Lecture 5
Hedging with options
Recap: Hedging with forwards/futures
To this point, we have used forward and futures contracts to
hedge various exposures:
– When we are exposed to rising (falling) prices, we enter a
forward/futures position that makes money in a rising (falling)
market.
– The profit (loss) on the derivative contract perfectly offsets the loss
(profit) in the underlying market.
– In effect, this allows us to ‘lock in’ a value/price/exchange rate etc
and shield ourselves from movements in the underlying asset.
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Recap: Hedging with forwards/futures
The Lecture 2 examples typically explored two ‘what ifs”:
If the price of the underlying asset moves against us:
– the forward/futures contract generates a profit which offsets the loss
on the underlying asset.
– In this case, we are very glad we hedged.
If the price of the underlying asset moves in a favourable direction:
– We benefit from the favourable movement in the underlying, but these
gains are cancelled out by a loss on the forward/futures contract.
– In this situation, we would have been better off not hedging, but at the
outset, there is no way of knowing which way price will move!
Hedging like this is great if prices do move against you; however
you also miss out on any upside if prices move favourably.
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Hedging with options
In this lecture, we will explore the use of options to hedge.
Compared to forwards/futures, options offer a greater degree of
flexibility:
– Forwards/futures “lock in” a price: a long (short) position is legally
obliged to buy (sell) the underlying asset.
– With options, a call (put) allows you to buy (sell) the underlying
asset at the strike price. However, you can also choose not to
exercise the option if it doesn’t suit you.
The flexibility to not exercise the option allows us to hedge
against unfavourable price movements, whilst maintaining
upside potential should prices move in a favourable direction.
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Hedging commodity price risk
Recall from Lecture 2 the risk faced when building a road in
China:
– The current (spot) price of bitumen is RMB 3450 per ton.
– We will need to purchase 500 tons of bitumen in mid 2025.
– We are exposed to the price of bitumen rising between now and
then.
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Hedging commodity price risk
In Lecture 2, we hedged this commodity price risk using
bitumen futures contract traded on the Shanghai Futures
Exchange:
– We entered long bitumen futures contracts covering 500 tons.
– The delivery price “F” was RMB 3640 per ton.
– This “locked in” the purchase cost of our bitumen at RMB
1,820,000.
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Hedging commodity price risk
F = RMB 3640
When the bitumen price rose to RMB 4500 per ton:
– We made a profit of RMB 430,000 on closing out the futures.
– Purchasing 500 tons of bitumen cost RMB 2,250,000.
– The overall cost was RMB 1,820,000 (2,250,000 – 430,000).
– We would be very glad we hedged.
When the bitumen price fell to RMB 2200 per ton:
– We made a loss of RMB 720,000 on closing out the futures.
– Purchasing 500 tons of bitumen cost RMB 1,100,000.
– The overall cost was RMB 1,820,000 (1,100,000 + 720,000).
– With the benefit of hindsight, we would have been better off had
we not hedged.
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Hedging commodity price risk
Depending on the availability of suitable derivatives, we may be
able to hedge this commodity price risk using an option contract.
The strategy to hedging with options remains the same:
Identify your risk/exposure in the asset:
– I need to purchase bitumen in mid 2025. I am exposed to the price
of bitumen rising between now and then.
Enter a derivatives position that makes money when this
unfavourable scenario occurs:
– With forward/futures contracts, the key question in establishing the hedge
was do we go long or short?
– With option hedging, the key questions is do we use calls or puts?
– A long call option makes money in a rising market.
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Long Call
Long Put
X
X
Decision rule:
exercise if ST > X
exercise if ST < X
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Hedging commodity price risk
Let’s assume that there are option contracts written on bitumen
(i.e., the asset underlying the option is the price of bitumen):
– Assume that a standard option contract covers 10 tons of bitumen.
– Assume that we can get an option contract with a strike price of
RMB 3640 per ton, with expiry in mid 2025.
To enter 50 long call options on bitumen, we would have to pay
the option premium:
– In the calculations that follow, I will ignore the option premium paid
(but always keep in mind that we do have to pay to enter an option
position).
