FV_n = PV * (e^r_s*N)

r_BD = [D/F] * [360/t]

r_BD = annualized yield on a bank discount basis

D = dollar discount (face value - purchase price)

F = face value of the bill

t = number of days until maturity

EAY = [(1+HPY)^365/t] - 1

HPY = holding period yield

t = number of days until maturity

R_mm = [360*r_BD] / [360-(t*r_BD)]

R_mm = HPY*(360/t)

X = Number of observations / Σ(1/x_i)

*Find what this measures/when it's used

Discount rate that equates the cash flows with the initial cash outlay

∑[CF_t / (1 + IRR)^t] = Outlay

L_y = [(n+1)*y] / 100

y = percentage point at which we are dividing the distribution

L_y = location (L) of the percentile (P_y) in the data set sorted in ascending order

MAD = Σ|x_i-X| / n

n = number of items in the data set

X = mean

| | = absolute value

σ^{2 =} Σ(x_i-μ)² / N

Variances = observation - population mean

s/X

Sample standard deviation / sample mean

[r_p-r_f] / s_p

(mean portfolio return - risk free return) / standard deviation of portfolio returns

[ [ [n*(n+1)] / [(n-1)(n-2)(n-3)] ] * [(Σ(x_i-X)⁴ / s⁴] ]   -  [ [3(n-1)²] / [(n-2)(n-3)] ]

As n becomes large, the first term becomes 1/n and the third term becomes 3

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

Probability of A and B is the probability of A given B times the probability of B

P(A) = P(AS) + P(AS^c)

*Don't know what this is at all

E(X) = Σ P(x_i)*x_i

xi = one of n possible outcomes

Cov (XY) = E{[X - E(X)][Y - E(Y)]}

Cov (R_A,R_B) = E{[R_A - E(R_A)][R_B - E(R_B)]}

_nC_r = (n over r) = n! / [(n-r)!*(r!)]

Used when the order in which the items assigned the labels is not important

P(X=x) = _nC_x*(p)^x*(1-p)^n-x

p = probability of success

1-p = probability of failure

nCx = number of possible combinations of having x successes in n trials. Aka number of ways to choose x from n when the order does not matter

Sampling error of the mean = Sample mean - Population mean

= X - μ

90% - x ± 1.65s

95% - x ± 1.96s

99% - x ± 2.58s

Mean ± ...

Sample mean ± (reliability factor * standord error)

Reliability factor = The standard normal random variable for which the probability of an observation lying in either tail is α / 2

[(X-μ₀)] / [(s / n^1/2)]

X = sample mean

μ₀ = hypothesized population mean

s = standard deviation of the sample

 n = sample size

Perfect competition: AR = ATC

Imperfect competition: TR = TC

MP₁ / P₁ = MP₂ / P₂ = ... = MP_N / P_N

where:

MP_N = marginal product of input N

P_N = cost of input N

N = number of inputs

Perfect competition: AR < AVC

Imperfect competition: TR < TVC

Profits are maximized when:

(MRP₁ / Price of input 1) = (MRP_n / Price of input n)

Value of goods and services included in GDP measured at current prices

Nominal GDP = quantity produced in Year t * Prices in Year t

Refers to the value of goods included in GDP measured at base-year prices

Real GDP = Quantity produced in Year t * Base-year prices

[Value of current year output at current year prices / value of current year output at base year prices] * 100

[Nominal GDP / Real GDP] * 100

GDP = consumer spending on goods and services

+ Business gross fixed investment

+ Change in inventories

+ Government spending on goods and services

+ Government gross fixed investment

+ Exports - imports

+ Statistical discrepancy

Money supply X velocity = price X real output

(MV = PY)

Sum of incomes received by all factors of production used to generate final output

Employee compensation, corporate and government enterprise profits before taxes, interest income, rent and unincorporated business net income, indirect business taxes less subsidies

Personal income - personal taxes

aka

Houseold consumption + Household saving

Growth in technology + W_c(growth in the capital-to-labor ratio)

where:

W_c = capital's percentage share of national income

Nominal interest rate (R_N) reflects the real interest rate (R_R) and the expected inflation rate (∏^C)

R_N = R_R + ∏^C

S_DC/FC * (P_FC / P_DC)

S_DC/FC = Nominal Spot exchange rate

P_FC = foreign price level (quoted in terms of the foreign currency)

P_DC = Domestic price level (qutoed in terms of the domestic currency)

ω_Xε_X + ω_M(ε_M - 1) > 0

Where:

ω_X = Share of exports in total trade

ω_M = Share of imports in total trade

ε_X = Price elasticity of demand for exports

ε_M = Price elasticity of demand for imports

EAY = [(1+HPY)^365/t] - 1

HPY = holding period yield

t = number of days until maturity

σ^{2 =} Σ(x_i-μ)² / N

Variances = observation - population mean

Cov (XY) = E{[X - E(X)][Y - E(Y)]}

Cov (R_A,R_B) = E{[R_A - E(R_A)][R_B - E(R_B)]}

Corr (R_A,R_B) = Cov (R_A,R_B) / [(σ_A)(σ_B)]

F_DC/FC = (1 / S_FC/DC) * [(1 + r_DC) / (1 + r_FC)]

or

F_DC/FC = S_DC/FC * [(1 + r_DC) / (1 + r_FC)]

F_t = S_t+1

[(S_{t + 1}) / S] - 1 = % change in S(DC/FC)_t + 1 = (r_DC - r_FC) / (1 + r_FC)

