Formulae Flashcards by Archie Henn

What is the equation for FV if simple r is used?

FV.1 = (1+r)P0

11,200 = (1+0.12)x 10,000

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What is the FV equation when compounding r is used?

FVt = P0 (1+r),t

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What is the PV equation?

PV0 = discount factor x P.t

remember discount factor equation is DFt = 1/ (1+r),t

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What is the discount factor equation?

DF1 = 1/ (1+r),t

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What is the equation for the PV of a perpetuity?

PV0 (perp) = C / r

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What is the equation to find the PV of an annuity?

PV = C / r [ 1 - 1/(1+r),t ]

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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

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What is the expanded PV of an annuity equation when derived from perpetuities?

C/r - C/r* 1/(1+r),t

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What is the EAR equation?

EAR = (1+APR/m),m - 1

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In bonds, What is denoted by P?

Price of a bond before maturity

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What is denoted by V?

The face/ par/ principle value of the bond paid by the issuer

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What is denoted by c?

Coupon rate

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In bonds, what is denoted by C?

Coupon

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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

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What equation do you use to compute bond returns?

rate of return = (coupon income + price change) / investment

aka

R = (C1 + P1-P0) / P0

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How do you compute the interest yield (IR) of a bond?

IR%= C / P0

Coupon / the clean price

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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

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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?

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?

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