PV)
(2) Rate ‘R’
(3) Time ‘T’
Find: Present Value of Stock @ T
Given:
(1) Dividend @ T
(2) Growth rate ‘g’
(3) Discount ‘r’
Find: MAD
Given:
Dataset
Sample Variance Formula
Sample Standard Deviation
Coefficient of Variation
Bayes’ Formula
Find: Correlation
Given:
Covariance; Stdevs
Safety First Ratio
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.
Roy’s safety-first criterion
states that the optimal portfolio minimizes the probability that portfolio return, RP, will fall below the threshold level, RL.
Covariance
Covariance indicates the direction of the linear relationship between variables
Correlation
Correlation measures both the strength and direction of the linear relationship between two variables
Correlation to Covariance
Covariance to Correlation
Portfolio of Two Assets:
Standard Deviation
Utility Function of an Investment
GP’s rate of return
(standard)
GP’s rate of return
(catch-up clause)
MOIC
Relationship between Forward and Spot Prices
Herfindahl–Hirschman Index
N-Firm Concentration Ratio
Fiscal Multiplier
Neutral Rate
Neutral rate = Trend growth + Inflation target
Real Exchange Rate
Direct Quote
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.
Indirect Quote
Rate = 1 / Direct Quote
Forward Rate
(Full Period)
Forward Rate
(Fractional Period)
Current Ratio
Quick Ratio
Cash Ratio
ROIC
WACC
Cost of Debt
nominal cost of debt * (1 – Tax rate)
MM Proposition:
Cost of Equity W/o Taxes
MM Proposition:
Cost of Equity W Taxes
MM Proposition:
Value of a Levered Firm
Static Trade-Off Theory:
Optimal Capital Structure
Leverage Ratio
(Portfolio)
Margin Math: Initial Investment
Number of Shares x Purchase Price x Initial Margin Requirement
Margin Math: Loan Amount
Loan Amount = Number of Shares x Purchase Price x (1 - Margin Requirement)
Margin Math: Interest on Loan
Interest on Loan=Loan Amount×Call Money Rate
Margin Math: Commission Costs
Commission Costs=Number of Shares×Commission per Share×2
Margin Math: Equity @ End
Equity at End=Total Sale Proceeds+Dividend Received−Loan Amount−Interest on Loan−Commission Costs
Margin Math: Total Return
Total Return=Initial InvestmentEquity at End−Initial Investment
Margin Math: Price @ Margin Call
Margin Math:
maintenance margin requirement
25 percent of the current value of the position
Return on equity (ROE)
Degree of Operating Leverage
DOL = % Δ Operating Profit/% Δ Sales
Degree of Financial Leverage
DFL = % Δ Net income/% Δ Operating income
Free Cash Flow to Equity
FCFE = CFO – FCInv + Net borrowing
DCF to Value Company (Using Equity)
Estimating a long-term growth rate
Current Yield
Yield-to-Maturity
The internal rate of return (IRR) on the bond if held until maturity, assuming all payments are made as scheduled.
Flat Price
The full price of a bond minus accrued interest. Flat prices are usually quoted by bond dealers.
bond’s accrued interest
Full Price
PVFull = PVFlat + AI.
duration gap
Duration gap = Macaulay duration – Investment horizon
Macaulay Duration
Modified Duration
forward points
The number of forward points equals the forward rate minus the spot rate x 10000
Find: Spot Rate
Given:
(1) Forward Points as a %
(2) Forward Rate
Spot rate × (1 + Forward points as a percentage) = Forward rate
Annualized Holding Return
Forward premium
Forward Premium = Forward Rate - Spot Rate
