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112 Cards in this Set

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Question
Answer
Future profit/loss (formula)
Future profit/loss = ticks x tick value x contracts
Simple Basis (formula)
Basis = Cash price - Futures price
Theoretical Basis (formula)
Theoretical Basis = Cash Price - Fair Value
Value Basis (formula)
Value Basis = Fair Value - Future
Put/Call Parity (formula - Non-dividend paying stock - ConDis)
C - P = S - K * e^(-rt)
Put/Call Parity (formula - Non-dividend paying stock - DisDis)
C - P = S - K / (1 + rt)
Put/Call Parity (formula - Dividend paying stock - ConDis)
C - P = S - D - K * e^(-rt)
Put/Call Parity (formula - Dividend paying stock - DisDis)
C - P = S - D - K / (1 + rt)
Put/Call Parity (formula - Stock Index Options - ConDis)
C - P = S * e^(-dt) - K * e^(-rt) (S = cash price of index, d = annual rate continuous dividend yield)
Put/Call Parity (formula - Stock Index Options - DisDis)
C - P = S / (1 + dt) - K / (1 + rt) (S = cash price of index)
Put/Call Parity (formula - Currency Options - ConDis)
C - P = S * e^(-ft) - K * e^(-rt) (S = spot price of currency, f = interest earned on currency)
Put/Call Parity (formula - Currency Options - DisDis)
C - P = S / (1 + ft) - K / (1 + rt) (S = spot price of currency)
Put/Call Parity (formula - Futures - premium margined)
C - P = S - K (C = call price, P = put price, S = stock price, K = exercise price)
Put/Call Parity (formula - Futures - Premium paid upfront - ConDis)
C - P = S * e^(rt) - K * e^(-rt) (S = price of the future)
Put/Call Parity (formula - Futures - Premium paid upfront - DisDis)
C - P = S / (1 + rt) - K / (1 + rt) (S = price of the future)
Long Call (Key Formulae)
MaRi: premium paid, MaRe: unlimited, BEaex: exercise price + premium.
Long Put (Key Formulae)
MaRi: premium paid, MaRe: exercise price - premium, BEaex: exercise price + premium.
Short Put (Key Formulae)
MaRi: exercise price - premium, MaRe: premium received, BEaex: exercise price - premium.
Short Call (Key Formulae)
MaRi: unlimited, MaRe: premium received, BEaex: exercise price + premium.
bull spread (Key Formulae calls)
MaRi: net initial debit, MaRe: difference between strikes - initial debt, BEaex: lower strike + initial debit.
bull spread (Key Formulae puts)
MaRi: difference between strikes - initial credit, MaRe: net initial credit, BEaex: higher strike + initial credit.
bear spread (Key Formulae calls)
MaRi: difference between strikes - initial credit, MaRe: net initial credit, BEaex: lower strike + initial credit.
bear spread (Key Formulae puts)
MaRi: net initial debit, MaRe: difference between strikes - initial debit, BEaex: higher strike price - initial debit.
synthetic long (Key Formulae)
MaRi: exercise price +/- net initial debit/credit, MaRe: unlimited, BEaex: exercise price +/- net initial debit/credit.
synthetic short (Key Formulae)
MaRi: unlimited, MaRe: exercise price -/+ net initial debit/credit, BEaex: exercise price -/+ net initial debit/credit.
synthetic long call (Key Formulae)
MaRi: initial value of stock/future - exercise price + put premium, MaRe: unlimited, BEaex: initial value of stock/future + put premium.
synthetic short call/covered put (Key Formulae)
MaRi: unlimited, MaRe: initial value of stock/future - exercise price + put premium, BEaex: initial value of stock/future + put premium.
synthetic short put/covered call (Key Formulae)
MaRi: initial value of stock/future - call premium, MaRe: exercise price - initial value stock/future + call premium, BEaex: initial value of stock/future - call premium.
