Chapter 27

Irwin/McGraw-Hill

27-27-11 The McGraw-Hill Companies, Inc., 1999

INVESTMENTSFourth Edition

Bodie Kane Marcus

Risk ManagementRisk Managementand Hedgingand Hedging

Chapter 27Chapter 27

Irwin/McGraw-Hill



Bodie Kane Marcus

Hedging Foreign Exchange RiskHedging Foreign Exchange Risk

US firm wants to protect against a decline in profit that would result from a decline in the pound

Estimated profit loss of $200,000 if the pound declines by $.10

Short or sell pounds for future delivery to avoid the exposure

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Bodie Kane Marcus

Hedge Ratio for Foreign Exchange Hedge Ratio for Foreign Exchange ExampleExample

Hedge Ratio in pounds

$200,000 per $.10 change in the pound/dollar exchange rate

$.10 profit per pound delivered per $.10 in exchange rate

= 2,000,000 pounds to be delivered

Hedge Ratio in contacts

Each contract is for 62,500 pounds or $6,250 per a $.10 change

$200,000 / $6,250 = 32 contracts

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Bodie Kane Marcus

Hedging Systematic RiskHedging Systematic Risk

To protect against a decline in level stock prices, short the appropriate number of futures index contracts

Less costly and quicker to use the index contracts

Use the beta for the portfolio to determine the hedge ratio

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Bodie Kane Marcus

Hedging Systematic Risk: Hedging Systematic Risk: Text ExampleText Example

Portfolio Beta = .8 S&P 500 = 1,000

Decrease = 2.5% S&P falls to 975

Portfolio Value = $30 million

Project loss if market declines by 2.5% = (.8) (2.5) = 2%

2% of $30 million = $600,000

Each S&P500 index contract will change $6,250 for a 2.5% change in the index

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Bodie Kane Marcus

Hedge Ratio: Text ExampleHedge Ratio: Text Example

H =

=

Change in the portfolio value

Profit on one futures contract

$600,000

$6,250= 96 contracts short

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Bodie Kane Marcus

Uses of Interest Rate HedgesUses of Interest Rate Hedges

Owners of fixed-income portfolios protecting against a rise in rates

Corporations planning to issue debt securities protecting against a rise in rates

Investor hedging against a decline in rates for a planned future investment

Exposure for a fixed-income portfolio is proportional to modified duration

Irwin/McGraw-Hill



Bodie Kane Marcus

Hedging Interest Rate Risk: Hedging Interest Rate Risk: Text ExampleText Example

Portfolio value = $10 million

Modified duration = 9 years

If rates rise by 10 basis points (.1%)

Change in value = ( 9 ) ( .1%) = .9% or $90,000

Present value of a basis point (PVBP) = $90,000 / 10 = $9,000

Irwin/McGraw-Hill



Bodie Kane Marcus

Hedge Ratio: Text ExampleHedge Ratio: Text Example

H =

=

PVBP for the portfolio

PVBP for the hedge vehicle

$9,000

$90= 100 contracts

Irwin/McGraw-Hill



Bodie Kane Marcus

Hedging On Mispriced OptionsHedging On Mispriced Options

Option value is positively related to volatility If an investor believes that the implied

volatility that is implied in an option’s price is too low, a profitable trade is possible

Profit must be hedged against a decline in the value of the stock

Performance depends on option price relative to the implied volatility

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Bodie Kane Marcus

Hedging and DeltaHedging and Delta

The appropriate hedge will depend on the delta

Recall from Chapter 21 the delta is the change in the value of the option relative to the change in the value of the stock

Delta = Change in the value of the option

Change of the value of the stock

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Bodie Kane Marcus

Mispriced Option: Text ExampleMispriced Option: Text Example

Implied volatility = 33%

Investor believes volatility should = 35%

Option maturity = 60 days

Put price P = $4.495

Exercise price and stock price = $90

Risk-free rate r = 4%

Delta = -.453

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Bodie Kane Marcus

Hedged Put PortfolioHedged Put Portfolio

Cost to establish the hedged position

1000 put options at $4.495 / option $ 4,495

453 shares at $90 / share 40,770

Total outlay 45,265

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Bodie Kane Marcus

Profit Position on Profit Position on Hedged Put PortfolioHedged Put Portfolio

Value of put option as function of stock price: implied vol. = 35%Stock Price 89 90 91

Put Price $5.254 $4.785 $4.347

Profit (loss) for each put .759 .290 (.148)

Value of and profit on hedged portfolio

Stock Price 89 90 91

Value of 1,000 puts $ 5,254 $ 4,785 $ 4,347

Value of 453 shares 40,317 40,770 41,223

Total 45,571 45,555 45,570

Profit 306 290 305

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Bodie Kane Marcus

Hedging Demands on Hedging Demands on Capital Market EquilibriumCapital Market Equilibrium

CAPM assume that investors face only risk about the uncertain value of securities

Many additional elements of risk are present

- Uncertain prices on consumption, energy or housing

- Uncertain future interest rates Hedging activity associated with these elements of

risk are consistent with the multifactor arbitrage pricing model

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Chapter 27