Formulae Flashcards
What is the equation for FV if simple r is used?
FV.1 = (1+r)P0
11,200 = (1+0.12)x 10,000
What is the FV equation when compounding r is used?
FVt = P0 (1+r),t
What is the PV equation?
PV0 = discount factor x P.t
remember discount factor equation is DFt = 1/ (1+r),t
What is the discount factor equation?
DF1 = 1/ (1+r),t
What is the equation for the PV of a perpetuity?
PV0 (perp) = C / r
What is the equation to find the PV of an annuity?
PV = C / r [ 1 - 1/(1+r),t ]
What is the equation of a perpetuity starting payment from year 1 + t?
(C/r) * 1/(1+r)t
This is because it is now adding a discount factor as it’s future cash
What is the expanded PV of an annuity equation when derived from perpetuities?
C/r - C/r* 1/(1+r),t
What is the EAR equation?
EAR = (1+APR/m),m - 1
In bonds, What is denoted by P?
Price of a bond before maturity
What is denoted by V?
The face/ par/ principle value of the bond paid by the issuer
What is denoted by c?
Coupon rate
In bonds, what is denoted by C?
Coupon
Annuity
How can we compute the value of a bond?
PV = annuity + 100/(1+r),t
PV = C / r [ 1 - 1/(1+r),t ] + 100/(1+r),t
- it is an annuity so we use its formula + the end bit
What equation do you use to compute bond returns?
rate of return = (coupon income + price change) / investment
aka
R = (C1 + P1-P0) / P0
How do you compute the interest yield (IR) of a bond?
IR%= C / P0
Coupon / the clean price
Under the zero growth model, what equation can you use to find P of a stock?
P = D / R
D = dividends R = nominal interest rate
D is not always constant. What equation can you use to find the P of a stock with D that grow at a constant rate?
P0 = D1/ R - g
obviously, higher g the higher the price of a constant growth stock
What equation can be used to help value a differential growth stock?
P.H = (D .H+1) / r - g
H and 1 are little
same as bond calculation
How can you calculate the expected return on a stock?
pays dividend D1 in t =1
r = (D1 + P1 - P0)/ P0
What is Gordon’s Dividend Growth Model?
P0 = [D0 (1+g) ] / r - g
What is the dividend payout ratio?
K = D/ eps
what is the plowback / retention ratio?
b = 1 - D/eps
What is the g equation using plowback ratio ?
g = plowback ratio x return on retained earnings
g = b * r.E
What is the price-earning ratio?
PE0 = P0 / eps0
aka current share price divided by the latest annual earning per share
What represents variance? (VAR)
σ squared
What represents Standard Deviation (SD)?
σ aka square root of VAR
What is the CORR equation?
CORR(rA,rB) = COV(rA,rB) / σA σB
ρA,B = same thing
What letter represents CORR?
ρ
What does w = in portfolio theory?
w= the % share of a security in a portfolio
What equation can you use to work out the rate of return of a portfolio?
for this eg the portfolio has just 2 assets
rp = wA rA + wB rB
all rs have a line above them
what do all w’s in a portfolio add up to?
1
If pA,B = 1, then what is the SD of a portfolio?
σp = wAσA + wBσB
If pA,B = -1, then what is the SD of a portfolio?
σp = wAσA - wBσB
difference between the weighted SDs
What does the portfolio SD of perfectly negatively correlating securities equal when combined?
SD of P = 0
What is the equation of the CML?
E(Rf) = [Rf + (E(R.M) - R.F) ] / σ.M, all multiplied by σ.P
the slope is just the middle bit aka market price of risk & Sharpe ratio
What is the market price of risk equation?
E(rf) = ( E(RM) - RF ) / σ.M
What is the beta equation?
beta = Cov (R.i, R.M) / σ (R.M)
In other words, it is the Covariance of the return of a security and the market portfolio divided by the variance of the return of the market portfolio
What equation do you use to work out a single securities expected rate of return?
This is the CAPM
Ri = R.F + B.i x (R.M - R.F)
risk-free rate + Beta of security x Market risk premium
Notation for options, what does S.T mean ?
Value / price of the underlying at expiry
Notation for options, what does T and E mean?
T is expiry
E is exercise price
What is the payoff equation of options?
(S.T - E)* shares owned
How do you work out the redemption yield?
r = C+V / P -1
What is the Fisher equation and what’s it used for?
1+r.nominal = (1+r.real)(1+inflation)
finding normal or real redemption yields