synthetic long put (Key Formulae)
MaRi: exercise price - initial value of stock/future + call premium, MaRe: initial value of stock/future - call premium, BEaex: initial value of stock/future - call premium.
diagonal spread (Key Formulae)
MaRi: difference between strikes - initial credit or initial debit, MaRe: at short-dated expiry, limited, BEaex: dependent on relative movements of premium.
cylinder (Key Formulae)
MaRi: limited, cap set by put, MaRe: limited, floor set by call, BEaex: stock price +/- net initial debit/credit.
long straddle (Key Formulae)
MaRi: premiums paid, MaRe: unlimited, BEaex: upside: exercise price + both premiums, downside: exercise price - both premiums.
short straddle (Key Formulae)
MaRi: unlimited, MaRe: limited to premiums, BEaex: upside: exercise price + both premiums, downside: exercise price - both premiums.
long strangle (Key Formulae - call strike > put strike)
MaRi: limited to premiums, MaRe: unlimited, BEaex: upside: higher strike + premium, downside: lower strike - premium.
long strangle (Key Formulae - call strike < put strike)
MaRi: limited to premium - difference between strikes, MaRe: unlimited, BEaex: upside: lower strike + premiums, downside: higher strike - premiums.
short strangle (Key Formulae - call strike > put strike)
MaRi: unlimited, MaRe: premiums received, BEaex: upside: higher strike + premiums, downside: lower strike - premiums.
short strangle (Key Formulae - call strike < put strike)
MaRi: unlimited, MaRe: premiums received - difference between strikes, BEaex: upside: lower strike + premiums, downside: higher strike - premiums.
short butterfly (Key Formulae)
MaRi: difference between one set of strikes less initial credit, MaRe: net initial credit, BEaex: lower strike + credit, higher strike - credit
long butterfly (Key Formulae)
MaRi: net initial debit, MaRe: difference between one set of strikes - initial debit, BEaex: lower strike + debit, higher strike - debit.
ratio back spread (Key Formulae puts)
MaRi: difference between strikes and net initial debit, MaRe: breakeven value, BEaex: lower strike - initial debit - difference between strikes.
ratio spread (Key Formulae calls)
MaRi: unlimited, MaRe: difference between strikes + initial credit, BEaex: higher strike + maximum profit.
horizontal spread (Key Formulae)
MaRi: net initial debit, MaRe: indeterminate, subject to relative changes in premiums, BEaex: indeterminate, subject to relative changes in premiums.
conversion (Key Formulae)
MaRi: none, MaRe: extend of pricing anomaly.
reversals (Key Formulae)
MaRi: none, MaRe: extend of pricing anomaly.
box (Key Formulae)
MaRi: none, MaRe: extend of pricing anomaly.
Simple Interest (formula)
i1 = D0 * r
Terminal value simple interest (formula)
D1 = D0 * (1+r)
Terminal value simple interest nth year (formula)
Dn = D0 * (1 + n * r)
Compound Interest (formula)
in = Dn-1 * r
Terminal value compound interest (formula)
Dn = D0 * (1+ r)^n
APR (formula)
APR = (1+ r/m)^m - 1
Discount factor at Time n (formula)
DFn = 1 / (1+ r)^n, r = discount rate, n = number of years
DVM (formula)
Market value = PV of the future expected receipts discounted at the investors required rate of return.
DDM (formula)
Value of Stock = Dividend per share / (Discount Rate - Dividend growth rate)
Volatility (formula)
σ = sqrt( sum((r - ř)^2) / n)
Volatility of 2 securities (formula)
σa+b = sqrt(pa^2*σa^2 + pb^2*σb^2 + 2pa*pb*σa*σb*cor(ab)), p = proportion of funds invested in each security, cor = correlation between the returns on two securities.
