Formulas Flashcards
Real Exchange Rate =?
nominal FX rate * (base currency CPI/ price currency CPI)
No-Arbitrage Forward Exchange Rate =?
Forward/Spot = 1+price currency IR / 1+base currency IR
Basic EPS =?
( net income - pref divs)/ weighted avg no. common shares outs…
Diluted EPS =?
Adj income available for common shares/ Weighted average common shares + potential common shares outstanding
Current Ratio =?
Current Assets/Current Liabilities
Quick Ratio =?
(Cash + Marketable Securities + Receivables)/Current Liabilities
Cash Ratio =?
(Cash + Marketable Securities)/Current Liabilities
Defensive Interval =?
(Cash + Marketable Securities + Receivables)/Daily Cash Expenditures
Receivables Turnover =?
Annual Sales/Average Receivables
Inventory Turnover =?
COGS/Average Inventory
Payables Turnover Ratio =?
Purchases/Average Trade Payables
Days of Sales Outstanding =?
365/Receivable Turnover
Days of Inventory on Hand =?
365/Inventory Turnover
Number of Days of Payables =?
365/Payables Turnover Ratio
Cash Conversion Cycle =?
Days of Inventory on Hand + Days of Sales Outstanding - Number of Days of Payables
Total Asset Turnover =?
Revenue/Average Total Assets
Fixed Asset Turnover =?
Revenue/Average Fixed Assets
Working Capital Turnover =?
Revenue/Average Working Capital
Gross Profit Margin =?
Gross Profit/Revenue
Operating Profit Margin =?
Operating Profit/Revenue OR EBIT/Net Sales
Net Profit Margin =?
Net Income/Revenue
Return on Assets (Total Capital) =?
EBIT/Average Total Capital
Debt-to-equity ratio =?
Total Debt/Total Equity
Total-Debt-Ratio =?
Total Debt/Total Assets
Interest Coverage =?
EBIT/Interest
Fixed Charge Coverage =?
(EBIT + Lease Payments)/(Interest + Lease Payments)
Growth Rate (g) =?
RR * ROE
Retention Rate =?
1 - (dividends declared/operating income after tax)
Traditional DuPont Equation, ROE =?
(Net Income/Sales)(Sales/Assets)(Assets/ Equity) OR (Net Profit Margin)(Asset Turnover)(Equity Multiplier)
Extended DuPont Equation =?
(Net Income/EBT)(EBT/EBIT)(EBIT/Revenue)(Revenue/Avg Total Assets)(Avg Total Assets/Avg Equity) OR:
ROE = tax burden × interest burden ×
EBIT margin × asset turnover × leverage
Return on Invested Capital (ROIC) =?
Net Operating Profit After Tax/Average Book Value of Total Capital
WACC =?
WACC = (wd)[kd(1 – t)] + (wce)(kce)
CAPM =?
= Rf + Beta(Rm-Rf)
Leverage Factor =?
1/Margin %
Levered return =?
HPR*Leveraged Factor
Margin Call Price =?
P(1 - initial margin %)/1 - maintenance margin %
Price Weighted Index =?
Sum of Stock Prices/Adjusted Divisor
Value-weighted Index =?
(∑current prices#shares)/(∑base year prices#base year shares) x base value
One Period Valuation Model =?
D1/(1+ke) + P1/(1+ke)
Supernormal growth model (multi-stage) DDM =?
D1/(1+ke) + Dn/(1+ke)^n + Pn/(1+ke)^n where Pn = Dn+1/(ke-gc)
Constant growth model: =?
D0(1+gc)/(ke-gc) = D1/ke-gc
Earnings Multiplier Model
P0/E1 = (D1/E1)/k-g = payout ratio/k-g
Leading P/E =?
Price per share/Forecast EPS over next 12 months
Trailing P/E =?
Price per share/EPS over previous 12 months
P/B =?
Price per share/Book value per share
P/S =?
Price per share/Sales per shares
P/CF =?
Price per share/Cash flow per share
Haircut =?
1 - 1/InitialMargin
Flat Price of a Bond =
Full Price - Accrued Interest
Accrued Interest of a Bond =?
coupon payment * (days from last coupon to settlement/days in coupon period)
What does a 1y3y mean?