Sum of discounted cash flows - Initial Cash Outlay

∑[CF_t / (1 + r)^t] - Outlay

Discount rate that equates the cash flows with the initial cash outlay

∑[CF_t / (1 + IRR)^t] = Outlay

WACC = [(w_d)(r_d)(1 - t)] + [(w_p)(r_p)] + [(w_c)(r_c)]

p = preferred stock

c = common equity

d = debt

P₀ = D₁ / [r_c - g]

g = expected constant growth rate of dividends

r_c = required rate of return on common equity

Rearranges to: r_c = [D₁ / P₀] + g

r_c = R_f + β[E(R_M) - R_F + CRP]

or

Sovereign yield spread * (Annualized SD of equity index / Annualized SD of Sovereign bond market in terms of the developed market currency)

PQ = VQ + F + C

P = Price per unit

Q = Number of units produced and sold

V = Variable cost per unit

F = Fixed operating costs

C = Fixed financial costs

Q_BE = (F + C) / (P - V)

PQ_OBE = PV + F

Q_OBE = F / (P - V)

P = Price per unit

Q = Number of units produced and sold

V = Variable cost per unit

F = Fixed operating costs

[1 + (Discount / (1 - Discount))]^{[365 / Days beyond discount period]} - 1

Not sure if -1 is raised up or not

R = [(P_T + D_T) / P₀] - 1

P_T = Price at end

D_T = Dividends paid

P₀ = Price at the beginning of the period

R = [(1 + R₁)*(1 + R₂)*...*(1 + R_N)] - 1

Rs are sub-period returns

**Return for WHOLE period

R = [[(1 + R₁)*(1 + R₂)*...*(1 + R_N)]^(1/n)] - 1

**ANNUAL return

σ_p = [w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ_1,2]^1/2

or

[w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov_1,2]^1/2

E(R_p) = w₁R_f + (1-w₁)E(R_m)

w₁ = Weight in risk free asset

E(R_m) = expected market return

E(R_p) = R_f + [(E(R_m) - R_f)/σ_m] * σ_p

Slope ((E(R_m) - R_f)/σ_m) is the market price of risk

P₀ * [(1-Initial Margin) / (1-Maintenance Margin)]

Gives price at which an investor who goes long on a stock recieves a margin call

w_i^M = Q_iP_i / ΣQ_jP_j

where:

w_i = Fraction of the portfolio that is allocated to security i or weight of security i

Q_i = Number of shares outstanding of security i

P_i = Share price of security i

N = Number of securities in the index

Non-callable, non-convertible, no maturity date, and pays fixed dividends:

V₀ = D₀ / r

Non-callable, non-convertible, preferred stock with maturity at time n:

V₀ = ΣD_t / (1+r)^t + [F / (1+r)ⁿ]

where:

V₀ = value of preferred stock today (t = 0)

D_t = expected dividend in year t, assumed to be paid at the end of the year

r = required rate of return on the stock

F = par value of preferred stock

[Yield on Bond X-Yield on Bond Y] / Yield on Bond y

Bond Y is the reference bond

= nominal risk-free rate

+ default risk premium

+ liquidy premium

+ maturity risk premium

[V_--V₊] / [2*V₀(Δy)

where:

Δy = change in yield in decimal

V₀ = initial price

V_- = price if yields decline by Δy 

V₊ = price if yields increase by Δy 

Portfolio duration = w₁D₁ + w₂D₂ +...+ w_ND_N

where:

N = Number of bonds in portfolio.

D_i = Duration of Bond i.

w_i = Market value of Bond i divided by the market value of portfolio

(bond price when yields fall - bond price when yields rise) / (2 X (initial price) X (change in yield in decimal form)

V_- - V₊ / (2V₀(Δy)

S_T < X: X - S_T

S_T = X: 0

S_T > X: 0

C + [X / (1 + RFR)^T] = (S₀ - PV_CF) + P

PV_CF = loan taken out to cover the present value of cash flows over the period

Minimum: EC_T ≥ 0

Maximum: EC_T ≤ S_T

Minimum: AC_T ≥ 0

Maximum: AC_T ≤ S_T

Minimum: EP_T ≥ 0

Maximum: EP_T ≤ [X / (1+RFR)^T

Minimum: AP_T ≥ 0

Maximum: AP_T ≤ X

Minimum: Max [0, S_T - [X / (1+RFR)^T]

Maximum: S_T

Minimum: Max [0, S_T - [X / (1+RFR)^T]

Maximum: S_T

Minimum: Max [0, [X / (1+RFR)^T] - S_T]

Maximum: X / (1+RFR)^T

Minimum: Max [0, X - S_T]

Maximum: X

Max (0, Underlying rate at expiration - Exercise Rate) * [(Days in underlying rate*NP) / 360]

where:

NP = Notional Principal

Max (0, Exercise rate - Underlying Rate at Expiration) * [(Days in underlying rate*NP) / 360]

where:

NP = Notional Principal

(Swap fixed rate - LIBOR_t-1 ) * (No. of days/360) * (NP)

where:

NP = Notional Principal

(Swap fixed rate - LIBOR_{t - 1})(number of days / 360) X notional principal

Number of days and divisor will be specified 

FCFF = NI + NCC + [Int * (1-t)] - FCInv - WCInv

FCFF = CFO + [Int * (1-t)] - FCInv