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## Individual bond futuresThe principle that underlies the fair value price of a bond future is the CCM as discussed. However, the calculation is more elaborate because of the existence of coupon payments, clean and dirty (all-in) prices, ex and cum interest and so on. The fair value price (FVP) of an individual bond future is made up of: Bond spot price (i.e. all-in price) + carry cost (i.e. rfr) - income. An example is required: LCC15729 bond future: Bond = LCC157 Maturity date = 15 September 2015 Coupon (c) =13.5% pa Coupon payment dates (cd1 & cd2) =15 March and 15 September Yield to maturity (ytm) = 8.2% Carry cost (rfr) = 7.5% pa Purchase (valuation) date of future (fvd) = 20 June Termination date of future (ftd) = 31 August30 Books (register) closes = one month before coupon dates31. As noted, the FVP of a bond future is made up of three parts: FVP = A + B - C (i.e. bond spot price + carry cost (excl income) - income 32) where A = dirty (all-in) price of underlying bond at market (current) rate on bond futures valuation date (fvd) 33 = 105.71077 (note: this price is assumed so that it does not date) B = A x {(rfr / 100) x [(ftd - fvd) / 365]} = 105.71077 x [0.075 x (72 / 365)] = 105.71077 x (0.075 x 0.19726) = 105.71077 x 0.014795 = 1.56394 C = (c / 2) x (1 + {(rfr / 100) x [(ftd - cd2) / 365)]}) [if the futures termination date crosses a books-closed date and its associated coupon date (i.e. is not ex-interest)] or = (c / 2) / (1 + {(rfr / 100) x [(cd2 - ftd) / 365)]) [if the futures termination date crosses a books closed date but not the associated coupon date (i.e. is in ex-interest period, which is the case here)] = (13.5 / 2) / (1 + {0.075 x [(cd2 - ftd) / 365]}) = 6.75 / {1 + [0.075 x (15 / 365)]} = 6.75 / [1 + (0.075 x 0.04110)] = 6.75 / 1.00308 = 6.72927. Thus: FVP = A + B - C = 105.71077 + 1.56394 - 6.72927 = 100.5454.
## Equity / share index futuresWe covered the case of equity / share index futures in our first example where the simple interest FVP = SP + CC = SP + {SP x [(rfr - I) x t]} = SP x {1 + [(rfr - I) x t]}. Here we provide another example (ALSI future): SP (spot price, i.e. index value) = 10765 rfr = 11.5% pa I (dividend yield, assumed) = 3.5% pa t (number of days to expiry of contract / 365) 245 / 365 FVP = SP + CC) = SP + {SP x [(rfr - I) x t]} = SP x {1 + [(rfr - I) x t]} = 10765 x {1 + [(0.115 - 0.035) x (245 / 365)]} = 10765 x (1 + (0.08 x 0.6712329)) = 10765 x 1.05369863 = 11343. ## Individual equity / share futuresIndividual equity / share futures are also called It is appropriate to mention a futures product which is closely allied with SSFs: the ## Commodity futuresWith commodities, where insurance and storage is payable (such as maize), and the amount is not proportional to the spot price, it is simply added to the FVP. An example follows [we assume there are only storage costs (SC); note: there is no income (I)]: Contract = WMAZ (white maize) Contract size = 100 metric tons Number of contracts = 1 Date of valuation = 31 March Expiry of contract = 21 September Days to expiry (dte) = 174 days (31 March to 21 September) t = dte / 365 = 174 / 365 rfr = 7.5% pa SP = LCC2 732.20 (per metric ton) Storage costs (SC) = 36 cents per ton per day FVP (per ton) = SP + CC = SP + [SP x (rfr x t)] + (SC x dte) = SP x [1 + (rfr x t)] + (SC x dte) = 2732.20 x [1 + (0.075 x 174 / 365)] + (0.36 x 174) = 2732.20 x 1.03575 + 62.64 = 2829.88 + 62.64 = LCC2 892.52 FVP (per contract) = 100 x 2892.52 = LCC289 252.00. ## Currency futuresCurrency futures are similar to foreign exchange forward contracts, and the where: SR = spot rate irvc = interest rate of variable currency for period to expiry irbc = interest rate for base currency for period to expiry t = number of days to expiry of contract / 365. An example is called for [base currency (i.e. the 1 unit currency) = GBP; variable currency = USD]: SR = GBP І USD 1.5 irvc = 5.5% vc irbc = S.5% pa t = 1S2 І 365 FVP = SR x {[1 + (irvc x t)] І [1 + (irbc x t)]} = USD 1.5 x {[1 + (0.055 x 1S2 І 365)] І [1 + (0.0S5 x 1S2 І 365)]} = USD 1.5 x (1.027425 І 1.0423S4) = USD 1.5 x 0.9S5649 = USD 1.47S47. It will be evident here that the formula is similar to the CCM, with the difference being that there are two rates of interest taken into account: the foreign rate and the local rate. ## Futures on other derivativesAs in the case of forwards (forwards on swaps) there are futures on other derivatives, for example futures on FRAs and futures on swaps. ## Other futuresAnother future listed on the JSE deserves mention: the The variances and standard deviations of returns on assets (like shares) change considerably from period to period. It is also a major input in the pricing of options. There is a need by some investors to hedge against this risk, and certain speculators seek exposure to this risk. These two parties make the trading of this instrument a possibility. In short, a variance future is a futures contract on realised annualised variance of returns on assets / indices. This instrument is regarded by some as a new asset class. |

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