Probability - idealistic (formula)
P(E) = The number of ways E can occur / Total number of equally likely outcomes
Probability - realistic (formula)
P(E) = The number of observed occurrences of E / Total number of observed occurrences
Binomial Expression (formula)
P(r) = n! / (r! * (n - r)! * p^r * (1 - p)^(n - r)
Z value (formula)
Z = (x - μ) / σ, μ = the mean, x = the observed value
Continuously compounded risk-free rate R (formula)
R = e^(r*t), r = quoted annual rate, t time period as proportion of a year.
Hedge Ratio (formula 1)
h = (Cu - Cd) / (Su - Sd), Cu = call value up, Cd = call value down, Su = share price up, Sd = share price down
Hedge Ratio (formula 2)
(hS - C) (e^rt) = hSu - Cu, (hS - C) (e^rt) = hSd - Cd
Binomial Model (formula probability upmove - equity index option)
p = (e^(rt - yt) - d) / (u - d), y = dividend yield
Hedge Ratio (formula - equity index options)
h = ((Cu - Cd) / (Su - Sd)) * e^(-yt), Cu = call value up, Cd = call value down, Su = share price up, Sd = share price down
Black Scholes (formula call)
C = S*N(d1) - X * e^(-rt) * N(d2)
Black Scholes (formula d1)
d1 = (ln(S/X) + (r + 0.5 * σ^2) * t) / (σ * sqrt(t))
Black Scholes (formula d2)
d2 = (ln(S/X) + (r - 0.5 * σ^2) * t) / (σ * sqrt(t)), or d2 = d1 - σ * sqrt(t)
Black Scholes (formula put)
P = X * e^(-rt) * N(-d2) - S * N(-d1)
Black Scholes (formula call on stock index)
C = S * e^(-dt) * N(d1) - X * e^(-rt) * N(d2)
Black Scholes (formula d1 of call on stock index)
d1 = (ln(S/X) + (r - d + 0.5 * σ^2) * t) / (σ * sqrt(t))
Black Scholes (formula call on a currency)
C = S * e^(-rft) * N(d1) - X * e^(-rdt) * N(d2), rf = the cont. Comp. Interest rate in domestic currency, rd = same for foreign currency
Black Scholes (formula d1 of call on a currency)
d1 = (ln(S/X) + (rd - rf + 0.5 * σ^2) * t) / (σ * sqrt(t))
Black Scholes (formula call on futures/forwards)
C = F * e^(-rt) * N(d1) - X * e^(-rt) * N(d2), F = the future/forward price
Black Scholes (formula d1 of call on a futures/forwards)
d1 = (ln(F/X) + (0.5 * σ^2) * t) / (σ * sqrt(t))
Black Scholes (formula call on futures/forwards, premiums immediately settled)
C = F * N(d1) - X * N(d2), F = the future/forward price
Delta (formula)
D = Change in value of option / Change in value of underlying security
Greeks on non dividend paying stock (formula)
Delta Call: N(d1), Delta Put: -N(-d1)
Greeks on dividend paying stock (formula)
Delta Call: N(d1), Delta Put: -N(-d1)
Greeks on stock index options (formula)
Delta Call: e^(-dt)*N(d1), Delta Put: -e^(dt)*N(-d1)
Greeks on currency options (formula)
Delta Call: e^(-ft)*N(d1), Delta Put: -e^(ft)*N(-d1)
Greeks on future options premium margined (formula)
Delta Call: N(d1), Delta Put: -N(-d1)
Greeks on future options premium upfront (formula)
Delta Call: e^(-rt)*N(d1), Delta Put: -e^(rt)*N(-d1)
Flat Yield (formula)
Y = Gross Coupon / Market Price
Dirty Price Gilt Market (formula cum div)
Price of Cum Div Stock: Clean Price + (Nominal value * 0.5 * Coupon) * (No. Days from the last payment day to one calendar day before settlement (inclusive) / No. Of days in interest period)
Dirty Price Gilt Market (formula ex div)
Price of Ex-Div Stock: Clean Price + (Nominal value * 0.5 * Coupon) * (No. Days from the settlement day to the calendar day before settlement (inclusive) / No. Of days in interest period)
