Week 2 Chapter 3 Lecture Slides (1).ppt

Chapter 3

Hedging strategies using futures

PowerPoint to accompany:

Basic principles

• Hedgers:

• Use futures market to reduce risk

• Take short futures position or long futures position

• Choose which futures contract should be used

• Decide the optimal size of the futures position

2 Copyright ©2014 Pearson Australia (a division of Pearson Australia Group Pty Ltd) –9781442532793/Hull Et Al/Fundamentals of Futures and Options Markets Australian/1e

Long and short hedges

• A 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 and want to lock in the price


Short hedge example

It is 15 October. An Australian wheat farmer wants to sell 1 million metric tonnes of Western Australian wheat in January. The futures price for January delivery on the ASX is AUD 275 per metric tonne.

• How can the farmer hedge his exposure?

• What is the gain/loss on the futures contract if the spot price of wheat on 19 January is:

• AUD 270 per metric tonne?

• AUD 285 per metric tonne?


Short hedge example (cont.)

• The farmer can hedge with the following transactions:

• 15 October: Short 50,000 January futures contracts on Western Australian wheat

• 19 January: Close out futures position

• Futures price on 19 January should be very close to the spot price

• If the spot price is AUD 270

Gains = AUD 275 – AUD 270 = AUD 5 per contract


Losses = AUD 285 – AUD 275 = AUD 10 per contract


Long hedge example

It is 15 October. A clothing manufacturer requires 100,000 kilograms of greasy wool on 16 December to meet a certain contract. The December futures price is AUD 200 per kilogram.

• How can the manufacturer hedge his exposure?

• What is the gain/loss on the futures contract if the spot price of wheat on 16 December is:

• AUD 205 per kilogram?

• AUD 195 per kilogram?


Long hedge example (cont.)

• The manufacturer can hedge with the following transactions:

• 15 October: Long position in 40 December futures contracts on greasy wool

• 16 December: Close out the position

• Futures price on 19 January should be very close to the spot price


Gains = 100,000 (AUD 205 – AUD 200) = AUD 500,000


Losses = 100,000 (AUD 200 – AUD 195) = AUD 500,000


Argument in favour of hedging

• Companies should focus on the main business they are in and take steps to minimise risks arising from interest rates, exchange rates and other market variables


Arguments against hedging

• Shareholders are usually well-diversified and can make their own hedging decisions

• It may increase risk to hedge when competitors do not

• Explaining a situation where there is a loss on the hedge and a gain on the underlying asset can be difficult


Basis risk

• Basis is the difference between spot and futures

• Basis risk arises because of the uncertainty about the basis when the hedge is closed out


Basis risk

Variation of basis over time

Figure 3.1, page 55


Short hedge and long hedge

• Suppose that:

S1: spot price at time t1

S2: spot price at time t2

F1: futures price at time t1

F2: futures price at time t2

b1: basis at time t1; b1 = S1 – F1

b2: basis at time t2; b2 = S2 – F2


Long hedge and short hedge

• You hedge the future sale of an asset by entering into a short futures contract

• You hedge the future purchase of an asset by entering into a long futures contract


Price realised = S2 + (F1 – F2) = F1 + b2

Cost of asset = S2 – (F2 – F1) = F1 + b2

Choice of contract

• Choose 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


Basis risk in a short hedge

It is 1 September. An Australian wool farmer expects to sell 100,000 kilograms of greasy wool on 25 September. The October futures price for greasy wool is currently AUD 220 per kilogram.

•What hedging strategy should the farmer follow?

•If the spot and futures prices are AUD 205 and AUD 210 per kilogram respectively:

• What is the basis?

• What is the gain/loss on futures?

• What is the net price of greasy wool after hedging?


Basis risk in a long hedge

It is 1 November. An Australian clothing manufacturer needs to purchase 100,000 kilograms of greasy wool on 18 November. The December futures price is currently AUD 215 per kilogram.

• What hedging strategy should the manufacturer follow?

• If the spot and futures prices are AUD 225 and AUD 220 per kilogram respectively:

• What is the basis?

• What is the gain/loss on futures?

• What is the net price of greasy wool after hedging?


Cross hedging

• Assets are different (jet fuel vs. heating oil)

• The hedge ratio is the ratio of the size of the position taken in futures contracts to the size of the exposure

• Cross hedging is setting the hedge ratio to minimise the variance of the value of the hedged position


Optimal hedge ratio

Proportion of the exposure that should optimally be hedged is:

where:

h*: the optimal hedge ratio

S: the standard deviation of S , change in the spot price during the hedging period

F: the standard deviation of F, change in the futures price during the hedging period

: the coefficient of correlation between S and F


ℎ∗= 𝜌𝜎𝑆𝜎𝐹

Optimal number of contracts

Optimal number of contracts:

where:

N*: the optimal number of futures contracts for hedging


QA: the size of position being hedged (units)

QF: the size of one futures contract (units)


𝑁∗= ℎ∗𝑄𝐴𝑄𝐹

Tailing the hedge

• Tailing the hedge incorporates an adjustment for the daily settlement of futures

• Optimal number of contracts:

where:

N*: the optimal number of futures contracts for hedging


VA: the dollar value of the position being hedged

VF: the dollar value of one futures contract (the futures price times the size of futures contract)


𝑁∗= ℎ∗𝑉𝐴𝑉𝐹

Hedging using index futures

To hedge the risk in a portfolio the number of contracts that should be shorted is:

where:

β: the beta of the portfolio

VA: the current value of the portfolio

VF: the current value of one futures contract


𝑁∗= 𝛽𝑉𝐴𝑉𝐹

Reasons for hedging an equity portfolio

• Desire to hedge systematic risk

• Desire to be out of the market for a short period of time

• Hedging may be cheaper than selling the portfolio and buying it back


Changing the beta of a portfolio

To change the beta of the portfolio from β to β*:

When β > β*, a short position in contracts is required

When β < β*, a long position in contracts is required


ሺ𝐵−𝐵∗ሻ𝑉𝐴𝑉𝐹

ሺ𝐵∗− 𝐵ሻ𝑉𝐴𝑉𝐹

Portfolio beta example

Futures price of SPI 200 is 4,200

Size of portfolio is AUD 2.1 million

Beta of portfolio is 1.5

One futures contract is for delivery of AUD 25 times the index

• What position in futures contracts on the SPI 200 is necessary to hedge the portfolio?

• What position is necessary to reduce the beta to 0.75?

• What position is necessary to increase the beta to 2.0?


Stock picking

• If you think you can pick stocks that will outperform the market, futures contracts can be used to hedge the market risk

• If you are right, you will make money whether the market goes up or down


Rolling the hedge forward

• We can use a series of futures contracts to increase the life of a hedge

• Each time we switch from one futures contract to another we incur a type of basis risk


Rolling the hedge forward example

It is 11 April. An American company knows it will have 100,000 barrels of oil to sell in June 2012. The current spot price is USD 69 per barrel. Only the first six delivery months have sufficient liquidity to meet the company’s needs.

What strategy should the company take?

What is the gain/loss from the futures contract?

Table 3.5, page 69


Week 2 Chapter 3 Lecture Slides (1).ppt

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