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ch10_PowerPoint_Lecture_Tools_PowerPoint_Images.pptChance/Brooks
An Introduction to Derivatives and Risk Management, 10th ed.
Chapter 10: Forward and Futures Hedging, Spread, and Target Strategies
The beauty of finance and speculation was that they could be different things to different men. To some: poetry or high drama; to others, physics, scientific and immutable; to still others, politics or philosophy. And to still others, war.
Michael M. Thomas
Hanover Place, 1990, p. 37
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Important Concepts in Chapter 10
- Why firms hedge
- Hedging concepts
- Factors involved when constructing a hedge
- Hedge ratios
- Examples of foreign currency hedges, intermediate- and long-term interest rate hedges, and stock index futures hedges
- Examples of spread and target strategies
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Why Hedge?
- The value of the firm may not be independent of financial decisions because
- Shareholders might be unaware of the firm’s risks.
- Shareholders might not be able to identify the correct number of futures contracts necessary to hedge.
- Shareholders might have higher transaction costs of hedging than the firm.
- There may be tax advantages to a firm hedging.
- Hedging reduces bankruptcy costs.
- Managers may be reducing their own risk.
- Hedging may send a positive signal to creditors.
- Dealers hedge their market-making activities in derivatives.
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An Introduction to Derivatives and Risk Management, 10th ed.
Why Hedge? (continued)
- Reasons not to hedge
- Hedging can give a misleading impression of the amount of risk reduced
- Hedging eliminates the opportunity to take advantage of favorable market conditions
- There is no such thing as a hedge. Any hedge is an act of taking a position that an adverse market movement will occur. This, itself, is a form of speculation.
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Hedging Concepts
- Short Hedge and Long Hedge
- Short (long) hedge implies a short (long) position in futures
- Short hedges can occur because the hedger owns an asset and plans to sell it later.
- Long hedges can occur because the hedger plans to purchase an asset later.
- An anticipatory hedge is a hedge of a transaction that is expected to occur in the future.
- See Table 10.1 for hedging situations.
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An Introduction to Derivatives and Risk Management, 10th ed.
Hedging Concepts (continued)
- The Basis
- Basis = spot price – futures price.
- Hedging and the Basis
- P (short hedge) = ST – S0 (from spot market)
– (fT – f0) (from futures market) - P (long hedge) = –ST + S0 (from spot market)
+ (fT – f0) (from futures market) - If hedge is closed prior to expiration,
P (short hedge) = St – S0 – (ft – f0)
- If hedge is held to expiration, St = ST = fT = ft.
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An Introduction to Derivatives and Risk Management, 10th ed.
Hedging Concepts (continued)
- The Basis (continued)
- Hedging and the Basis (continued)
- Example: Buy asset for $100, sell futures for $103. Hold until expiration. Sell asset for $97, close futures at $97. Or deliver asset and receive $103. Make $3 for sure.
- Basis definition
- initial basis: b0 = S0 – f0
- basis at time t: bt = St – ft
- basis at expiration: bT = ST – fT = 0
- For a position closed at t:
- P (short hedge) = St – ft – (S0 – f0) = –b0 + bt
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An Introduction to Derivatives and Risk Management, 10th ed.
Hedging Concepts (continued)
- The Basis (continued)
- This is the change in the basis and illustrates the principle of basis risk.
- Hedging attempts to lock in the future price of an asset today, which will be f0 + (St – ft).
- A perfect hedge is practically non-existent.
- Short hedges benefit from a strengthening basis.
- All of this reverses for a long hedge.
- See Table 10.2 for hedging profitability and the basis.
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An Introduction to Derivatives and Risk Management, 10th ed.
Hedging Concepts (continued)
- The Basis (continued)
- Example: March 30. Spot gold $1,387.15. June futures $1,388.60. Buy spot, sell futures. Note:
b0 = 1,387.15 − 1,388.60 = −1.45. If held to expiration, profit should be change in basis or 1.45. - At expiration, let ST = $1,408.50. Sell gold in spot for $1,408.50, a profit of 21.35. Buy back futures at $1,408.50, a profit of −19.90. Net gain =1.45 or $145 on 100 oz. of gold.
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An Introduction to Derivatives and Risk Management, 10th ed.
