Recap of last week
The previous lecture introduced forward and futures contracts:
– The mechanics of how they work.
– The notion of entering long or short contracts.
– At expiry, either delivering the underlying asset or closing out.
– Calculating whether we made a profit or a loss.
Now that we understand how these contracts work, we can start
to consider how they can be utilised to manage as assortment of
risks (or speculate).
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Speculation v hedging
Speculation is akin to betting/gambling:
– You have a prediction on the direction of price movements
– You enter a derivatives position that will profit if you guess right
– And, of course, your derivatives position will lose if you guess
wrong.
– Effectively, a speculator is taking on risk (“putting their money
where their mouth is”).
– Usually, a speculator does not have any position/exposure in the
underlying asset itself.
– e.g., Lecture 1 example of speculating on falling gold price via short
forward contract.
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Speculation v hedging
Hedging is about removing risk:
– The hedger is not predicting/guessing which way prices will move.
– Rather, s/he knows what price movement will hurt them, and
– They enter a derivatives position to make money if price moves in
this unfavourable direction.
– Usually, the hedger does have a position/exposure in the
underlying asset.
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Basic principles of hedging
People hedge when they do not want to be exposed to
movements in the price of an asset.
The idea of hedging is to enter a derivatives position that
provides a payoff that offsets price movements in the particular
asset to which they are exposed.
The aim is to eliminate (or at least reduce) your exposure to the
price movements.
Strategy:
– Identify your risk/exposure in the asset.
– Enter a derivatives position that makes money when this
unfavourable scenario occurs.
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Example: Hedging commodity price risk
My business is in building roads and highways. I have just been
awarded a contract to construct a road in China:
– It is a long-term construction project, with the road due to be
completed by the end of 2020.
– Towards the end of the construction process, I will need to
purchase about 500 tons of bitumen.
– The current (spot) price of bitumen is RMB 2800 per ton, but I have
no idea what the price will be in late 2020.
With a little investigation, I discover that the Shanghai Futures
Exchange offers futures contract on bitumen.
http://business.financialpost.com/investing/worlds-first-bitumen-futures-make-strong-debut-in- 6
shanghai/wcm/cc304a30-f63a-4bf0-b9aa-d75f1cd437b8
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Example: Hedge commodity price risk
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Example: Hedging commodity price risk
I should be able to use the SHFE bitumen futures contract to
manage my risk exposure on this project. It’s just a matter of
deciding whether to enter a long or a short futures position.
Identify your risk/exposure in the asset:
– I need to purchase bitumen in late 2020. 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:
– Long futures positions make money in a rising market.
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Example: Hedging commodity price risk
Hence, I will enter a long hedge using the SHFE bitumen futures
contract:
– Looking at the contract specs, I note that each contract covers 10
tons of bitumen. Given that my construction project requires 500
tons, 50 futures contracts are required.
– SHFE offers a range of expiry dates. Given that I will be laying the
bitumen in late 2020, I will choose the contract expiring in
December 2020 (“bu2012”).
– bu2012 has a delivery price (F) of 2998. Hence, I can lock in a
purchase price of RMB 2998 per ton for my bitumen.
– I enter 50 long bu2012 futures contracts.
Once I enter these 50 long futures contracts, I know exactly how
much my bitumen will cost: 50 10 2998 = RMB 1,499,000
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If bitumen price rises to RMB 4000
Even though it is possible to physically take delivery of 500 tons
of bitumen, let’s assume that we close out just prior to expiry.
When the expiry date arrives, the quoted futures price on
bu2012 contracts will equal the spot price for bitumen:
– Given that my original position was 50 long bu2012 contracts,
– I close out by entering 50 short bu2012 contracts.
– Profit on futures contracts: 50 10 (4000-2998) = RMB 501,000
– I still need 500 tons of bitumen, so I purchase it on the spot market
at a cost of 500 4000 = RMB 2,000,000
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Tute 1 Q6
If bitumen price rises to RMB 4000
The total cost to purchase 500 tons of bitumen is:
– RMB 2,000,000 – 501,000 = RMB 1,499,000
– Of course, this equates to RMB 2998 per ton (the purchase price
locked in by the futures contract).
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1,499,000 500 tons
= 2998 per ton
Hedging means locking in a price
Being hedged means being locked in to a price:
– This is great if prices move against you.
