copyright 2014 by diane s. docking1 risk management: hedging with futures

Copyright 2014 by Diane S. Docking 1

Risk Management:Hedging with Futures

Learning Objectives

• Know how risk can be hedged with forward and futures contracts

• Distinguish a microhedge from a macrohedge

• Be able to construct a micro- and macro-hedge


Hedging with Financial Futures

contracts



Purpose of Trading Financial Futures

To Speculate_ – Take a position with the goal of profiting from

expected changes in the contract’s price– No position in underlying asset (naked

position)– Used by risk seekers

To Hedge_– Minimize or manage risks– Have position (or soon will have a position) in

spot market with the goal to offset risk– Used by the risk averse


Long vs. Short Hedges

Long Hedge (Anticipatory Hedge)• Involves purchasing futures contracts now as a

temporary substitute for the purchase of the cash market commodity at a later date

• Purpose is to lock in a __________ price

Short Hedge• Initiate with a sale of a futures contract as a temporary

substitute for a later cash market sale of the underlying asset.

• Purpose is to lock in a __________ price


Long Hedge• Lock in buying price• Lock in inventory purchase

prices• Lay off (transfer) price risk• Avoid lower than expected

yields from loans and securities investments

• To protect against changing FX rates

Why Hedge?

Short Hedge:• Lock in selling price • Protect inventory value• Avoid higher borrowing costs• Avoid declining investment

portfolio values• To protect against changing

FX rates


Micro vs. Macro Hedge

Micro Hedge

A hedge strategy designed to reduce risk of a transaction associated with a specific asset, liability, or commitment or a portfolio of similar assets

Macro Hedge

A hedge strategy designed to reduce risk associated with a bank’s entire balance sheet position or portfolio of dissimilar assets.


Steps in Executing a Hedge• Step 1: Identify cash market risk/exposure• Step 2: Determine long or short hedge• Step 3: Decide on futures contract to use• Step 4: Determine number of contracts• Step 5: Execute hedge• Step 6: Unwind hedge before expiration of

futures and compute net gain or loss on hedge

Copyright 2014 by Diane S. Docking

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Determining number of contracts for a Microhedge

brPD

PD

ff

cc

fN

Where:Dc = Duration in cash marketPc = Price in cash marketDf = Duration of futures contract

Pf = Price of futures contractbr = change in futures prices/change in spot prices

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Example: Micro-Hedging Bonds with T-bond Futures

• Julie wants to protect the value of $100,000,000 of bonds over the near term . How best does she do this?

• She knows the following:– The duration of these bonds is 8 years.– The duration of the underlying T-bond futures is 6.5 years– br = 1.111– The T-bond futures contract with 6-months to expiration is as

follows:Treasury Notes (CBT) - $100,000; pts. 32nds of 100%

Open High Low Settle Chg.

6-months 114’215 115’020 109’225 110’000 -0’165


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Solution to Example: Micro-Hedging Bonds with T-bond Futures

• Julie needs to ____________ the futures contracts.

• How many futures contracts does she need to sell?

Ksbr

09.007,1111.1000,110$5.6

000,000,100$8

PVD

PVD N

ff

ccf


Always round DOWN

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Example: Micro-Hedging Bonds with T-bond Futures (cont.)

• Julie decides to sell 1,007 near-term futures contracts.

• Over the next month, interest rates increase 1%.• The T-bond futures price falls to 102’27. (There are five

months left in the futures contract)

• How did this short hedge perform?

• That is, how much protection did selling futures contracts provide to her bonds?


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Solution to Example: Micro-Hedging Bonds with T-bond Futures (cont.)

Portfolio Futures market

(Cash Mkt) Price Quote

t0:

Current bonds value $100,000,000

Sell futures contracts at F0 110.00

t1-month:

Current bonds value

$100 mill. +[-8 x (+.01) x $100 mill.] $ 92,000,000

Unwind hedge:

Buy futures contracts at F1 (102 27/32) <102.84375>

Loss in portfolio value <$ 8,000,000>

Gain in futures market 7.15625Copyright 2014 by Diane S. Docking

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Solution to Example: Micro-Hedging Bonds with T-bond Futures (cont.)

