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

1

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.

1

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.

1

2

3

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