Reading 38: Risk Management Applications of Forward and Fu equity, adjust, across, 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 e, (Part 1): Demonstrate the use of futures to adjust the allocation of a portfolio across equity sectors.

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A manager wishes to make a synthetic adjustment of a mid-cap stock portfolio. The goal is to increase the beta of the portfolio by 0.5. The beta of the futures contract the manager will use is one. If the value of the portfolio is 10 times the futures price, then the futures contract position needed is a:

A) short position in 5 contracts.

B) long position in 20 contracts.

C) short position in 20 contracts.

D) long position in 5 contracts.

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Answer and Explanation

We should recall our formula for altering beta,

number of contracts = ({target beta - B_portfolio }* V) / (B_futures * futures price)

the provided information gives:

number of contracts = 5 = 0.5*10*(futures price)/(1*futures price).

We should recall our formula for altering beta,

number of contracts = ({target beta - B_portfolio }* V) / (B_futures * futures price)

the provided information gives:

number of contracts = 5 = 0.5*10*(futures price)/(1*futures price).

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A manager of $30 million in mid-cap equities would like to move half of the position to an exposure resembling small-cap equities. The beta of the mid-cap position is 1.0, and the average beta of small-cap stocks is 1.6. The betas of the corresponding mid and small-cap futures contracts are 1.05 and 1.5 respectively. The mid and small-cap futures prices are $260,000 and $222,222 respectively. What is the appropriate strategy?

A) Short 17 mid-cap futures and go long 17 small-cap futures.

B) Short 17 small-cap futures and go long 17 mid-cap futures.

C) Go long 48 mid-cap futures and go short 66 small-cap futures.

D) Short 55 mid-cap futures and go long 72 small-cap futures.

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Answer and Explanation

We should recall our formula for altering beta,

number of contracts = ({target beta - B_portfolio }* V) / (B_futures * futures price)

In this case, for the first step where we convert the mid-cap position to cash, V=$15 million, and the target beta is 0. The current beta is 1.0, and the futures beta is 1.05:

-54.95 = (0-1)*($15,000,000)/(1.05*$260,000)

The manager should short 55 of the futures on the mid-cap index. Then the manager should take a long position in the following number of contracts on the small-cap index:

72.00 = (1.6-0)*($15,000,000)/(1.5*$222,222)

Thus, the manager should take a long position in 72 of the contracts on the small-cap index.

We should recall our formula for altering beta,

number of contracts = ({target beta - B_portfolio }* V) / (B_futures * futures price)

In this case, for the first step where we convert the mid-cap position to cash, V=$15 million, and the target beta is 0. The current beta is 1.0, and the futures beta is 1.05:

-54.95 = (0-1)*($15,000,000)/(1.05*$260,000)

The manager should short 55 of the futures on the mid-cap index. Then the manager should take a long position in the following number of contracts on the small-cap index:

72.00 = (1.6-0)*($15,000,000)/(1.5*$222,222)

Thus, the manager should take a long position in 72 of the contracts on the small-cap index.

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A manager of $40 million of mid-cap equities would like to move $5 million of the position to large-cap equities. The beta of the mid-cap position is 1.1, and the average beta of large-cap stocks is 0.9. The betas of the corresponding mid and large-cap futures contracts are 1.1 and 0.95 respectively. The mid and large-cap futures prices are $252,000 and $98,222 respectively. What is the appropriate strategy? Short:

A) 29 mid-cap futures and go long 29 large-cap futures.

B) 29 large-cap futures and go long 29 mid-cap futures.

C) 20 mid-cap futures and go long 48 large-cap futures.

D) 23 mid-cap futures and go long 42 large-cap futures.

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Answer and Explanation

We should recall our formula for altering beta,

number of contracts = ({target beta - B_portfolio }* V) / (B_futures * futures price)

In this case, for the first step where we convert the mid-cap position to cash, V=$5 million, and the target beta is 0. The current beta is 1.1, and the futures beta is 1.1:

-19.84 = (0-1.1)*($5,000,000)/(1.1*$252,000)

The manager should short 20 of the futures on the mid-cap index. Then the manager should take a long position in the following number of contracts on the large-cap index:

48.23 = (0.9-0)*($5,000,000)/(0.95*$98,222)

Thus, the manager should take a long position in 48 of the contracts on the large-cap index.

We should recall our formula for altering beta,

number of contracts = ({target beta - B_portfolio }* V) / (B_futures * futures price)

In this case, for the first step where we convert the mid-cap position to cash, V=$5 million, and the target beta is 0. The current beta is 1.1, and the futures beta is 1.1:

-19.84 = (0-1.1)*($5,000,000)/(1.1*$252,000)

The manager should short 20 of the futures on the mid-cap index. Then the manager should take a long position in the following number of contracts on the large-cap index:

48.23 = (0.9-0)*($5,000,000)/(0.95*$98,222)

Thus, the manager should take a long position in 48 of the contracts on the large-cap index.

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The practice of taking long positions in futures contracts to create an exposure that converts a yet-to be received cash position into a synthetic equity or bond position is:

A) illegal.

B) called leveraging down.

C) called pre-investing.

D) not achievable with futures contracts.

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Answer and Explanation

This is the definition of pre-investing using futures contracts, and it is not illegal.

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A portfolio manager has a net long position in both stocks and bonds and no cash. When pre-investing a future cash inflow, to replicate the existing portfolio, using bond and stock futures, which of the following will most likely be TRUE? The manager will:

A) go long the stock futures but short the bond futures.

B) go long both stock and bond futures.

C) have to choose a single futures contract and net the bond and stock position.

D) go long the bond futures and short the stock futures.

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Answer and Explanation

Since the original portfolio is long in both stocks and bonds, the manager will go long both stock and bond futures contracts.

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A portfolio manager knows that a $10 million inflow of cash will be received in a month. The portfolio under management is 70 percent invested in stock with an average beta of 0.8 and 30 percent invested in bonds with a duration of 5. The most appropriate stock index futures contract has a price of $233,450 and a beta of 1.1. The most appropriate bond index futures has a duration of 6 and a price of $99,500. How can the manager pre-invest the $10 million in the appropriate proportions? Take a:

A) short position in 25 of the bond futures and 22 of the stock futures.

B) long position in 22 of the stock futures and 25 of the bond futures.

C) long position in 19 of the stock futures and 28 of the bond futures.

D) long position in 25 of the stock futures and 28 of the bond futures.

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Answer and Explanation

The goal is to create a $7 million equity position with a beta of 0.8 and a $3 million bond position with a duration of 5:

number of stock futures = 21.8 = (0.8-0)*($7,000,000)/(1.1*$233,450)

number of bond futures = 25.13 = (5-0)*($3,000,000)/(6*$99,500)

The manager should take a long position in 22 of the stock index futures and 25 of the bond index futures.

The goal is to create a $7 million equity position with a beta of 0.8 and a $3 million bond position with a duration of 5:

number of stock futures = 21.8 = (0.8-0)*($7,000,000)/(1.1*$233,450)

number of bond futures = 25.13 = (5-0)*($3,000,000)/(6*$99,500)

The manager should take a long position in 22 of the stock index futures and 25 of the bond index futures.