Reading 38: Risk Management Applications of Forward and Fu stock

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CFA Institute Area 8-11, 13: Asset Valuation
Session 13: Risk Management Applications of Derivatives
Reading 38: Risk Management Applications of Forward and Futures Strategies
LOS b: Construct a synthetic stock index fund using cash and stock index futures (equitizing cash).

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When using stock index futures contracts and cash to create a synthetic stock index, the larger the index multiplier:

A) the greater the number of needed contracts.

B) the number of contracts is not affected.

C) there is no such thing as an index multiplier.

D) the fewer the number of needed contracts.

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Answer and Explanation

The formula is:

Number of contracts_Unrounded = (V*(1 + risk free rate)^T) / (futures price * multiplier)

As the multiplier increases, the number of needed contracts declines.

The formula is:

Number of contracts_Unrounded = (V*(1 + risk free rate)^T) / (futures price * multiplier)

As the multiplier increases, the number of needed contracts declines.

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Which of the following statements about portfolio hedging is FALSE?

A) Futures contracts have a symmetrical payoff profile.

B) To synthetically create the risk/return profile of an underlying common equity security, buy the corresponding futures contract, sell the common short, and invest in a T-bill.

C) For a fixed portfolio insurance horizon, using put options generally requires less rebalancing and monitoring than with the use of futures contracts.

D) The delta of the call option changes as the market value of the underlying security changes. Rebalancing is therefore necessary to maintaining a delta neutral portfolio position.

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Answer and Explanation

To synthetically create the risk/return profile of an underlying common equity security, buy the corresponding futures contract and invest in a T-bill.

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To create a synthetic cash position:

A) buy the common equity, sell short the corresponding futures contract, invest in a T-bill.

B) buy the common equity and sell short the corresponding futures contract.

C) sell short the common equity, buy the corresponding futures contract.

D) sell short the common equity, buy the corresponding futures contract, invest in a T-bill.

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Answer and Explanation

Security Futures = Cash, therefore, buy the common equity and sell short the corresponding futures contract.

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To synthetically create the risk/return profile of an underlying common equity security:

A) Sell short the corresponding futures contract and invest in a T-bill.

B) Buy the corresponding futures contract and borrow at the risk-free rate.

C) Sell short the corresponding futures contract and borrow at the risk-free rate.

D) Buy the corresponding futures contract and invest in a T-bill.

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Answer and Explanation

Futures + Cash = Security, therefore, buy the corresponding futures contract and invest in a T-bill.

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An investor has a $100 million stock portfolio with a beta of 1.1. He would like to hedge his portfolio using S& 500 futures contracts, which are currently trading at 596.70. The futures contract has a multiple of 250. Which of the following is the CORRECT trade required to create a synthetic T-bill?

A) Buy 670 contracts.

B) Sell 670 contracts.

C) Buy 737 contracts.

D) Sell 737 contracts.

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Answer and Explanation

The position created by risk-minimizing hedging is essentially the creation of a synthetic T-Bill. The number of futures contracts required for the risk-minimizing hedge is computed as follows:

Number of contracts = Portfolio value/Futures contract value x beta
$100 million/(596.70 x $250) x 1.1 = 737 contracts

Therefore, the investor has to sell 737 S& 500 futures contracts short.

The position created by risk-minimizing hedging is essentially the creation of a synthetic T-Bill. The number of futures contracts required for the risk-minimizing hedge is computed as follows:

Number of contracts = Portfolio value/Futures contract value x beta
$100 million/(596.70 x $250) x 1.1 = 737 contracts

Therefore, the investor has to sell 737 S& 500 futures contracts short.

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An investor has a cash position currently invested in T-Bills but would like to "equitize" it by using S& futures contracts. Which of the following trades will create the desired synthetic equity position?

A) Buying S& 500 futures contracts.

B) Selling S& 500 futures contracts short.

C) Selling the T-Bills and buying S& 500 futures contracts.

D) Selling the T-Bills and selling S& 500 futures contracts.

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Answer and Explanation

The trader can buy stock index futures and hold them in conjunction with T-Bills to mimic a stock portfolio. So we have:

Synthetic stock portfolio =T-Bills + stock index futures.

The trader can buy stock index futures and hold them in conjunction with T-Bills to mimic a stock portfolio. So we have:

Synthetic stock portfolio =T-Bills + stock index futures.