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## Payoff with futures (risk profile)The gains and losses on futures are symmetrical around the difference between the spot price on expiry of the futures contract and the futures price at which the contract was purchased. A simple example may be useful (see Figure 6): one futures contract = one share of ABC Corporation Limited. On the vertical axis we have the profit or loss scale of the future. On the horizontal axis we have the price of the future at expiry (= spot price). If the long future is bought at LCC70 and the price at expiry is LCC71, the profit is LCC1, i.e. for each LCC1 increase in the price of the future, the profit is LCC1. Thus, if the spot price on maturity is LCC90, the profit is LCC20 (LCC90 - LCC70).
It will be apparent that if the spot price on maturity is SPm, and the purchase price is PP, then the payoff on a It follows that the payoff in the case of a It will also be clear that the payoff on a future is a
## Pricing of futures (fair value versus trading price)The reader should at this stage already have a good idea of the principle involved in the pricing of futures contracts. Some elaboration, however, will be useful. All or some of the following factors influences the (FVP):fair value price • Current (or "spot") price of the underlying asset. • Financing (interest) costs involved. • Cash flows (income) generated by the underlying asset. • Other costs such as storage and transport costs and insurance. The theoretical price / FVP of a future is determined according to the where: rfr = risk free rate25 (i.e. the financing cost for the period) I = income earned during the period (dividends or interest) t = days to expiry (dte) of the contract / 365 OC = other costs (which apply in the case of commodities: usually transport, insurance and storage). Thus, in the case of financial futures: FVP = SP + CC = SP + {SP x [(rfr - I) x t]} = SP x {1 + [(rfr - I) x t]}. An example may be handy. The table and graph shown earlier (Table 1 and Figure 3) are expanded to include the fair value prices (FVPs) at the end of each month26 (see Table 3 and Figure 8). Taking April 2010 as an example, we have the following: SP (index value) = 15357 rfr (assumed) = 8.0% pa I (assumed dividend yield) = 2.0% pa t = dte / 365 = 319 / 365 FVP = SP + CC = SP + {SP x [(rfr - I) x t]} = SP x {1 + [(rfr - I) x t]} = 15357 x {1 + [(0.08 - 0.02) x (319 / 365)]} = 15357 x [1 + (0.06 x 0.873973)] = 15357 x 1.052438 = 16162. As can be seen from Table 3, the March 2011 future traded (15870) at lower than its FVP (16162).
It will be apparent that in the above use was made of simple interest. In the case of FVP = SP x [1 + (rfr - I)]t Using the above example: FVP = SP x [1 + (rfr - I)]t = 15357 x 1.060.87397 = 15357 x 1.052244 = 16159. It is clear that compounding makes little difference in the case of short-term contracts. |

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