A 3 year forward rate, 1 year from now
Approximate Modified Duration =?
(V-)-(V+)/ (2×V0×ΔYTM)
where:
V0 = the initial price
V− = the price of the bond if YTM is decreased by ΔYTM
V+ = the price of the bond if the YTM is increased by ΔYTM
Approximate Convexity =?
(V-)+(V+)-(2V0)/ V0×(ΔYTM)^2
where:
V0 = the initial price
V− = the price of the bond if YTM is decreased by ΔYTM
V+ = the price of the bond if the YTM is increased by ΔYTM
Percentage Change in full Bond Price =?
(−annual modified durationΔYTM)
+(0.5annual
convexity * (ΔYTM)^
2)
Money Convexity =?
annual convexity × full price of bond position
Effective Convexity =?
(V-)+(V+)-(2V0)/ V0×(Δcurve)^2
Effective Duration =?
(V-)-(V+)/(2×V0×Δcurve)
With convexity adjustment, what is the change in the full bond price?
− (effective duration)(Δcurve) + (1/2)(effective convexity)(Δcurve)^2
Forward Contract Value =?
Vt(T) = [St + PVt(costs)– PVt(benefits)] – F0(T)*(1 + Rf)^–(T–t)
Intrinsic Value of a Call Option?
= Max[0, S – X]
Intrinsic Value of a Put Option?
Max[0, X – S]
European Put Call Parity Relationship =?
c + X(1 + Rf)^-T = S + p
Contango =?
Futures Price > Spot Price
Backwardation =?
Futures Price < Spot Price
Annualised return =?
(1+HPR)^365/days -1
Continuously Compounded Return =?
= ln (1+HPR)
Nominal Risk Free Rate =?
nominal risk-free rate ≈ real risk-free rate + expected inflation rate.
Geometric Mean Return =?
=n√(1+R1)×(1+R2)×..×(1+Rn)-1
Harmonic Mean Return =?
number of observations/sum of the reciprocal of each number in the series.
Often used for calculating average cost of shares over time.
Coefficient of Variation=?
Standard Deviation/Arithmetic Mean
Target Downside Deviation =?
Starget=⎷n∑alXi–B * (Xi–B)^2/(n–1)
where B = the target
Bayes Formula =?
P(A|B) = P(B|A)/P(B) × P(A)
Correlation (A,B) =?
Covariance A,B/(std dev A * std dev B)
Variance of a 2 stock portfolio
VarP= w^2Aσ^2A+w^2Bσ^2B+ 2wAwBCovA,B
How to calculate covariance of two assets in a portfolio?
CovA,B = E{[RA − E(RA)][RB − E(RB)]}
Roy’s safety first criterion =?
SFRatio=(E(Rp)−RL)/σp
In a normal distribution, 68% of observations fall within how many s?
68% of observations fall within ± 1s
In a normal distribution, 90% of observations fall within how many s?
90% fall within ± 1.65s.
In a normal distribution, 95% of observations fall within how many s?
95% fall within ± 1.96s.
In a normal distribution, 99% of observations fall within how many s?
99% fall within ± 2.58s.
How do we calculate a z-score?
z = (observation - population mean)/
standard deviation
How do we find R^2 =?
R^2 = SSR / SST
How do we find Mean Squared Error (MSE)?
MSE= SSE/n-2
How do we find the standard error of estimate? What does it mean for the model fit?
SEE= √MSE where a lower SEE means a better model fit
How do we calculate the F-statistic, and what is this used for?
F = MSR / MSE
we can use to test whether the slope coefficient is statistically significant.
When is a z test used?
z-test is used to determine whether two population means are different when the variances are known and the sample size is large
When is a paired comparisons test used?
A paired comparisons test is appropriate to test the mean differences of two samples believed to be dependent
When is a chi-squared test used?
a chi-square test is used for tests concerning the variance of a single normally distributed population.
When is an F-Test used?
to test the difference between the variances of two normally distributed populations with random independent samples
When is a non-parametric test appropriate?
When the samples consist of ranked values, parametric tests are not appropriate. In such cases, nonparametric tests are most appropriate.
When would you not use a parametric test?
Numerical Values- particularly with a large sample size
