ICMF478_Risk Management_Module 2_Financial Instruments and R
时间：2026-01-27
risk management
ICMF478 Risk ManagementModule 2 Financial Instruments for Risk Management
Dr. Jun Jiang icjun@mahidol.ac.th Copyright© Mahidol University
risk management
Section 1 Mechanics of Futures MarketsAvailable on a wide range of underlyings Exchange traded Specifications need to be defined:What can be delivered, Where it can be delivered,& When it can be delivered
Settled daily2
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MarginsA margin is cash or marketable securities deposited by an investor with his or her broker The balance in the margin account is adjusted to reflect daily settlement Margins minimize the possibility of a loss through a default on a contract3
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ExampleAn investor takes a long position in 2 December gold futures contracts on June 5contract size is 100 oz. futures price is US$400 margin requirement is US$2,000/contract (US$4,000 in total) maintenance margin is US$1,500/contract (US$3,000 in total)
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A Possible OutcomeFutures Price (US$) 400.00 5-Jun 397.00 . . . . . . 13-Jun 393.30 . . . . . . 19-Jun 387.00 . . . . . . 26-Jun 392.30 (600) . . . (420) . . . (1,140) . . . 260 (600) . . . (1,340) . . . (2,600) . . . (1,540) Daily Gain (Loss) (US$) Cumulative Gain (Loss) (US$) Margin Account Margin Balance Call (US$) (US$) 4,000 3,400 . . . 0 . . .
Day
2,660+ 1,340= 4,000 . . . . .< 3,000 2,740+ 1,260= 4,000 . . . . . . 5,060 05
They are settled daily Closing out a futures position involves entering into an offsetting trade Most contracts are closed out before maturity
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Forward Contracts vs Futures ContractsFORWARDS Private contract between 2 parties Non-standard contract Usually 1 specified delivery date Settled at end of contract Delivery or final cash settlement usually occursSome credit risk
FUTURES Exchange traded Standard contract Range of delivery dates Settled daily Contract usually closed out prior to maturityVirtually no credit risk6
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Section 2 Hedging Strategies Using FuturesLong& Short HedgesA long futures hedge is appropriate when you know you will purchase an asset in the future and want to lock in the price A short futures hedge is appropriate when you know you will sell an asset in the future& want to lock in the priceCompanies should focus on the main business they are in and take steps to minimize risks arising from interest rates, exchange rates, and other market variables7
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Convergence of Futures to Spot (Hedge initiated at time t1 and closed out at time t2)
Futures Price
Spot PriceTime t1 t28
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Basis Risk
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2 Examples
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Choice of ContractChoose a delivery month that is as close as possible to, but later than, the end of the life of the hedge When there is no futures contract on the asset being hedged, choose the contract whose futures price is most highly correlated with the asset price. This is known as cross hedging.14
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Cross HedgingHedge Ratio: the ratio of the size of the position taken in futures contracts to the size of exposureProportion of the exposure that should optimally be hedged is
σS h*
=ρσ Fwhere sS is the standard deviation of DS, the change in the spot price during the hedging period, sF is the standard deviation of DF, the change in the futures price during the hedging period r is the coefficient of correlation between DS and DF.15
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