Total Loss in bonds: = <$8,000,000>

Total Gain in Futures market:

7.15625 x $1,000 x 1,007Ks = $7,206,343.75

Net gain/<loss> on hedge < $793,656.25>

Value of bonds at t1-month, including hedge effects:

$92,000,000 + $7,206,344= $99,206,344

Or

$100,000,000 - $793,656 = $99,206,344



Basis Risk

Basis in a futures contract is (in prices):

Basist = Spott - Futurest

Basis in a futures contract is (in interest rates):

Basist = Futurest - Spott

Example: Change in basis hedge – Eurodollar portfolio

• Union State Bank expects to receive a $100 million loan repayment in a few weeks. The Bank plans on investing the proceeds in 90-day Eurodollar deposits currently offering 1.42%. The bank is forecasting that ED rates will decrease in the next few weeks.

• How can the bank protect itself against a decrease in revenues using Eurodollar futures contracts? ED futures contracts expiring in 3 months are currently priced at 98.800. Assume br = 1.


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Solution to Example: Change in basis hedge – Eurodollar portfolio

• The bank needs to ____________ the futures contracts.

• How many futures contracts does the bank need to buy?

Where: Dc = (ED = 3 months = 3/12 = 0.25 yrs.)

Df= duration of underlying security (3-mo. ED) =3/12 = 0.25 yrs.

Pf = Settle = 98.800

Discount = 100 – 98.80 = 1.20% = 120 bp x $25 tick = $3,000

1 mill. – 3,000 = $997,000

Ksbr

10030.1001000,997$25.0

000,000,100$25.0

PVD

PVD N

ff

ccf


go long

Example: Change in basis hedge – Eurodollar portfolio

• Union State Bank receives the $100 million loan repayment in a few weeks. At this time rates on 90-day Eurodollar deposits have dropped to 1.22%. The ED futures contracts expiring in 3 months are now priced at 98.95.

• How did this hedge perform?


Solution to Example: Change in basis hedge – ED portfolio (cont.)

Cash Market Futures market Basis($/K)

t0:

Opportunity lost on EDs at S0 1.42% 98.58

Buy futures contracts at F0 1.20% 98.80 98.58 – 98.80 = -0.22%

-22 bp x $25 tick =

-$550 / K

t1-month:

Invest $100 million at ED spot of S1 1.22% 98.78

Unwind hedge:

Sell futures contracts at F1 1.05% 98.95 98.78 – 98.95 = -0.17%

-17 bp x $25 tick =

-$425 / K +0.05%

Opportunity Loss in cash market <0.20%>

Gain in futures market 0.15%

Change in basis +$125/KCopyright 2014 by Diane S. Docking 19


How did this hedge perform? (cont.)

Total Loss in cash market (lost interest revenue on EDs):

$100 mill. x 0.0020 x 90/360 = <$50,000>


0.15% = 15 bp x $25 tick x 100 Ks = $37,500

Net loss on hedge < $12,500>*

*Note: Change in basis = +$125/K x 100 Ks = $12,500. Were long a contract and basis narrowed; therefore, this results in a net loss on the hedge.



What is the Bank’s effective interest revenue on this ED investment?Actual ED revenue = 100 mill. x .0122 x 0.25 = $305,000Gain on futures = 15 bp x $25 tick x 100 Ks = 37,500 Net 3-month interest revenue on ED = $342,500

Annualized rate: (342,500/100 mill.) x (360/90) = 1.37%

ORWhat is the Bank’s effective interest revenue?

Original ED rate = 1.42%- change in basis = - 0.05%

Spread = 1.37%

Had Bank not hedged?Interest revenue = 1.22%



Determining number of contracts for a Macrohedge

where Nf = number of futures contractsDGAPK = Duration Gap of bank capital or portfolio duration*.TA = total assets of bank or portfolioDf = duration of futures contractPf = current price of futures contractbr = change in futures prices/change in spot prices

brff

P D

TA DGAPN K

f


Example: Immunize Financial Institution Balance Sheet(Remember from DGAP Management)

Given the average duration items from First NationalBank’s Balance Sheet (see next slide), we calculated theDuration Gap of capital and saw what happens if interest rates decrease from 6% to 4.5%. (See next slides)

Example: Immunize Financial Institution Balance Sheet (cont.)