Hedging Concepts (continued)
- The Basis (continued)
- Example: (continued)
- Instead, close out prior to expiration when
St = $1,377.52 and ft = $1,378.63. - Profit on spot = −9.63. Profit on futures = 9.97.
- Net gain = 0.34 or $34 on 100 oz.
- Note that change in basis was bt − b0 or
−1.11 − (−1.45) = 0.34. - Behavior of the basis, see Figure 10.1.
- In forward markets, the hedge is customized so there is no basis risk.
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An Introduction to Derivatives and Risk Management, 10th ed.
Hedging Concepts (continued)
- Some Risks of Hedging
- cross hedging
- spot and futures prices occasionally move opposite
- quantity risk
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Hedging Concepts (continued)
- Contract Choice
- Which futures underlying asset?
- High correlation with spot
- Favorably priced
- Which expiration?
- The futures with maturity closest to but after the hedge termination date subject to the suggestion not to be in a contract in its expiration month
- See Table 10.3 for example of recommended contracts for T-bond hedge
- Concept of rolling the hedge forward
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An Introduction to Derivatives and Risk Management, 10th ed.
Hedging Concepts (continued)
- Contract Choice (continued)
- Long or short?
- A critical decision! No room for mistakes.
- Three methods to answer the question.
See Table 10.4.
worst case scenario method
current spot position method
anticipated future spot transaction method
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An Introduction to Derivatives and Risk Management, 10th ed.
Hedging Concepts (continued)
- Margin Requirements and Marking to Market
- low margin requirements on futures, but
- cash will be required for margin calls
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An Introduction to Derivatives and Risk Management, 10th ed.
Determination of the Hedge Ratio
- Hedge ratio: The number of futures contracts to hedge a particular exposure
- Naïve hedge ratio
- Appropriate hedge ratio should be
- Nf = −DS/Df
- Note that this ratio must be estimated.
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An Introduction to Derivatives and Risk Management, 10th ed.
Determination of the Hedge Ratio (continued)
- Minimum Variance Hedge Ratio
- Profit from short hedge:
- P = DS + DfNf
- Variance of profit from short hedge:
- sP2 = sDS2 + sDf2Nf2 + 2sDSDfNf
- The optimal (variance minimizing) hedge ratio is
- Nf = −sDSDf/sDf2
- This is the beta from a regression of spot price change on futures price change.
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An Introduction to Derivatives and Risk Management, 10th ed.
Determination of the Hedge Ratio (continued)
- Minimum Variance Hedge Ratio (continued)
- Hedging effectiveness is
- e* = (risk of unhedged position − risk of hedged position)/risk of unhedged position
- This is coefficient of determination from regression.
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Determination of the Hedge Ratio (continued)
- Price Sensitivity Hedge Ratio
- This applies to hedges of interest sensitive securities.
- First we introduce the concept of duration. We start with a bond priced at B:
- where CPt is the cash payment at time t and yB is the yield, or discount rate.
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An Introduction to Derivatives and Risk Management, 10th ed.
Determination of the Hedge Ratio (continued)
- Price Sensitivity Hedge Ratio (continuation)
- An approximation to the change in price for a yield change is
- with DURB being the bond’s duration, which is a weighted-average of the times to each cash payment date on the bond, and represents the change in the bond price or yield.
- Duration has many weaknesses but is widely used as a measure of the sensitivity of a bond’s price to its yield.
- Modified duration (MD) measures the bond percentage price change for a given change in yield.
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An Introduction to Derivatives and Risk Management, 10th ed.
Determination of the Hedge Ratio (continued)
- Price Sensitivity Hedge Ratio (continuation)
- The hedge ratio is as follows:
- Where MDB » −(DB/B) /DyB and
MDf » −(Df/f) /Dyf - Note the concepts of implied yield and implied duration of a futures. Also, technically, the hedge ratio will change continuously like an option’s delta and, like delta, it will not capture the risk of large moves.
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An Introduction to Derivatives and Risk Management, 10th ed.
Determination of the Hedge Ratio (continued)
- Price Sensitivity Hedge Ratio (continued)
- Alternatively,
- Nf = −(Yield beta)PVBPB/PVBPf
where Yield beta is the beta from a regression of spot bond yield on futures yield and
PVBPB, PVBPf is the present value of a basis point change in the bond and futures prices.