– This is a minor disadvantage of hedging with options, compared to
forwards/futures (which you do not have to pay to enter).
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If bitumen price rises to RMB 4500
X = RMB 3640
In mid 2025, around the time we need to purchase 500 tons of
bitumen, the spot price of bitumen is RMB 4500 per ton.
– Our long call option gives us the right (but not obligation) to
purchase 500 tons of bitumen at the strike price of RMB 3640 per
ton.
– Since the spot price of bitumen (4500) is well above the strike
(3640), this is a deep in-the-money call option.
– We will exercise our right to purchase 500 tons of bitumen at the
strike price of RMB 3640 per ton.
– The overall cost of our bitumen is RMB 1,820,000 (500 tons 
3640), plus whatever it cost us to buy the call options.
The outcome here is identical to that achieved when we hedged
using long bitumen futures contracts (except for the premium
paid to purchase the call options).
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If bitumen price falls to RMB 2200
X = RMB 3640
In mid 2025, around the time we need to purchase 500 tons of
bitumen, the spot price of bitumen is RMB 2200 per ton.
– Our long call option gives us the right (but not obligation) to
purchase 500 tons of bitumen at the strike price of RMB 3640.
– Since the spot price of bitumen (2200) is way below the strike
(3640), this is a deep out-of-the-money call option.
– It would be irrational to exercise an OTM call option! We would
simply let the call option lapse.
– Instead, we purchase the required bitumen at the spot price. The
overall cost of our bitumen is RMB 1,100,000 (500 tons  2200),
plus whatever it cost us to buy the call options.
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Options provide flexibility
It is this latter case that demonstrates the advantage of hedging
using options:
– The call option protects us against unfavourable price movements.
No matter how high bitumen price rises, the most we will pay is the
strike price 3640 per ton.
– Yet we are still able to benefit in the event that bitumen price falls.
We simply let the call option lapse and purchase bitumen at the low
spot price (2200).
– The flexibility to not exercise the option means that we are not as
‘locked in’ as we are with a futures contract.
– Hence, we maintain the potential to benefit should prices move in a
favourable direction.
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Hedging with options
Like car insurance
or home insurance
In many respects, options are similar to an insurance policy:
– You pay an upfront cost for this insurance (the option premium).
– If nothing bad happens, all you have lost is the money spent on the
premium.
– If, however, things go badly for you, then the option gives you a
handsome payoff to offset the loss suffered elsewhere.
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Hedging foreign exchange risk
In August, you make a sale to a customer based in London
worth GBP 10m. You will receive payment in GBP in December.
spot rate AUD 1.00 = GBP 0.5754 (i.e., GBP 1.00 = AUD
1.7379)
In Lecture 2, how did we hedge using forwards?
We hedged the forex risk by entering a short forward contract on
GBP:
– The forward rate was:
AUD 1.00 = GBP 0.5700.
– In other words:
GBP 1.00 = AUD 1.7544.
– This short forward position “locked in” the exchange rate at which
we could convert the GBP 10m into AUD.
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F: GBP 1.00 = AUD 1.7544
Hedging foreign exchange risk
When the GBP weakened to 1.5385:
– We made a profit of AUD 2.159m on closing out the forward.
– Converting GBP 10m at the spot rate generated AUD 15,384,615.
– The overall cashflow was AUD 17,543,615 (15,384,615 + 2.159m).
– We would be very glad we hedged.
When the GBP strengthened to 2.0833:
– We made a loss of AUD 3.289m on closing out the forward.
– Converting GBP 10m at the spot rate generated AUD 20,833,333.
– The overall cashflow was AUD 17,544,333 (20,833,333 –
3,289,000).
– With the benefit of hindsight, we would have been better off had
we not hedged.
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Hedging foreign exchange risk
As an alternative, let’s assume that the bank is willing to offer us
an option contract on GBP:
– The option has a strike ‘price’ of:
AUD 1.00 = GBP 0.5700
– In other words, the strike price is:
GBP 1.00 = AUD 1.7544
– The option expires in December.
