PowerPoint Presentation
IC301
Derivative Securities
2
IC301 – Topic 2
Forwards and Futures Hedging & Speculation
Hedging
Spot (ST)
Profit or Loss (+/-)
Spot (ST)
K
Underlying price risk
Hedge by selling short
K
10
Hedging
4
Hedging doesn’t mean “no risk”
It matters what the competition does
Consider two companies (A&B) that both benefit when the price of gold rises (Hull, p75)
Gold Price Rises A – hedged A – unhedged
B – hedged Neutral A gains at the
expense of B
B – unhedged B gains at the expense of A Both A & B increase profits
Hedging
5
What makes a good hedge?
What if you cannot hedge precisely?
What strategies can you deploy?
Does it matter if corporate treasuries lose money on
hedging?
Japan basis trade example – cash is everything (what are futures?) Hull p 75 “hedging can lead to a worse outcome” i.e. if no hedge then would have been profitable
“Stack and Roll”
6
Maturity
Forward Curve (today)
Price
105
100
110
Problem
Futures for 3, 6, 9m are steeply upward sloping
Need to buy 9m forward
What are the choices?
3m
6m
9m
Problem for running a long hedge – also problem for commodity ETFs e.g. agricultural, metals anything in contango
“Stack and Roll”
7
6m
Maturity
Forward Curve (over time)
Price
110
105
100
Solution?
If the forward curve retains its shape over time
Buy 3m forward
Roll to next contract just before expiry
Repeat
3m
9m
“Stack and Roll”
20
Strategy
Assuming the curve retains its shape, each ‘roll’ will be at roughly flat
prices (no spread)
The strategy is exposed to the shape of the forward curve in the future Note that the strategy is exposed to basis risk and not outright price risk
Buy + F1
Buy/Sell + F2 – F1 just before the expiry of F1
Buy/Sell + F3 – F2 just before the expiry of F2
“Stack and Roll”
9
6m
Maturity
Price
Forward Curve (better)
100
105
110
3m
9m
6m
Maturity
Price
Forward Curve (worse)
100
105
110
3m
9m
Roll -5
Roll -5
Roll +5
Roll +10
“Stack and Roll”
10
Strategy
Buy
Buy/Sell
Buy/Sell
+ F1
+ F2 – F1
+ F3 – F2
Total
Base Case
Better
Worse
+100
+0
+0
100 90 115
Compare to original 9 month hedge rate of 110
+100
-5
-5
+100
+5
+10
Case study: Metallgesellschaft (1993)
Hull page 91 (See Business Snapshot 3.2)
11
MG Refining and Marketing (US entity) lost $1.5bn through hedging Long-term fixed rate supply contract with certain cancellation clauses Price risk hedged with long position in short-dated futures
Rolling hedging strategy
Market in Contango
Fall in short-dated prices
Cash crisis
Market in Backwardation
Accounting mismatch
Board dismissed – Positions closed out
Hedging
12
A good hedge provides an equal and opposite economic exposure to the underlying risk
The closer the match between the hedge and
the risk, the better the hedge
Volatility from hedging
26
If a hedge is not perfect, there will be a residual volatility to the position from the basis
Example: Bond portfolio
– Basis risk
– Curve risk
– Spread risk
Hedging a liquidity bond portfolio : basis risk, curve risk, spread risk
Convergence of Futures to Spot (Figure 2.1, page 51)
IC 301
14
Time
Time
(a)
(b)
Futures
Price
Futures
Price
Spot Price
Spot Price
Positive carry (b) – willing to pay more on trade date
Hedging interest rates with futures
Short term interest rates (STIRs): 3 month contracts fixed vs LIBOR
Bond futures: typically 10-year futures
– With a perfect hedge the futures track the underlying asset perfectly, but:
– curve risk
– spread risk
– basis risk
Curve risk: non-parallel yield curve shifts
Managing curve risk – US yield curve 2002-2006
17
https://stockcharts.com/freecharts/yieldcurve.php [click on ANIMATE to see dynamic yield curve]
17
Yield curve spreads – US market
Can change dramatically through time:
18
Spread risk
Credit spread vs benchmark rates (risk free government bonds)
Rating agencies
Market rating
Corporate borrowing rates ( varies with issuance, demand, economic environment)
Spreads can widen or narrow
Not dependent on direction of rates
19
Basis risk
Cash versus futures (or spot vs futures)
Positive or negative carry?
