P1.T3. Hull, Chapter 3 Bionic Turtle FRM Video Tutorials ... · Agenda • Hull, Options, Futures,...

P1.T3. Hull, Chapter 3

Bionic Turtle FRM Video Tutorials

By: David Harper CFA, FRM, CIPM

Note: This tutorial is for paid members only. You know who you are. Anybody else is using an illegal copy and also violates GARP’s ethical standards.

Agenda

• Hull, Options, Futures, andOther Derivatives (8th Edition) – Chapter 3: Hedging Strategies Using Futures


2

Learning Spreadsheets


WorkbookExam Relevance(XLS not topic) Spreadsheets

T3.12.3 Futures Hedge High 12.3. Minimum Variance Hedge

Medium 12.3. Basis Risk

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3

Hull, Chapter 3: Hedging Strategies Using Futures

4

Define and differentiate between short and long hedges and identify situations where they are appropriate.

P1.T3. Hull, Chapter 3: Hedging Strategies Using Futures

Long forward (or futures) hedge: agreement to buy in the future

A short forward (or futures) hedge: agreement to sell in the future

Hedger does not currently own the asset. Expects to purchase in the future.

Hedger already owns the asset.

An airline depends on jet fuel. Enters into futures contract (a long hedge)to protect from exposure to high oil prices

Farmer wants to lock in a sales price to protect against a price decline.

5

In favor of hedgingIn favor of hedging

• Companies should focus on their core business and minimize risks arising from financial variables and market variables (e.g., interest rates, exchange rates)

Against hedgingAgainst hedging

• Shareholders are diversified and can make their own hedging decisions

• May increase risk to hedge when competitors do not

• Explaining a loss on the hedge (if gain on the underlying) can be difficult


Describe the arguments for and against hedging and the potential impact of hedging on firm profitability.

6

Define and compute the basis.

Basis =

Spot Price (S0) minus (–) Futures Price (F0)

= S0 – F0


$3.80

$4.00

$4.20

$4.20

$0.20 $0.00

$3.80

$4.00

$4.20

$4.20

$0.20 $0.00

Financial Assets:Futures Price (F0) – Spot Price (S0)

Financial Assets:Futures Price (F0) – Spot Price (S0)

7



Basis “weakens” (decreases) from $0.20 to $0Basis “weakens” (decreases) from $0.20 to $0

May-13 May-14

Spot $4.00 $4.20

Futures $3.80 $4.20

Basis $0.20 $0.00

Spot ($4.20)

Futures (gain/loss) $0.40

Total cost ($3.80)

$0.20

$0.00

$3.80

$4.00

$4.20

$4.20

8



Company will buy: 25,000 lbs of copper in Sep-09Contract (pounds) 25,000Number of contracts 1

Forward in Time: Basis convergesMay-09 Sep-09 Sep-09 Sep-09

Spot $1.90 $1.95 $2.00 $2.05 Futures $2.00 $1.95 $2.00 $2.05 Basis ($0.10) $0.00 $0.00 $0.00

Unhedged CostCost ($48,750) ($50,000) ($51,250)

Long HedgeFutures gain, per lb ($0.05) $0.00 $0.05 Total Futures Gain ($1,250) $0 $1,250

Net Cost ($50,000) ($50,000) ($50,000)

9



Company will buy: 25,000Contract (pounds) 25,000Number of contracts 1

Basis Weakens (vs. expected 0)

Basis strengthens (vs. expected 0)

May-09 Sep-09 Sep-09Spot $1.90 $2.00 $2.00 Futures $2.00 $2.05 $1.95 Basis ($0.10) ($0.05) $0.05

Unhedged CostCost ($50,000) ($50,000)

Long HedgeFutures gain, per lb $0.05 ($0.05)Total Futures Gain $1,250 ($1,250)

Net Cost ($48,750) ($51,250)

10

Define the various sources of basis risk and explain how basis risks arise when hedging with futures.


• Strengthening of the basis: Spot price increases by more than the futures price basis increases. – If unexpected, strengthening is favorable for a short hedge and

unfavorable for a long hedge

• Weakening of the basis: Futures price increases by more than the spot price basis declines – If unexpected, weakening is favorable for a long hedge and unfavorable for

a short hedge

11

Define the various sources of basis risk and explain how basis risks arise when hedging with futures.

• But basis risk arises because often the characteristics of the futures contract differ from the underlying position.– Contract ≠ Commodity.

– Contract is standardized (e.g., WTI oil futures)– Commodities are not exactly commodities (e.g., hedger has a position in

different grade of oil)


Trade-offLiquidity(exchange)

Basis risk

12

Define cross hedging.

• Cross hedge: When asset underlying hedge is different from asset being hedged


Hedging purchaseof jet fuel

Not futures for jet fuelso use heating oil

13

Define, compute and interpret the minimum variancehedge ratio and hedge effectiveness.

• The optimal hedge ratio (a.k.a., minimum variance hedge ratio) is the ratio of futures position relative to the spot position that minimizes the variance of the position.

σS standard deviation of ΔS, change in spotσ F standard deviation of ΔF, change in futures ρ is the coefficient of correlation between Δ S and Δ F.


* S

F

h *

* A

F

h QN

Q

14



Spot

Forward

Regressing Spot on Forward

15



(heating oil futures)

(jet fuelspot)

Standard Dev $3.13 $2.63Correlation 0.928(MV) Hedge ratio 0.78

Airline will purchase 2,000,000NYMEX oil futures (gallons) 42,000Number of contracts 37.01

2.63

* (0.928)3.13

S

F

h

* 0.78 2,000,000*

42,000A

F

h QN

Q

16 16

Define, compute and interpret the optimal number of futures contracts needed to hedge an exposure …

• For example, if the volatility of the spot price is 20%, the volatility of the futures price is 10%, and their correlation is 0.4, then:


* S

F

h20%

* (0.4) 0.810%

h

Number of contracts

Number of contracts

** A

F

h NN

Q

17

… including a “tailing the hedge” adjustment.

Tailing the hedge:• Replace units with values:

• The net effect is to multiply the original hedge ratio by the ratio of [spot price/futures price]


*

* A

F

h VN

V

** A

F

h QN

Q

18

Demonstrate how stock index futures contracts can be used to change a stock portfolio’s beta.

• Given

– a portfolio beta (), – Current value of the portfolio (P), and – Value of stocks underlying one futures contract (A),

• The number of stock index futures contracts (i.e., minimizes the portfolio variance) is given by:


PN

A

19


• When the goal is to shift portfolio beta from () to a target beta (*), the number of contracts required is given by:


( * )P

NA

20


• Assume:– Value of portfolio is $10 million– S&P 500 Futures Price = 1240

– Portfolio beta () is 1.5– Contract = $250 × Index– Target beta = 1.2


We short ~ 9.7 contracts. (-) = short (+) = long

We short ~ 9.7 contracts. (-) = short (+) = long

$10,000,000

( * ) (1.2 1.5) 9.7(1240)(250)

PN

A

21

Describe what is meant by “rolling the hedge forward” and discuss some of the risks that arise from such a strategy.

• When the delivery date of the futures contract occurs prior to the expiration date of the hedge, the hedger can roll forward the hedge: close out a futures contract and take the same position on a new futures contract with a later delivery date.

• Exposed to:– Basis risk (original hedge)– Basis risk (each new hedge) = “rollover basis risk”


22

End of P1.T3. Hull, Chapter 3

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