First National BankAmount Duration Weight Wtd.Duration($ millions) (years) (%) (years)

AssetsReserve and cash items 5 0.0 5% 0.000Securities Less than 1 year 5 0.4 5% 0.020 1 to 2 years 5 1.6 5% 0.080 Greater than 2 years 5 5.5 5% 0.275Residential mortgages Variable-rate 10 0.5 10% 0.050 Fixed-rate (30-year) 10 6.0 10% 0.600Commercial loans Less than 1 year 25 0.7 25% 0.175 1 to 2 years 20 1.4 20% 0.280 Greater than 2 years 5 2.3 5% 0.115Physical capital 10 0.0 10% 0.000 Total Assets 100 100% DA 1.595

LiabilitiesCheckable deposits 5 0.1 5% 0.005MMDAs 6 0.5 6% 0.032Savings deposits 8 1.0 8% 0.084CDs Variable-rate 3 0.5 3% 0.016 Less than 1 year 5 0.2 5% 0.011 1 to 2 years 15 1.9 16% 0.300 Greater than 2 years 23 5.6 24% 1.356Fed funds 5 0.0 5% 0.000Borrow ings Less than 1 year 2 0.3 2% 0.006 1 to 2 years 8 1.5 8% 0.126 Greater than 2 years 15 5.3 16% 0.837 Total Liabilities 95 100% DL 2.773 DGAPK -1.039

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• $ D in K if rates decrease:

TE_current $5,000,000

K <$1,470,283>

TE_new $3,529,717

Ai1

ΔiDGAPΔK

0K

$1,470,283 million 100$1.06

.0151.039-ΔK

Regulatory capital requirements could be in trouble and bank in danger of being declared insolvent!



You want to protect the capital of the bank over the next 3 months.

How best can you do this using T-bond futures contracts expiringin 6 months, with a duration on 6.5 years?

Treasury Notes (CBT) - $100,000; pts. 32nds of 100%

Open High Low Settle Chg.

6-months 114’215 115’020 109’225 110’000 -0’165


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Solution to Example: Immunize Financial Institution Balance Sheet

1. How can the Bank hedge this risk?– If interest rates decrease, prices increase; therefore a futures

contract.

2. How many futures contracts does the bank need to buy?

contracts

315.145

$110,000 x .56

000000100x 1.039-

P x D

TAx DGAP N

ff

Kf

,,

28


• Assume that over the next three months, interest rates decrease 1.60% to 4.4%.

• The T-bond futures price rises to 120’24. (There are three months left in the futures contract)

• How did this long hedge perform?


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Solution to Example: Immunize Financial Institution Balance Sheet (cont.)

3. How did this long hedge perform? Capital Futures

market

(Cash Mkt) Price Quote

t0:

Current capital balance $5,000,000

Buy futures contracts at F0 < 110.00>

t3-month:

Current capital balance

$5 mill. – 1,568,302** = $3,431,698

Unwind hedge:

Sell futures contracts at F1 120.75

**Change in Capital if rates decrease 1.6%:

- (-1.039) x (-.016/1.06) x $100 mill. = <$1,568,302>

Gain in futures market 10.75Copyright 2014 by Diane S. Docking

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Solution to Example: Immunize Financial Institution Balance Sheet (cont.)

3. How did this long hedge perform? (cont.)

Total Loss in capital = <$1,568,302>


10.75 x $1,000 = $10,750/K

$10,750/K x 145Ks = $1,558,750

Net gain/<loss> on hedge <$ 9,552>

4. Capital value with macro hedge =

$5 mill – 9,552 = $4,990,448



Complications in using financial futures

• Accounting and regulatory guidelines.• Macrohedge of the bank’s entire portfolio -- cannot defer gains and

losses on futures, so earnings are less stable with this hedge strategy.• Microhedge linked to a specific asset -- can defer gains and losses

on futures until contracts mature.• Basis risk is the difference between the cash and futures prices.

These two prices are not normally perfectly correlated (e.g., corporate bond rates in a cash position versus T-bill futures rates).

• Bank gaps are dynamic and change over time.• Futures options allow the execution of the futures position only to

hedge losses in the cash position. Gains in the cash position are not offset by losses in the futures position.

copyright 2014 by diane s. docking1 risk management: hedging with futures

Documents

hedge slide

futures slide

hedge strategy

price slide

macro hedge copyright

short hedge step

expiration of futures

futures priceschange