Reading 38: Risk Management Applications of Forward and Fu adjust, between, allocation

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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 d: Demonstrate the use of equity and bond futures to adjust the allocation of a portfolio between equity and debt.

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The performance of a synthetically reallocated portfolio, e.g., a synthetic adjustment from stocks to bonds, would not exactly match the target position for all of the following reasons EXCEPT:

A) rounding of the number of contracts used.

B) the risk free rate is not zero.

C) the assets and futures prices are not perfectly correlated.

D) duration is not constant.

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Answer and Explanation

The risk free rate does not enter into the formulas for determining the strategy for synthetically adjusting a stock/bond portfolio. Although the risk free rate may play a role in some futures strategies to synthetically adjust a portfolio, the effectiveness of the strategy would not depend upon its value.

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A manager has a 70/30 stock and bond portfolio. To synthetically create a portfolio that is 60 percent stock and 40 percent bonds, the manager should:

A) short the bond futures and go long the stock index futures.

B) short both bond futures and stock index futures.

C) go long the bond futures and short the stock index futures.

D) go long both bond futures and stock index futures.

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Answer and Explanation

This move will accomplish the goal by reducing the exposure to equity and increasing the exposure to bonds.

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A manager has a $100 million portfolio that consists of 50 percent stock and 50 percent bonds. The beta of the stock position is 1. The modified duration of the bond position is 5. The manager wishes to achieve an effective mix of 60 percent stock and 40 percent bonds. The price and beta of the stock index futures contracts are $277,000 and 1.1 respectively. (The futures price includes the effect of the index multiplier.) The price, modified duration, and yield beta of the futures contracts are $98,000, 6, and 1 respectively. The duration on cash is 0.2. What is the appropriate strategy?

A) Short 82 bond futures and go long 33 stock index futures.

B) Short 40 bond futures and go long 106 stock index futures.

C) Go long 106 bond futures and go short 40 stock index futures.

D) Go long 53 bond futures and go long 40 stock index futures.

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Answer and Explanation

Since the manager wishes to increase the equity position and decrease the bond position by $10 million (10 percent of $100 million), the correct strategy is to take a short position in the bond futures, use the cash from the sale of the bond futures to take a long position in the stock index futures:

number of bond futures = -81.63 = [(0.20-5)/6]($10,000,000/$98,000)

number of stock futures = 32.82 = [(1 - 0)/1.1]($10,000,000/$277,000)

Since the manager wishes to increase the equity position and decrease the bond position by $10 million (10 percent of $100 million), the correct strategy is to take a short position in the bond futures, use the cash from the sale of the bond futures to take a long position in the stock index futures:

number of bond futures = -81.63 = [(0.20-5)/6]($10,000,000/$98,000)

number of stock futures = 32.82 = [(1 - 0)/1.1]($10,000,000/$277,000)