Formula Flashcards
Arithmetic Mean
Sum of no/ total of no
Geometric mean
N √(1+X) X (1+X2) X (1+X3)
Population standard deviation
√sum(X-X)2/n
Sample standard deviation
√Sum (X-X)2/n-1
Variance population
Sum (X-X)2/n
Variance sample
Sum (X-X)2/n-1
Correlation coefficient
Covariance (X,Y)/ SDx X SDy
Linear regression
Y=a+bX
Compounding formula
TV=PV(1+R)n
Compounding continuously
TV=PVxE(RxN)
Single cashflow discounting
PV=TV/(1+R)n
Annuity formula
PV=£X x1/Rx(1-1/(1+R)n
Perpetuity formula
PV=£X/R
Effective annual rate
AER=(1+R/N)n -1
Index factor for price weighted indices
Sum stock prices new/ sum stock prices bases
Index factor for market value weighted indices
Sum price today x no shares/ sum base x no shares
Holding period return
P end-p start +income / p start
Gordon’s growth model
Ex div share price= Do (1+g)/ (r-g)
Warrant value
Formula value + premium value
Percent premium
Premium per share/ market price per share
Conversion price
NV of bond/conversion ratio
Conversion premium
Market price bond/ conversion ratio - market price per share
Theoretical convertible bond price
Price of vanilla bond + (call premium/ 1+% increase in stock) x conversion ratio
PV of bond
Bond price = £coupon x 1/R x (1-1/(1+R)n) + CAP/(1+R)n
Flat yield
Gross annual coupon/ clean price
Gross redemption yield
Bond price= £Coupon x 1/R x (1-1/(1+R)n)+ CAP/(1+R)n
Net redemption yield
Bond price= £Coupon (1-t) x 1/R x (1-1/(1+R)n)+ CAP/(1+R)n
Macaulay duration
Sum PV cashflows x time to cashflow/ sum PV cashflows
Interest rate parity
Forward/spot = (1+R var)/ (1+R base)
Purchasing power
Forward/spot = (1+I var)/ (1+ I base)
Fair value if future
Spot price of asset + cost of carry
Basis
Spot price of asset - current futures price
Basic hedge
No contracts to hedge = val of portfolio / val of futures contract
Beta hedge
No contracts to hedge = val of portfolio / val of futures contract x Beta
Option premium
Intrinsic value + time value
Delta
Change in prem val/ change in price of underlying
Rental yield
(Gross rent- expenses) / total cost of purchase
Money weighted rate of return
PV= CF/(1+r) + CF / (1+r)2 + TV/(1+r)n
Time weighted rate of return
(HP1 end/ HP1 start x HP2 end/HP2 start) -1
Total risk
√var market risk + var specific risk
Beta
Cov (Rm Rj) / var Rm
CAPM
ER= Rf + beta (Rm-RF)
Jensen
RP-Rcapm
Sharpe
RP-RF/ standard deviation of portfolio
Treynor
RP-RF/ beta
Information ratio
RP-R benchmark/ standard deviation of excess return
Bond performance
RP-RF/ (DP/DM)
Bond CAPM
ER= Rf + DP/DM (Rm-RF)
Annual depreciation
Cost of asset - residual val / useful life
Depreciation charge
1 - n√expected residual val / original cost
Earnings per share
Profit available to ords / no or ord shares
Earnings yield
EPS/ ex div price
Div yield
Net div / ex div price
Div cover
EPS / net div
Price earnings ratio
Share price / EPS
Debt to equity
Total long term debt / total equity
Operational gearing
Sales rev - var costs / trading profit = trading prof + fixed costs / trading profit
Interest cover
PBIT / interest expense
Current ratio
Current assets / current liabilities
Quick ratio
Current assets - inventory / current liabilities = receivables + cash / current liabilities
ROCE
Operating profit / cap employed = PBIT / CAP + reserves + borrowing
Price elasticity of demand
% change in quantity / % change in price
Income elasticity of demand
% change in quantity / % change in income
Cross elasticity of demand
% change in quantity demand / % change in price of substitute or complement
Basic multiplier
1/ (1-MPC)
Full multiplier
1/ (1-MPC)t -MPM
Money multiplier
1/ reserve requirement
Quantity theory of money
MV= PT
