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Hedging Strategies Using Futures. ISSUES. ASSUME. 3.1 Basic Principle. 3.2 Arguments For and Against Hedging. 3.3 Basis Risk. 3.4 Cross Hedging. 3.5 Stock Index Futures. 3.6 Rolling the Hedging Forward. ISSUES. - PowerPoint PPT Presentation
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Hedging Strategies Using Futures
ISSUES
ASSUME
3.1 Basic Principle
3.2 Arguments For and Against Hedging
3.3 Basis Risk
3.4 Cross Hedging
3.5 Stock Index Futures
3.6 Rolling the Hedging Forward
1. When is a short futures position appropriates ?
2. When is a long futures position appropriate ?
3. Which futures contract should be used ?4. What is the optimal size of the futures position for reducing risk ?
ISSUES
ASSUME
Hedge-and forget
Futures contracts as forward contracts
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2
3.1 Basic Principles-Short Hedge ( 空頭避險 )
3.1 Basic Principles-Long Hedge ( 多頭避險 )
Hedges that involve taking a long position in a futures contract are known as long hedges.
Long hedge can be used to manage an existing short position.
A long hedge is appropriate when a company knows it will have to purchase a certain assets in the future and wants to lock a price now.
3.2 Arguments For and Against Hedging• Hedging and Shareholders
Shareholders can do the hedging themselves. It assumes that shareholders have as much information about the risks faced by a company as does the company’s management. Shareholders can do far more easily than a corporation is diversify risk.
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2
3
3.2 Arguments For and Against Hedging• Hedging and Competitors
3.2 Arguments For and Against Hedging
All implications of price changes on a company’s profitability should be taken into account in the design of a hedging
strategy to protect against the price changes.
3.3 Basis Risk
The asset whose price is to be hedged may not be exactly the same as the asset underlying the futures contract. The hedger may be uncertain as to the exact when the asset will be bought or sold.
The hedge may require the futures contract to be closed out before its delivery month.
These problem gives rise to what is termed basic risk.
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3.3 Basis Risk
The basis in a hedging situation is as follows:Basis = Spot price of asset to be hedged – Futures price of contract used
An increase in the basis is referred to a .
A decrease in the basis is referred to as a
= S – F
strengthening of the basis
weakening of the basis
3.3 Basis Risk
Spot price
Futures price
t1 t2
Figure 3.1 Variation of basic over time
S1
F1
F2
S2b2
b1b1 = S1 –F1
b2 =S2– F2
Suppose thatF1 : Initial Futures PriceF2 : Final Futures PriceS2 : Final Asset Price
Long Hedge :You hedge the future purchase of an asset by entering into a long futures contractThe effective price( 有效支付價格 ) that is paid with hedge is S2 + F1 – F2 = F1 + b2Short Hedge :You hedge the future sold of an asset by entering into a short futures contractThe effective price( 有效價格 ) that is obtained for the asset with hedge is S2 + F1 – F2 = F1 + b2
basis risk( 基差風險 )
One key factor affecting basis risk is the choice of the futures contract to be used for hedging. This choice has two components:1.The choice of the assets underlying the futures contracts2.The choice of the delivery month
3.3 Basis RiskChoice of Contract
A contract with a later delivery month is usually chosen in these circumstances.
3.4 Cross Hedging Calculating the Minimum Variance Hedge Ratio ( 最小變異的避險比率 )
F
Sh*
h* : Hedge ratio that minimizes the variance of the hedger’s position. : Coefficient of correlation between ΔS and ΔF
ΔS : Change in spot price, S, during a period of time equal to the life of the hedge.ΔF : Change in future price, F, during a period of time equal to the life of the hedge.σS : Standard deviation of ΔS
σF : Standard deviation of ΔF
3.4 Cross Hedging Optimal Number of Contracts ( 最適契約數量 )
F
A
QNhN **
NA : Size of position being hedged (unit)
QF : Size of one futures contract (unit) N* : Optimal number of futures contracts for hedging
The futures contracts used should have a face value of
h* NA
3.5 Stock Index Future Hedging Using Stock Index Futures
APN *
N*: Optimal number of futures contracts for hedgingP : Current value of the portfolioA : Current value of one futures contractβ : From the capital asset pricing model to determined the appropriate hedge ratio
3.5 Stock Index Future
Value of S&P 500 index =1000S&P 500 futures price =1010Value of portfolio = $5,000,000Risk-free interest rate = 4% per annumDividend yield on index = 1% per annumBeta of portfolio = 1.5
Example
Current value of one futures contract = 250*1000 = 250,000
One future contract is for delivery of $250 times the
index
Optimal number of futures contracts for hedging
30000,250000,000,55.1*
APN
Value of index in three months : 900 950 1 ,000 1,050 1,100
Futures price of index today : 1,010 1,010 1,010 1,010 1,010
Futures price of index in three months : 902 952 1,003 1,053 1,103
Gain on futures position : 810,000 435,000 52,500 –
322,500–
697,500
Return on market : – 9.750%
– 4.750% 0.250% 5.250% 10.250%
Expected return on portfolio : –
15.125%–
7.625%–
0.125% 7.375% 14.875%
Expected portfolio value in three months(including dividends) :
4,243,750
4,618,750
4,993,750
5,368,750
5,743,750
Total expected value of position in three months :
5,053,750
5,053,750
5,046,250
5,046,250
5,046,250
3.5 Stock Index Future
The gain from the short futures position = 30* ( 1,010 – 902 ) *250 = $ 810,000
121)01.004.0(
900
e
Time to maturity
= $ 5,000,000*(1 – 0.15125) = $4,243,750
• The risk-free interest rate = 1 % per 3 months • Expected return on portfolio = 1 + 1.5*( – 9.75 – 1 ) = – 15.125 %
•The loss on the index = 10 %•The index pays a dividend of 0.25%per 3 months•An investor in the index would earn = – 9.75 % =$ 4,243,750 + $810,000
3.5 Stock Index Future Reasons for Hedging an Equity
Portfolio
A hedge using index futures removes the risk arising from market and leaves the hedger exposed only to the performance of the portfolio relative to the market.
The hedger is planning to hold a portfolio for a long period of time and requires short-term protection.
3.5 Stock Index Future Changing the Beta of a Portfolio
To reduce the beta of the portfolio to 0.75
)(15000,250000,000,5)75.05.1(*)( short
AP
To increase the beta of the portfolio to 2.0
)(10000,250000,000,5)5.12()*( long
AP
3.5 Stock Index Future
Exposure to the Price of an Individual Stock
Similar to hedging a well-diversified stock portfolio
The performance of the hedge is considerably worse, only against the risk arising from market movements
3.6 Rolling The Hedge Forward
This involves entering into a sequence of futures contracts to increase the life of a hedge
Rollover basis risk