With forward/futures contracts, the key question in establishing
the hedge was do we go long or short?
With option hedging, the key questions is do we use calls or
puts?
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Hedging foreign exchange risk
What is the risk?
1/0.5446 = 1.8362
– We will be receiving British pounds in December.
– Currently, each GBP is worth AUD 1.7379.
– We are exposed to movements in the value of the GBP.
– We will suffer if the GBP depreciates (i.e., becomes less valuable).
How to hedge this risk?
– We need to make money in a falling market (if value of GBP drops).
– put options profit in a falling market (i.e., we want the right to sell
GBP 10m at a fixed rate).
Hence, we will enter a long put option giving us the right (but not
obligation) to sell GBP 10m at a strike ‘price’ of 1.7544.
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X: GBP 1.00 = AUD 1.7544
What if GBP weakens
GBP 1.00 = AUD 1.5385
Assume that, in Dec, AUD 1.00 = GBP 0.6500
– This is what we were worried about (the pound weakening).
– We are about to receive GBP 10m. If we sold them in the spot
market, they are only worth AUD 1.5385 each.
– However, we have a put option that allows us to sell them for AUD
1.7544 each.
– Is this option in or out of the money?
– This is an in-the-money put option (ST < X). Naturally, we will
exercise our right to sell GBP under the put option.
When our customer pays us GBP 10m:
– We exercise our right under the put option to sell the GBP 10m for
AUD 1.7544 each.
– The gross payoff from our sale is AUD 17,544,000.
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X: GBP 1.00 = AUD 1.7544
What if GBP weakens
This payoff under the option contract (AUD 17,544,000) is
virtually identical to the payoff when we hedged using a forward
contract (AUD 17,543,615). A minor difference due to rounding.
Therefore, so far, there is little difference between hedging using
a forward or an option.
– We will see the utility of hedging with an option when the GBP
strengthens.
Keep in mind that, unlike a forward contract, where there is no
upfront cost, we had to pay the option premium to enter the long
put option. This example does not explicitly factor in the option
premium.
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X: GBP 1.00 = AUD 1.7544
What if GBP strengthens
GBP 1.00 = AUD 2.0833
Assume that, in Dec, AUD 1.00 = GBP 0.4800
We were hedging against the pound becoming less valuable.
This has not happened; in fact, the pound has strengthened!
Recall that, when hedging with a forward contract, we made a
loss on the forward when the pound strengthened. The overall
payoff under the forward was the locked-in AUD 17,544,333.
However, while our put option gives us the right to sell GBP for
the strike price of 1.7544, we don’t have to do this:
– It would be irrational to exercise our right to sell GBP for 1.7544
when they are worth 2.0833 on the spot market. This is an out-ofthe-money put option (ST > X). We simply let the put option lapse.
– When our customer pays us GBP 10m,
– We convert GBP 10m into AUD at spot rate: 10m  2.0833 = AUD21
20,833,000.
What if GBP strengthens
When we locked in an exchange rate using a forward contract,
the payoff when the GBP strengthened to 0.48 was AUD
17,544,333. [see slide #25 from Lecture 2]
In contrast, the put option protects us from unfavourable
movements (GBP weakening) whilst maintaining upside
potential:
– If GBP strengthens to 0.48, we end up with AUD 20.833m.
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Hedging stock portfolios
You are a fund manager with a portfolio of Australian stocks
currently worth $100m as at 1st July.
Your portfolio has done very well in recent months, but you have
reason to be concerned:
– International borders have re-opened and tourism is rebounding.
Alas, new variants of covid are appearing and you fear that further
lockdowns may occur if things get out of control.
– The military conflict in Europe is showing no signs coming to an
end. Sanctions imposed on Russia are dramatically affecting oil
price and impeding global supply chains.
– All of these things make you very pessimistic. You are fearful of a
sharp market correction in the second half of 2024.
In lecture 2, what was our strategy?
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Hedging stock portfolios
As we saw in Lecture 2, you could enter short SPI200 futures to
“lock in” your portfolio value at around $100m.
But who knows? Maybe the equity market will continue rising
for the remainder of the year.
