futures and forwards chapter 23 © 2008 the mcgraw-hill companies, inc., all rights reserved....
TRANSCRIPT
Futures and Futures and ForwardsForwards
Chapter 23
© 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.McGraw-Hill/Irwin
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Overview
Derivative securities have become increasingly important as FIs seek methods to hedge risk exposures. The growth of derivative usage is not without controversy since misuse can increase risk. This chapter explores the role of futures and forwards in risk management.
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Futures and Forwards
Second largest group of interest rate derivatives in terms of notional value and largest group of FX derivatives. Swaps are the largest.
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Derivatives
Rapid growth of derivatives use has been controversial Orange County, California Bankers Trust Allfirst Bank (Allied Irish)
As of 2000, FASB requires that derivatives be marked to market Transparency of losses and gains on financial
statements
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Spot and Forward Contracts
Spot Contract Agreement at t=0 for immediate delivery and
immediate payment. Forward Contract
Agreement to exchange an asset at a specified future date for a price which is set at t=0.
Counterparty risk
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Futures Contracts
Futures Contract similar to a forward contract except: Marked to market Exchange traded
Rapid growth of off market trading systems Standardized contracts
Smaller denomination than forward Lower default risk than forward contracts.
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Hedging Interest Rate Risk
Example: 20-year $1 million face value bond. Current price = $970,000. Interest rates expected to increase from 8% to 10% over next 3 months.
From duration model, change in bond value:
P/P = -D R/(1+R)
P/ $970,000 = -9 [.02/1.08]
P = -$161,666.67
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Example continued: Naive hedge
Hedged by selling 3 months forward at forward price of $970,000.
Suppose interest rate rises from 8%to 10%.
$970,000 - $808,333 =$161,667
(forward (spot price
price) at t=3 months) Exactly offsets the on-balance-sheet loss. Immunized.
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Hedging with futures
Futures more commonly used than forwards. Microhedging
Individual assets. Macrohedging
Hedging entire duration gap Found more effective and generally lower cost.
Basis risk Exact matching is uncommon Standardized delivery dates of futures reduces
likelihood of exact matching.
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Routine versus Selective Hedging
Routine hedging: reduces interest rate risk to lowest possible level.
Low risk - low return. Selective hedging: manager may selectively
hedge based on expectations of future interest rates and risk preferences.
Partially hedge duration gap or individual assets or liabilities
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Macrohedging with Futures
Number of futures contracts depends on interest rate exposure and risk-return tradeoff.
E = -[DA - kDL] × A × [R/(1+R)]
Suppose: DA = 5 years, DL = 3 years and interest rate expected to rise from 10% to 11%. A = $100 million.
E = -(5 - (.9)(3)) $100 (.01/1.1) = -$2.091 million.
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Risk-Minimizing Futures Position
Sensitivity of the futures contract:
F/F = -DF [R/(1+R)]
Or,
F = -DF × [R/(1+R)] × F and
F = NF × PF
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Risk-Minimizing Futures Position
Fully hedged requires
F = E
DF(NF × PF) = (DA - kDL) × A
Number of futures to sell:
NF = (DA- kDL)A/(DF × PF)
Perfect hedge may be impossible since number of contracts must be rounded down.
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Futures Price Quotes
T-bond futures contract: $100,000 face value
T-bill futures contract: $1,000,000 face value quote is price per $100 of face value Example: 112 23/32 for T-bond indicates
purchase price of $112,718.75 per contract Delivery options
Conversion factors used to compute invoice price if bond other than the benchmark bond delivered
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Basis Risk
Spot and futures prices are not perfectly correlated.
We assumed in our example that
R/(1+R) = RF/(1+RF) Basis risk remains when this condition does
not hold. Adjusting for basis risk,
NF = (DA- kDL)A/(DF × PF × br) where
br = [RF/(1+RF)]/ [R/(1+R)]
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Hedging FX Risk
Hedging of FX exposure parallels hedging of interest rate risk.
If spot and futures prices are not perfectly correlated, then basis risk remains.
Tailing the hedge Interest income effects of marking to market
allows hedger to reduce number of futures contracts that must be sold to hedge
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Basis Risk
In order to adjust for basis risk, we require the hedge ratio,
h = St/ft
Nf = (Long asset position × estimate of h)/(size of one contract).
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Estimating the Hedge Ratio
The hedge ratio may be estimated using ordinary least squares regression:
St = + ft + ut
The hedge ratio, h will be equal to the coefficient . The R2 from the regression reveals the effectiveness of the hedge.
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Hedging Credit Risk
More FIs fail due to credit-risk exposures than to either interest-rate or FX exposures.
In recent years, development of derivatives for hedging credit risk has accelerated. Credit forwards, credit options and credit swaps.
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Credit Forwards
Credit forwards hedge against decline in credit quality of borrower. Common buyers are insurance companies. Common sellers are banks. Specifies a credit spread on a benchmark bond
issued by a borrower. Example: BBB bond at time of origination may have
2% spread over U.S. Treasury of same maturity.
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Credit Forwards
CSF defines agreed forward credit spread at time contract written
CST = actual credit spread at maturity of forward
Credit Spread Credit Spread Credit Spread
at End Seller Buyer
CST> CSF Receives Pays
(CST - CSF)MD(A) (CST -C SF)MD(A)
CSF>CST Pays Receives
(CSF - CST)MD(A) (CSF - CST)MD(A)
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Futures and Catastrophe Risk
CBOT introduced futures and options for catastrophe insurance. Contract volume is rising. Catastrophe futures to allow PC insurers to
hedge against extreme losses such as hurricanes.
Payoff linked to loss ratio (insured losses to premiums)
Example: Payoff = contract size × realized loss ratio – contract size × contracted futures loss ratio. $25,000 × 1.5 - $25,000 – 0.8 = $17,500 per contract.
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Regulatory Policy
Three levels of regulation: Permissible activities Supervisory oversight of permissible activities Overall integrity and compliance
Functional regulators SEC and CFTC
As of 2000, derivative positions must be marked-to-market.
Exchange traded futures not subject to capital requirements: OTC forwards potentially subject to capital requirements
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Regulatory Policy for Banks
Federal Reserve, FDIC and OCC require banks Establish internal guidelines regarding hedging. Establish trading limits. Disclose large contract positions that materially
affect bank risk to shareholders and outside investors.
Discourage speculation and encourage hedging Allfirst/Allied Irish: Existing (and apparently
inadequate) policies were circumvented via fraud and deceit.