Key Formulas

risk free rate, inflation premium, default risk premium, liquidity premium and maturity premium

what are the 5 parts of a rate?

1 + nominal = (1+ real)(1 + inflation)

write the Fisher equation

PV(1 + r)^n

FV for N periods =

FV / (1 + r)^n

PV for N periods =

PVe^(rs\*n)

FV w/ continuous compounding =

FVe^(1 / rs\*n)

PV w/ continuous compounding

(1 + periodic IR)^m - 1

EAR for N periods =

e^rs - 1

EAR w/ continuous compounding =

1 + r

what do you multiply an ordinary annuity by to get an annuity due?

1 / (sum of reciprocals / n)

harmonic mean formula

n - 1

what’s the denominator in the variance formula?

sum(Xi - u)^3 / sd^3

skewness formula

covariance of xy / (sd of x\*sd of y)

correlation for x & y =

fat-tailed

if kurtosis is > 3, it is

mesokurtic

if kurtosis is 3>x>-3, it is

thin-tailed

if kurtoses is < -3, it is

n - 1

covariance of xy = sum\[(x - Ux)(y - Uy)\] / _______

(n + 1)(y / 100)

location of y in sorted range =

Xa + (Ly -a)(Xb - Xa)

percentile of y in sorted range =

P(E) / (1 - P(E))

probability as odds for E =

(1 - P(E)) / P(E)

probability as odds against E =

P(A) \* P(B)

independent P(AB)

P(A|B) \* P(B)

dependent P(AB)

P(AB) / P(B)

dependent P(A|B)

P(A) + P(B) - P(AB)

dependent P(A or B)

\[P(new info|event) / P(new info)\] \* P(event)

Bayes formula: P(event|new info) =

multiply each deviation by their probability

the SD w/ probability formula is the same as the normal SD formula, except you _____________

w12o12 + w22o22 + 2w1w2cov12

variance of a 2-asset portfolio

both a’s

in a covariance matrix, the variance of a is where __________ intersect

a and b

in a covariance matrix, the covariance of a & b is where __________ intersect

1 / (b - a)

uniform PDF function, where a < x < b, is

(nCr)(p^x)(1-p)^(n-x)

P(x) in a binomial dist. =

(x - u) / SD

z-score =

\[E(Rp) - RL\] / SD

shortfall ratio =

x\*sqrt(250)

annualized daily volatility =

ln(1 + HPR)

continuous compounding HPR =

SD / n

standard error =

X +/- (Za/2)(SE)

2-sided CI formula =

define null and alternative hypothesis

first step of hypothesis testing

pick test statistic

second step of hypothesis testing

pick level of significance

third step of hypothesis testing

decision rule & calculate critical values

fourth/final step of hypothesis testing

actual Y - expected Y

regression error term =

actual Y - estimated Y

regression residual =

SSE + SSR

regression SST =

SSE

total variation in a regression =

SSR

explained variation in a regression =

SST / df

variance of Y in a regression =

SSR / k

regression MSR =

SSE / (n-k-1)

regression MSE =

SSR / SST

R^2 in a regression =

MSR / MSE

regression F-dist. test stat to see if a regression is statistically significant =

sqrt(MSE)

regression SE =

(% change Qd) / (% change of variable)

elasticity formula =

a - b(Qd)

demand curve, Px =

(wage rate \* hours of labor) *+ (*rental rate \* hours of machine usage)

total cost =

TP / (change in Q / change in L)

marginal product =

variable costs

SR marginal costs =

variable and fixed costs

LR marginal costs =

increase Q

if MR > MC, you should ___________

sum of squares of the x largest market shares

the Herfindahl-Herschmann index for x companies is the?

N largest firms’ market share / total market share

concentration ratio for N companies =

rent + interest + profits

operating surplus =

(nominal GDP / real GDP) \* 100

GDP Deflator =

nominal GDP / (GDP deflator / 100)

real GDP =

C + I + G + (X-M)

GDP = Y =

C + Sc

personal disposable income = PDI =

wages + gross operating surplus + gross mixed income + (taxes - subsidies)

GDI =

1 - MPC

MPS =

C / Y

avg propensity to consume = APS =

TFP growth + labor growth + capital growth

potential GDP growth =

LT growth rate of hours worked + LT growth rate of labor productivity

potential growth rate =

change in economic activity

classical business cycle =

change in economic potential

growth business cycle =

change in growth rates

growth rate business cycle =

(consumption bundle 1 / consumption bundle 0) - 1

Laspeyres index for inflation rate =

\[(Qa1Pa1 + Qb1Pb1) / (Qa1P0 + Qb1P0)\] \* 100

Paasche index for inflation rate =

geometric mean of Laspeyres and Paasche indices

Fisher index for inflation =

MV = PY

what is the quantity equation of exchange?

1 / rr

money multiplier =

real economic growth trend + inflation target

neutral inflation rate =

output - net taxes

disposable income =

1 / (MPS(1-t))

fiscal multiplier =

domestic / foreign

spot FX rate =

spot rate \* foreign price

foreign price level in domestic currency =

spot rate \* (foreign price / domestic price)

real FX rate =

price

is the price or base currency in the numerator?

domestic / foreign

direct exchange rate =

foreign / domestic

indirect exchange rate =

(forward rate - spot rate) \* 10000

FX rate points or pips =

spot rate \* (1 + foreign IR)

1 + domestic IR =

gross profit - operating expenses

EBIT = operating profit =

net income / weighted average of outstanding shares

basic eps =

net income / (weighted avg of outstanding shares + new shares that would’ve been issued)

If-converted diluted eps method =

(net income + after-tax interest on convertible debt - preferred dividends) / (weighted avg of outstanding shares + new shares that would’ve been issued)

with outstanding convertible debt diluted eps method =

(net income - preferred dividends) / (weighted avg of outstanding shares + (new - repurchased shares)\*(proportion of year they were outstanding))

treasury stock diluted eps method =

cash received - cash paid + cash on balance sheet in year 0

cash on balance sheet in year 1 =

beginning accounts receivable + revenues - cash collected on statement of cash flows

ending accounts receivable =

net income + depreciation + (interest expense)(1 - t) - FC and WC investment

FCFF=

CFO / total debt

debt coverage ratio