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An Introduction to Derivatives and Risk Management, 10th ed.
Determination of the Hedge Ratio (continued)
- Stock Index Futures Hedging
- Appropriate hedge ratio is
- Nf = −(bS/bf)(S/f)
- where bS is the beta from the CAPM and bf is the beta of the futures, often assumed to be 1.
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An Introduction to Derivatives and Risk Management, 10th ed.
Hedging Strategies
- Long Hedge With Foreign Currency Futures
- American firm planning to buy foreign inventory and will pay in foreign currency.
- See Table 10.5.
- Short Hedge With Foreign Currency Forwards
- British subsidiary of American firm will convert pounds to dollars.
- See Table 10.6.
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An Introduction to Derivatives and Risk Management, 10th ed.
Hedging Strategies (continued)
- Intermediate and Long-Term Interest Rate Hedges
- First let us look at the CBOT T-note and bond contracts
- T-bonds: must be a T-bond with at least 15 years to maturity or first call date
- T-note: three contracts (2-, 5-, and 10-year)
- A bond of any coupon can be delivered but the standard is a 6% coupon. Adjustments, explained in Chapter 9, are made to reflect other coupons.
- Price is quoted in units and 32nds, relative to $100 par, e.g., 93 14/32 is $93.4375.
- Contract size is $100,000 face value so price is $93,437.50
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An Introduction to Derivatives and Risk Management, 10th ed.
Hedging Strategies (continued)
- Intermediate and Long-Term Interest Rate Hedges (continued)
- Hedging a Long Position in a Government Bond
- See Table 10.7 for example.
- Anticipatory Hedge of a Future Purchase of a Treasury Note
- See Table 10.8 for example.
- Hedging a Corporate Bond Issue
- See Table 10.9 for example.
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Hedging Strategies (continued)
- Stock Market Hedges
- First look at the contracts
- We primarily shall use the S&P 500 futures. Its price is determined by multiplying the quoted price by $250, e.g., if the futures is at 1300, the price is 1300($250) = $325,000
- Stock Portfolio Hedge
- See Table 10.10 for example.
- Anticipatory Hedge of a Takeover
- See Table 10.11 for example.
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Spread Strategies
- Intramarket Spreads
- Based on changes in the difference in carry costs
- See Figure 10.2 for illustration.
- Treasury Bond Futures Spreads
- See Figure 10.3 and Figure 10.4 for illustration the relationship between changes in spreads and interest rates.
- See Table 10.12 for calculation of Tbond futures spread profits.
- See Figure 10.5 for illustration of stock index spreads
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Intermarket Spread Strategies
- Intermarket spread strategies involve two futures contracts on different underlying instruments
- Intermarket spread strategies tend to be more risky than intramarket spreads because there is both the change in spreads and the change in underlying instruments
- NOB denotes notes over bonds
- Intermarket spread strategies could also involve various equity markets
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An Introduction to Derivatives and Risk Management, 10th ed.
Target Strategies: Bonds
- Target Duration with Bond Futures
- Number of futures needed to change modified duration
- Goal is to move the modified duration from its current value to a new target value
- See Table 10.13 for illustration.
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An Introduction to Derivatives and Risk Management, 10th ed.
Target Strategies: Equities
- Alpha Capture
- Number of futures to hedge systematic risk
- Goal is to move the eliminate systematic risk
- See Table 10.14 for illustration.
- Target Beta (see Table 10.15 for illustration.)
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An Introduction to Derivatives and Risk Management, 10th ed.
Target Strategies: Equities (continued)
- Tactical Asset Allocation
- Strategic asset allocation – long run target weights for each asset class
- Tactical asset allocation – short run deviations in weights for each asset class
- See Table 10.16 for illustration.
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Summary
- Table 10.17 recaps the types of hedge situations, the nature of the risk and how to hedge the risk
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N
f
B
T
*
f
÷
ø
ö
ç
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æ
b
-
=
f
S
N
S
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f
(
)
÷
ø
ö
ç
è
æ
b
-
b
-
=
f
S
N
S
T
*
f
