LOS e, (Part 1): Demonstrate the use of futures to adjust the allocation of a portfolio across equity sectors.

Q1. 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)   long position in 20 contracts.

B)   short position in 5 contracts.

C)   long position in 5 contracts.

Q2. 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)   23 mid-cap futures and go long 42 large-cap futures.

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

Q3. 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 55 mid-cap futures and go long 72 small-cap futures.

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

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

LOS e, (Part 1): Demonstrate the use of futures to adjust the allocation of a portfolio across equity sectors. fficeffice" />

Q1. 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)   long position in 20 contracts.

B)   short position in 5 contracts.

C)   long position in 5 contracts.

Correct answer is C)

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).

Q2. 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)   23 mid-cap futures and go long 42 large-cap futures.

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

Correct answer is C)

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.

Q3. 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 55 mid-cap futures and go long 72 small-cap futures.

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

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

Correct answer is A)

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.

Thx!