– But it also means that you don’t benefit if prices move favourably.
– When you are (fully) hedged, you are completely shielded from
movements in the price of the underlying asset.
– Your final outcome is insensitive to what happens with the
underlying asset.
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If bitumen price falls to RMB 2200
When I close out, the quoted price on bu2012 futures will be
2,200:
– Given that I have 50 long bu2012 contracts,
– I close out by entering 50 short bu2012 contracts.
– Loss on futures contracts: 50 10 (2200-2998) = RMB 399,000
– I still need 500 tons of bitumen, so I purchase it on the spot market
at a cost of 500 2200 = RMB 1,100,000
– Overall cost: RMB 1,100,000 + 399,000 = RMB 1,499,000
– This is an identical outcome to the previous scenario. It equates to
RMB 2998 per ton (the purchase price locked in by futures
contract).
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Example: Hedging commodity price risk
This example illustrates the use of a futures contract to remove
our exposure to fluctuations in the price of bitumen:
– Given that we will need to purchase bitumen in the future, we were
exposed to a price rise in the cost of bitumen.
– We entered long futures contracts because long futures positions
make money when the price of the underlying asset rises.
– Gains or losses on the futures position offset what happens in the
underlying asset:
• When bitumen price rises to 4000, it costs us more to buy bitumen, but this is
offset by a gain on the long futures position.
• When bitumen price falls to 2200, the bitumen is cheaper to buy but this is offset
by a loss on the long futures position.
– Therefore, irrespective of what happens to the price of bitumen, we
know that the overall cost of bitumen will be RMB 2998 per ton.
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Hedging foreign exchange risk
Hedging and speculation involving foreign exchange can
sometimes cause confusion because an exchange rate can be
expressed in two ways:
– I saw on the news last night (4 Mar-2020) that the AUD/USD
exchange rate is 0.66
– This means that: AUD 1.0000 buys USD 0.66
– Equivalently, it also means that: USD 1.000 costs AUD 1.5152
To avoid confusion, just treat the currency in the same way you
would any other commodity (gold, oil, bitumen, etc). Ask
yourself: what does a USD cost?
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1/0.66 =
1.5152
Hedging foreign exchange risk
AUD USD GBP EUR YEN RMB
AUD 1 0.6600 0.5100 0.5900 70.4400 4.5800
USD 1 0.7800 0.8900 106.9000 6.9600
GBP 1 1.1500 137.5000 8.9300
EUR 1 119.4700 7.7800
YEN 1 0.0650
RMB 1
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Exchange rates as at 4 Mar-2020
Hedging foreign exchange risk
AUD USD GBP EUR YEN RMB
AUD 1 0.6600 0.5100 0.5900 70.4400 4.5800
USD 1.5152 1 0.7800 0.8900 106.9000 6.9600
GBP 1.9608 1.2821 1 1.1500 137.5000 8.9300
EUR 1.6949 1.1236 0.8696 1 119.4700 7.7800
YEN 0.0142 0.0094 0.0073 0.0084 1 0.0650
RMB 0.2182 0.1437 0.1120 0.1285 15.3846 1
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Exchange rates as at 4 Mar-2020
Example: Hedging forex 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 0.51
fwd rate for Dec delivery: AUD 1.00 = GBP 0.5140
Useful to think about this using direct quotes:
– spot rate GBP 1.00 = AUD 1.9608
– fwd rate GBP 1.00 = AUD 1.9455
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Calculation of
“F” is shown
in Lecture 3
Example: Hedging forex risk
What is the risk?
– We will be receiving British pounds in December.
– Currently, each GBP is worth AUD 1.9608.
– We are exposed to movements in the value of the GBP.
– We will suffer if GBP depreciates (i.e., becomes less valuable).
how to hedge this risk?
– need to make money in a falling market (if value of GBP drops).
– short forward position (i.e., lock in the price at which we can
sell/convert GBP 10m in December).
– We will profit if GBP falls; and we will lose if GBP rises.
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Once I enter this short forward contract, I know exactly how many
AUD I will get in December: GBP 10m 1.9455 = AUD 19,455,000
What if GBP weakens
Assume that, in December, AUD 1.00 = GBP 0.6500.