Long the basis = Long the asset, short the futures contract
Short the basis = Short the asset, long the futures contract
20
Margins
A margin is cash or marketable securities deposited by an investor with his or her broker
The balance in the margin account is adjusted to reflect daily settlement
Margins minimize the possibility of a loss through a default on a contract
A trader has to bring the balance in the margin account up to the initial margin when it falls below the maintenance margin level
IC 301
21
Example of a Futures Trade (page 49-51)
An investor takes a long position in 2 December gold futures contracts on June 5
contract size is 100 oz.
futures price is US$1,450
initial margin requirement is US$6,000/contract (US$12,000 in total)
maintenance margin is US$4,500/contract (US$9,000 in total)
IC 301
22
A Possible Outcome (Table 2.1, page 52)
IC 301
23
Day Trade Price ($) Settle Price ($) Daily Gain ($) Cumul. Gain ($) Margin Balance ($) Margin Call ($)
1 1,450.00 12,000
1 1,441.00 −1,800 − 1,800 10,200
2 1,438.30 −540 −2,340 9,660
….. ….. ….. ….. ……
6 1,436.20 −780 −2,760 9,240
7 1,429.90 −1,260 −4,020 7,980 4,020
8 1,430.80 180 −3,840 12,180
….. ….. ….. ….. ……
16 1,426.90 780 −4,620 15,180
23
Key Points About Futures
They are settled daily
Closing out a futures position involves entering into an offsetting trade
Most contracts are closed out before maturity
IC 301
24
Collateralization in OTC Markets
It is becoming increasingly common for transactions to be collateralized in OTC markets
Traditionally most transactions have been cleared bilaterally in OTC markets
Following the 2007-2009 crisis, the has been a requirement for most standardized OTC derivatives transactions between dealers to be cleared through central counterparties (CCPs)
CCPs require initial margin, variation margin, and default fund contributions from members similarly to exchange clearing houses
IC 301
25
See Hull Fig 2.2 p57
CCP
Delivery
If a futures contract is not closed out before maturity, it is usually settled by delivering the assets underlying the contract. When there are alternatives about what is delivered, where it is delivered, and when it is delivered, the party with the short position chooses.
A few contracts (for example, those on stock indices and Eurodollars) are settled in cash
IC 301
26
Mechanics of futures trading – Terminology : Types of Orders
Limit
Stop-loss
Stop-limit
Market
Market-if touched
Discretionary
Time of day
Open
Good till cancelled (GTC)
Fill or kill
IC 301
27
27
Forward Contracts vs Futures Contracts
(Table 2.3, page 65)
IC 301
28
Contract usually closed out
Private contract between 2 parties
Exchange traded
Non-standard contract
Standard contract
Usually 1 specified delivery date
Range of delivery dates
Settled at end of contract
Settled daily
Delivery or final cash
settlement usually occurs
prior to maturity
FORWARDS
FUTURES
Some credit risk
Virtually no credit risk
16
Optimal Hedge Ratio (page 81)
Proportion of the exposure that should optimally be hedged is
where
sS is the standard deviation of DS, the change in the spot price during the hedging period,
sF is the standard deviation of DF, the change in the futures price during the hedging period
r is the coefficient of correlation between DS and DF.
IC301
29
h* minimum variance hedge ratio (slope of best fit line from linear regression of ΔS against ΔF – see figure 3.2)
Example (Page 83)
Airline will purchase 2 million gallons of jet fuel in one month and hedges using heating oil futures
From historical data sF =0.0313, sS =0.0263, and r= 0.928
Contracts needed to hedge:
0.78*2,000,000/42,000 = 37 to be sold
[42,000 gallons is one contract on the CME]
IC301
30
If correl coeff is 1 and std spot = std fut then h* is 1 (to 1) i.e. futures price mirrors spot perfectly
30
Hedging Using Index Futures
(Page 86)
To hedge the risk in a portfolio the number of contracts that should be shorted is
where VA is the value of the portfolio, b is its beta, and VF is the value of one futures contract
IC301
31
Example
S&P 500 futures price is 1,010
Value of Portfolio is $5.05 million
Beta of portfolio is 1.5
1 futures contract = $250 x index
What position in futures contracts on the S&P 500 is necessary to hedge the portfolio?
IC301
32
Va = 5,050,000 Vf = 1010*250=252,500 … so 1.5(5,050,000/252,500)= 30 contracts see page 87 Hull
Changing Beta
What position is necessary to reduce the beta of the portfolio to 0.75?
What position is necessary to increase the beta of the portfolio to 2.0?
IC301
33
Why hedge Equity Returns?
May want to be out of the market for a while. Hedging avoids the costs of selling and repurchasing the portfolio
Suppose stocks in your portfolio have an average beta of 1.0, but you feel they have been chosen well and will outperform the market in both good and bad times. Hedging ensures that the return you earn is the risk-free return plus the excess return of your portfolio over the market.
IC301
34
F
S
h
s
s
r
=
*
*
0.0263
0.9280.78
0.0313
h
=´=
F
A
V
V
b
/docProps/thumbnail.jpeg