Fair Value (formula)
Fair Value = Cash price + Cost of carry
Fair Value (bond future formula)
Fair Value = Dirty price of bond + Cost of financing over holding period - Interest received over holding period and accrued to delivery
Invoice amount (formula)
Invoice Amount = Price of future * Price Factor + Accrued Interest
Invoice amount bond future (formula)
Bond Future = EDSP * Price factor * Scaling factor * No. Of contracts + Accrued Interest
Fair Value (bond future formula)
Fair Value = Futures Price * Price Factor
Basis (bond future formula)
Gross Basis = Cash price - (Futures Price * Price Factor)
Zero Gross Basis Future Price (formula)
Zero Gross Basis Future Price = Bond Price / Price Factor
Value Basis of Bond Future (formula)
Price of CTD * (Actual repo rate - Implied repo rate * Days / 360 or 365)
Futures Price CTD (formula)
Futures Price = (Price of deliverable bond + Finance cost - Bond Income) / Price Factor
Theoretical Futures Price CTD (formula)
Fair Price = (Dirty Price + (Dirty Price * Finance Rate * Days in the holding period / 365) - Interest paid and accrued) / Price Factor
Implied Repo Rate (formula)
Implied Repo Rate = ( Invoice amount - Initial cost ) / ( Initial cost * Days in holding period / 365 )
Implied Repo Rate - interest payment in holding period (formula)
Implied Repo Rate = ( Invoice amount - Initial cost - Interest received ) / ( Initial cost * Days in holding period / 365 )
Implied Repo Rate - dividend received (formula)
Implied Repo Rate = ( Invoice amount - Initial cost - Interest received ) / ( ( Initial cost * Days in holding period / 365 ) - ( Interest received * Days between receipt of interest and delivery date of future ) / 365 )
Hedging CTD (formula)
Number of contracts = ( Nominal value of CTD / Face Value of future ) * Price Factor of CTD
BPV (formula)
BPV = Modified duration * Dirty Price of Bond * 0.01 / 100
Hedging Non-CTD (formula)
Number of contracts = ( Nominal Value of Portfolio / Nominal Value of future ) * Price factor of CTD * ( BPV hedge bond / BPV CTD )
Hedging Non-CTD (formula better)
Number of contracts = ( Nominal value of hedge bind / Nominal value of future ) * Price factor of CTD * ( MD bond / MD CTD ) * ( Dirty price of bond / Dirty price of CTD )
Hedging Non-CTD (formula using GRY)
Number of contracts = ( Nominal value of hedge bond / Nominal value of future ) * ( Price factor of CTD / Price of CTD ) * ( Duration bond / Duration CTD ) * ( 1 + GRY of CTD ) / ( 1 + GRY of hedge bond ) )
Interest Rate Parity (formula)
Forward Rate = ( 1 + rd) / ( 1 + rf ) * Spot Rate, rd = domestic exchange rate, rf = foreign exchange rate
Hedging with futures (formula)
σ total ^2 = σu^2 + σs^2
Weighted average portfolio (formula)
( Holding_1 * Price_1 * Beta_1 + ... + Holding_n * Price_n * Beta_n ) / (Holding_1 * Price_1 + ... + Holding_n * Price_n )
Calculate number of futures (formula)
Value of Portfolio / (Future * Tick value ) * Portfolio Beta, rounding up
Hedging with stock options (formula)
No. of Puts = No. Of shares held / No. Of shares per contract
Hedging with stock options (formula better)
No. of Puts = ( No. Of shares held / Contract size ) * ( 1 / Option delta )
settlement amount (FRA - formula)
((reference rate - contract rate) * contract period/day basis * contract amount) / ( 1 + reference rate * contract period/day basis))