Our short forward contract is an agreement that allows us to sell
GBP at AUD 1.9455.
profit on closing:
10m (1.9455 – 1.5385) = AUD 4,070,000
We receive GBP 10m and convert to AUD at spot rate:
10m / 0.65 = AUD 15,384,615
net receipts AUD 19,454,615 (15,384,615 + 4,070,000).
GBP 1.00 = AUD 1.5385
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What if GBP strengthens
Assume that, in December, AUD 1.00 = GBP 0.48.
Our short forward contract allows us to sell GBP at AUD 1.9455.
loss on closing:
10m (1.9455 – 2.0833) = AUD 1,378,000
We receive GBP 10m and convert to AUD at spot rate:
10m / 0.48 = AUD 20,833,333
net receipts AUD 19,455,333 (20,833,333 – 1,378,000)
GBP 1.00 = AUD 2.0833
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The net receipts in these two examples (19,454,615 v 19,455,333) should be
identical. A small difference has arisen because I round forward rates to 4 dps.
Example: Hedging forex risk
Once again, we see how a forward contract can remove our
exposure to fluctuations in an exchange rate (i.e., the price of
GBP):
– Given that we will need to sell GBP in the future, we were exposed
to a fall in the value of GBP.
– We entered short forward contract because short positions make
money when the price of the underlying asset falls.
– Gains or losses on the forward position offset what happens in the
underlying asset:
• When the GBP weakened to 0.65, we don’t get as much for the GBP10m when
we convert them, but this is offset by a gain on the short forward position.
• When the GBP strengthened to 0.48, we get more AUD when we convert the
GBP 10m, but this is offset by a loss on the short forward position.
– Therefore, irrespective of what happens to the price of GBP, we
know that the overall value of our sale will be AUD 19.455m. 24
Overview of equity market indices
A stock index tracks changes in a hypothetical portfolio of
stocks.
Most countries have a benchmark index that depicts a portfolio
of all stocks in the market (or subsets of the entire market).
– Dow Jones Industrial Average (DJIA): 30 blue chip US stocks
– S&P500: 400 industrials, 40 utilities, 20 transport, 40 financial
– Russell 1000: largest 1,000 US stocks
– FTSE100: largest 100 stocks on London Stock Exchange
– DAX: 30 major stocks trading on Frankfurt Stock Exchange
– Nikkei: a broad portfolio of Japanese stocks
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Overview of equity market indices
In Australia, Standard & Poors construct a variety of equity
indices
– S&P/ASX 20, 50, 100, 200, 300
– S&P/ASX MidCap50, SmallOrdinaries, All Ordinaries + more
– http://www.asx.com.au/asx/statistics/indexInfo.do
The benchmark S&P/ASX 200 is a value-weighted index of the
Top 200 Australian stocks.
– Daily index change is an average of price change on each stock,
with weights determined according to market cap.
– Dividends paid by stocks are not included in index.
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Stock index futures
In many countries, futures contracts trade on the benchmark
stock index.
Index futures allow people to hedge the risks associated with
stock portfolios.
And, of course, stock index futures also facilitate speculation on
market movements.
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ASX SPI200 futures
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Example: Hedging stock portfolios
You are a fund manager with a portfolio of AUS stocks currently
worth $100m as at 1 January.
Your portfolio has done very well lately, but your research
suggests that there may be a sharp correction in equities during
the first half of 2020.
– One possible course of action is to liquidate your portfolio and hold
cash (bad idea – transaction costs will hurt!), or
– Use SPI200 futures to hedge (i.e., lock in) the value.
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Example: Hedging stock portfolios
Assume that:
– Today is 1 Jan-2020.
– The S&P/ASX 200 index is currently 6300.
– Jun-2020 expiry SPI200 futures are quoted at 6351.
– Your stock portfolio has a beta of 1.20.
To establish the hedge, we just need to decide:
– Whether to go long or short the SPI200 futures, and
– How many futures contracts to enter.
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Example: Hedging stock portfolios
What is the risk?
– if the stock market falls, so too does our portfolio value.
Enter a derivatives position that makes money when this
unfavourable scenario occurs:
– need to make money in falling market.
– a short futures position makes money in a falling market.
– we will enter 756 short Jun-2020 expiry SPI200 futures at 6351.
– The futures position will profit if market falls; and it will lose if
market rises.
