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CMFAS Exams

Appendix D — Formulae sheet (consolidated)

Futures

Section titled “Futures”

F0,t=S0(1+C0,t)F_{0,t} = S_0(1 + C_{0,t})

P=100(1−R)P = 100(1 - R) for short-rate futures.

(1+d1r1360)(1+d2r2360)=(1+DR360)\left(1 + \frac{d_1 r_1}{360}\right)\left(1 + \frac{d_2 r_2}{360}\right) = \left(1 + \frac{DR}{360}\right) for long-rate futures.

F=S×1+Rc(n/360)1+Rb(n/360)F = S \times \frac{1 + R_c(n/360)}{1 + R_b(n/360)} for interest-rate parity.

F=S[1+r(t/360)]−DF = S\left[1 + r(t/360)\right] - D for equity-index futures.

target hedge rate=futures rate+target-rate basis\text{target hedge rate} = \text{futures rate} + \text{target-rate basis}

Vt=St+(F−Ft)=F+(St−Ft)V_t = S_t + (F - F_t) = F + (S_t - F_t)

bond hedge ratio=PVBP(hedged security)PVBP(CTD)×conversion factor\text{bond hedge ratio} = \frac{\text{PVBP(hedged security)}}{\text{PVBP(CTD)}} \times \text{conversion factor}

h=ΔSΔFh = \frac{\Delta S}{\Delta F}; contracts for a delta-neutral loan =−h×loan valuecontract size= \frac{-h \times \text{loan value}}{\text{contract size}}

N=VPF×T×βN = \frac{VP}{F \times T} \times \beta for equity futures hedging.

Options

Section titled “Options”

option price=intrinsic value+time value\text{option price} = \text{intrinsic value} + \text{time value}

call IV=max⁡(0,S−X)\text{call IV} = \max(0, S - X); put IV=max⁡(0,X−S)\text{put IV} = \max(0, X - S)

C+PV(X)=P+SC + \text{PV}(X) = P + S

delta=change in option pricechange in underlying\text{delta} = \frac{\text{change in option price}}{\text{change in underlying}}; gamma=change in deltachange in underlying\text{gamma} = \frac{\text{change in delta}}{\text{change in underlying}}

Warrants and CBBCs

Section titled “Warrants and CBBCs”

gearing=share pricewarrant price×n\text{gearing} = \frac{\text{share price}}{\text{warrant price} \times n}; effective gearing=delta×gearing\text{effective gearing} = \text{delta} \times \text{gearing}

call IV=max⁡[0,(S−X)/n]\text{call IV} = \max[0, (S - X)/n]; put IV=max⁡[0,(X−S)/n]\text{put IV} = \max[0, (X - S)/n]

call conversion price=X+nWP\text{call conversion price} = X + nWP; put conversion price=X−nWP\text{put conversion price} = X - nWP

call cash settlement=(S−X)/n\text{call cash settlement} = (S - X)/n; put cash settlement=(X−S)/n\text{put cash settlement} = (X - S)/n

bull CBBC=(underlying−strike)+financial costconversion ratio\text{bull CBBC} = \frac{(\text{underlying} - \text{strike}) + \text{financial cost}}{\text{conversion ratio}}

bear CBBC=(strike−underlying)+financial costconversion ratio\text{bear CBBC} = \frac{(\text{strike} - \text{underlying}) + \text{financial cost}}{\text{conversion ratio}}

R-CBBC residual: bull (settlement−strike)/n(\text{settlement} - \text{strike})/n; bear (strike−settlement)/n(\text{strike} - \text{settlement})/n; N-CBBC residual is zero at MCE.

Structured products

Section titled “Structured products”

CPPI cushion=portfolio−floor\text{CPPI cushion} = \text{portfolio} - \text{floor}; multiplier=1/crash size\text{multiplier} = 1/\text{crash size}; risky=M×cushion\text{risky} = M \times \text{cushion}; risk-free=portfolio−risky\text{risk-free} = \text{portfolio} - \text{risky}

RAN payout=P1nN+P2N−nN\text{RAN payout} = P_1\frac{n}{N} + P_2\frac{N - n}{N}

inverse floater coupon=max⁡[X%−leverage×floating index, minimum coupon]\text{inverse floater coupon} = \max\left[X\% - \text{leverage} \times \text{floating index},\ \text{minimum coupon}\right]

participation rate=discount sumcall premium\text{participation rate} = \frac{\text{discount sum}}{\text{call premium}} under the structured-product convention.