Week 6

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INVESTMENTS | BODIE, KANE, MARCUS

Direct Versus Indirect Quotes

• Direct exchange rate quote:
• The exchange rate is expressed as dollars per unit of foreign currency
• Indirect exchange rate quote:
• The exchange rate is expressed as foreign currency units per dollar

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INVESTMENTS | BODIE, KANE, MARCUS

Hedging Foreign Exchange Risk

A US exporter wants to protect against a decline in profit that would result from depreciation of the pound. The current futures price is $2/£1. Suppose FT = $1.90?

• The exporter anticipates a 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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INVESTMENTS | BODIE, KANE, MARCUS

Hedge Ratio for Foreign Exchange Example

Hedge Ratio in contracts

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

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

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INVESTMENTS | BODIE, KANE, MARCUS

Figure 23.3 Profits as a Function of the Exchange Rate

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INVESTMENTS | BODIE, KANE, MARCUS

Stock Index Contracts

• Available on both domestic and international stocks
• Settled in cash
• Advantages over direct stock purchase
• lower transaction costs
• better for timing or allocation strategies
• takes less time to acquire the portfolio

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INVESTMENTS | BODIE, KANE, MARCUS

Table 23.1 Major Stock-Index Futures

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INVESTMENTS | BODIE, KANE, MARCUS

Table 23.2 Correlations among Major U.S. Stock Market Indexes

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INVESTMENTS | BODIE, KANE, MARCUS

Creating Synthetic Positions
with Futures

• Index futures let investors participate in broad market movements without actually buying or selling large amounts of stock.
• Results:
• Cheaper and more flexible
• Synthetic position; instead of holding or shorting all of the actual stocks in the index, you are long or short the index futures

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INVESTMENTS | BODIE, KANE, MARCUS

Creating Synthetic Positions
with Futures

• Speculators on broad market moves are major players in the index futures market.
• Strategy: Buy and hold T-bills and vary the position in market-index futures contracts.
• If bullish, then long futures
• If bearish, then short futures

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INVESTMENTS | BODIE, KANE, MARCUS

Index Arbitrage

Exploiting mispricing between underlying stocks and the futures index contract

• Futures Price too high - short the future and buy the underlying stocks
• Futures price too low - long the future and short sell the underlying stocks

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INVESTMENTS | BODIE, KANE, MARCUS

Index Arbitrage and Program Trading

• This is difficult to implement in practice
• Transactions costs are often too large
• Trades cannot be done simultaneously
• Other traders may act first

• Development of Program Trading
• Used by arbitrageurs to perform index arbitrage
• Permits quick acquisition of securities

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INVESTMENTS | BODIE, KANE, MARCUS

Hedging Systematic Risk

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

• Less costly and quicker
• Use the beta for the portfolio to determine the hedge ratio.

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INVESTMENTS | BODIE, KANE, MARCUS

Hedging Systematic Risk
Example

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

Decrease = 2.5% S&P falls to 975

Portfolio Value = $30 million

Projected 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. (The contract multiplier is $250).

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INVESTMENTS | BODIE, KANE, MARCUS

Hedge Ratio Example

H =

=

Change in the portfolio value

Profit on one futures contract

$600,000

$6,250

= 96 contracts short

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INVESTMENTS | BODIE, KANE, MARCUS

Figure 23.4 Predicted Value of the Portfolio as a Function of the Market Index

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INVESTMENTS | BODIE, KANE, MARCUS

Uses of Interest Rate Hedges

• A bond fund manager may seek to protect gains against a rise in rates.
• Corporations planning to issue debt securities want to protect against a rise in rates.
• A pension fund with large cash inflows may hedge against a decline in rates for a planned future investment.

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INVESTMENTS | BODIE, KANE, MARCUS

Hedging Interest Rate Risk
Example

Portfolio value = $10 million

Modified duration = 9 years

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

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

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

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INVESTMENTS | BODIE, KANE, MARCUS

Hedge Ratio Example

H =

=

PVBP for the portfolio

PVBP for the hedge vehicle

$9,000

$90

= 100 T-Bond contracts

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INVESTMENTS | BODIE, KANE, MARCUS

Hedging

• The T-bond contracts drive the interest rate exposure of a bond position to zero.
• This is a market neutral strategy. Gains on the T-bond futures offset losses on the bond portfolio.
• The hedge is imperfect in practice because of slippage – the yield spread does not remain constant.

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INVESTMENTS | BODIE, KANE, MARCUS

Figure 23.5 Yield Spread

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INVESTMENTS | BODIE, KANE, MARCUS

Swaps

• Swaps are multi-period extensions of forward contracts.

• Credit risk on swaps

• An interest rate swap calls for exchanging cash flows based on a fixed rate for cash flows based on a floating rate.
• The foreign exchange swap calls for an exchange of currencies on several future dates.

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INVESTMENTS | BODIE, KANE, MARCUS

Interest Rate Swap: Text Example

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INVESTMENTS | BODIE, KANE, MARCUS

The Swap Dealer

• Dealer enters a swap with Company A
• Pays fixed rate and receives LIBOR
• Dealer enters another swap with Company B
• Pays LIBOR and receives a fixed rate
• When two swaps are combined, dealer’s position is effectively neutral on interest rates.

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INVESTMENTS | BODIE, KANE, MARCUS

Figure 23.6 Interest Rate Swap

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INVESTMENTS | BODIE, KANE, MARCUS

Figure 23.7 Interest Rate Futures

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INVESTMENTS | BODIE, KANE, MARCUS

Pricing on Swap Contracts

Swaps are essentially a series of forward contracts.

We need to find the level annuity, F *, with the same present value as the stream of annual cash flows that would be incurred in a sequence of forward rate agreements.