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Number of SPI200 contracts required
The number of contracts required depends on:
– the beta of your stock portfolio,
– the value of the stock portfolio to be hedged, and
– The dollar value of a single SPI200 futures contract
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portfolio
Number of Amount to be hedged
Contracts Value of one contract
1.2 $100,000,000
6351 $25
756 contracts
If market falls to 5670
If the market does fall, we cannot avoid value being wiped off
our portfolio.
But, when the market falls, we will make a gain on the short
SPI200 futures.
To see where we end up, we need to calculate:
– By how much the value of our portfolio has fallen, and
– What is the gain on the short SPI200 futures position.
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Calculating change in portfolio value
Dividend yield on market portfolio:
– Assume that the dividend yield on market portfolio is 4% pa.
– Hence, over the 6-month period (Jan-Jun), the market portfolio
would have generated 2% in dividends.
Riskfree interest rate:
– Assume that the riskfree interest rate is 2% pa.
– Hence, over the 6-month period (Jan-Jun), this is about 1%.
Return on market portfolio:
– The market index has fallen by 10% (5670/6300 – 1)
– Factoring in dividends, the overall return on the market portfolio
over the hedging period is -8% (-10% + 2%)
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Calculating change in portfolio value
Noting that our portfolio (=1.2) is riskier than the market
(=1.0),
it follows that, if the market fell by 8%, the value of our portfolio
will have fallen by even more fall by more than 8%.
Plugging this information into the CAPM, the estimated fall in
our portfolio value is 9.8%:
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9.8%
0.01 1.2 0.08 0.01
p f p m f R R R R
If market falls to 5670
Portfolio value will drop to:
– (1-0.098) $100m = $90.2m
but we will gain on the short SPI200 futures contracts
– 756 25 (6351 – 5670) = $12,870,900
Our overall net worth is 90.2m + 12,870,900 = $103,070,900
So, even though the market dropped sharply, the gain on the
SPI200 futures compensated for the fall in our portfolio value.
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If market rises to 6552
If the market rises, our share portfolio will be worth a lot more
But, when the market rises, we will make a loss on the short
SPI200 futures.
To see where we end up, we need to calculate:
– By how much the value of our portfolio has risen, and
– What is the loss on the short SPI200 futures position.
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Calculating change in portfolio value
Return on market portfolio:
– The market index has risen by 4% (6552/6300 – 1)
– Factoring in dividends, the overall return on the market portfolio
over the hedging period is 6% (4% + 2%).
Since our portfolio (=1.2) is riskier than the market (=1.0), it
follows that, if the market rises by 6%, the value of our portfolio
will rise by even more fall by more than 6%.
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7.0%
0.01 1.2 0.06 0.01
p f p m f R R R R
If market rises to 6552
Portfolio value will rise to:
– (1+0.07) $100m = $107m
but we lose on the short SPI200 futures contracts
– 756 25 (6351 – 6552) = -$3,798,900
Our overall net worth is 107m – 3,798,900 = $103,201,100
This time, even though the market rose sharply, the increase in
portfolio value is largely offset by the loss on the SPI200 futures.
In essence, we have locked in the value of our portfolio at
approximately $103m.
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These two cases illustrate that we were effectively hedged
against price movements in the ASX200 index. Irrespective of
whether the index rises or falls, our portfolio value was secured
at around $103m.
S&P/ASX200 index
in Jun 2020 5000 5670 6100 6552 6800
Portfolio gain (loss)
Short hedge gain (loss)
(22,561,905)
25,533,900
(9,800,000)
12,870,900
(1,609,524)
4,743,900
7,000,000
(3,798,900)
11,723,810
(8,486,100)
Net Position 102,971,995 103,070,900 103,134,376 103,201,100 103,237,710
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No matter where the S&P/ASX 200 index finishes, our
portfolio value is locked in at around $103m
Key takeaways from this lecture
Forward and futures contracts can be used to manage a wide
variety of risks.
Since they ‘lock in’ the price at which you can buy or sell in the
future, they effectively remove all exposure to movements in the
underlying price.
Implementing a hedge essentially amounts to choosing to
whether to go either long or short.
Strategy:
– Identify your risk/exposure in the asset.
– Enter a derivatives position that makes money when this
unfavourable scenario occurs.
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