In Lecture 2, we hedged away the stock market risk by entering
short SPI200 futures contracts:
– We entered 713 short Dec-2024 SPI200 futures with delivery price
F = 6730.
– This effectively locked in our net worth at about $100m.
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F = 6730
Hedging stock portfolios
When the market fell to 6120:
– We made a profit of $10,873,250 on closing out the futures.
– Our share portfolio was worth $90.2m.
– Our overall worth was $101,073,250 (90.2m + 10,873,250).
– We would be very glad we hedged.
When the market rose to 7072:
– We made a loss of $6,096,150 on closing out the futures.
– Our share portfolio was worth $107m.
– Our overall worth was $100,903,850 (107m – 6,096,150).
– With the benefit of hindsight, we would have been better off had
we not hedged.
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Hedging stock portfolios
As an alternative, we can use SPI200 index options to hedge
our share portfolio.
Assume that:
– The S&P/ASX 200 index is currently 6800 (1 July 2024).
– Your share portfolio has a beta of 1.20.
– The ASX trades options written on the S&P/ASX 200 with Dec2024 expiry.
We want to protect the value of our portfolio against a market
decline, whilst maintaining potential to profit if market rises.
With futures hedging, we entered short SPI200 futures.
With options hedging, the question is whether to use calls or
puts?
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Hedging stock portfolios
What is the risk?
– if the stock market falls, so too does our portfolio value.
How to hedge this risk?
– We need to make money in a falling stock market.
– put options profit in falling market.
Assume that we can enter long put options on the S&P/ASX 200
index with a strike price of 6730 and Dec-2024 expiry.
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Number of put option contracts required
The number of contracts required depends on:
– the beta of your stock portfolio
– the value of the stock portfolio to be hedged
– The dollar value of a single S&P/ASX 200 option contract
Amount to be hedged
Number of
= 𝛽portfolio
Contracts
Value of one contract
$100,000,000
= 1.2 ×
6730 × $10
= 1783 contracts
Contract size for
index options is
$10 × strike
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Hedging stock portfolios
We will use put options to establish a ‘floor’ of about $100m.
Enter 1783 long put options.
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X = 6730
If market falls to 6120
See calculation
in Lecture 2
Portfolio value will drop to:
– (1- 0.098)  $100m = $90.2m
Our index puts allow us to sell at the strike price of 6730, while
the underlying market is only worth 6120:
– These are in-the-money puts and we will exercise!
– These index options cannot be physically delivered; they are cash
settled.
– The payoff from the put options is: 1783 x $10 x (6730 – 6120) =
$10,876,300.
net worth is $90,200,000 + $10,876,300 = $101,076,300.
– Even though our portfolio value fell by 9.8%, the payoff from the
long puts ensured that we are still worth about $100m.
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X = 6730
If market rises to 7072
Recall that, when we hedged using SPI200 futures, the short
SPI200 position lost money when the market rose to 7072. That
loss offset the gains in our portfolio value, leaving us with a
locked in value of about $100m (see slide 48 in Lecture 2).
However, here we are hedging with put options:
– The put options give us a right to sell at the strike price of 6730, but
we don’t have to do this. In fact, it would be irrational to exercise
this out-of-the-money put option (ST > X). We simply let the options
lapse.
– Our portfolio value will rise to (1+0.07)  $100m = $107m.
– net worth is $107m.
Using long put options has protected us from unfavourable
movements (stock market falling) whilst maintaining upside
potential should the market rise.
See calculation
in Lecture 2
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Key takeaways from this lecture
Hedging with forwards/futures allows us to remove all the
exposure to risk:
– We can lock in a value. If prices move unfavourably, we are glad
that we hedged. If prices do not move unfavourably, with hindsight,
we would have been better off not hedging.
Hedging with options provides attractive flexibility:
– They provide protection against unfavourable movements in the
underlying price, yet
– Our ability to choose whether or not we exercise the option allows
us to maintain the potential to benefit if prices move favourably.
– Although my calculations have not explicitly factored it in, keep in
mind that options must be bought (they cost money upfront).
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