Reading 38: Risk Management Applications of Forward and Fu equity, interpret, number, achieve, required

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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 a: Demonstrate the use of equity futures contracts to achieve a target beta for a stock portfolio and calculate and interpret the number of futures contracts required.

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An investor has an $80 million stock portfolio with a beta of 1.1. He would like to partially hedge his portfolio using S& 500 futures contracts. The contracts are currently trading at 596.70. The futures contract has a multiple of 250. Which of the following is the CORRECT trade to reduce the portfolio beta by 50 percent?

A) Buy 295 contracts.

B) Buy 590 contracts.

C) Sell 590 contracts.

D) Sell 295 contracts.

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Answer and Explanation

The number of futures contracts required for the 100% risk-minimizing hedge (or to reduce the beta to zero) is computed as follows:

Number of contracts = Portfolio value/Futures contract value x beta
$80 million/(596.70 x $250) x 1.1 = 590 contracts

Therefore, to reduce the by 50% we simply use half this number of contracts or 295 contracts.

The number of futures contracts required for the 100% risk-minimizing hedge (or to reduce the beta to zero) is computed as follows:

Number of contracts = Portfolio value/Futures contract value x beta
$80 million/(596.70 x $250) x 1.1 = 590 contracts

Therefore, to reduce the by 50% we simply use half this number of contracts or 295 contracts.

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An investor has a $100 million stock portfolio with a beta of 1.2. He would like to alter his portfolio beta using S& 500 futures contracts. The contracts are currently trading at 596.90. The futures contract has a multiple of 250. Which of the following is the CORRECT trade required to double the portfolio beta?

A) Sell 804 contracts.

B) Buy 1608 contracts.

C) Sell 1608 contracts.

D) Buy 804 contracts.

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Answer and Explanation

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/(596.90 x $250) x 1.2 = 804 contracts

Selling this many contracts reduces the beta to zero so to double the beta we simply buy this many contracts, or buy 804 contracts.

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/(596.90 x $250) x 1.2 = 804 contracts

Selling this many contracts reduces the beta to zero so to double the beta we simply buy this many contracts, or buy 804 contracts.

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Robert Zorn, CFA, manages an equity portfolio with a current market value of $150 million. The beta of the portfolio is 1.23 and Zorn is forecasting a short-term market adjustment that will significantly lower equity values and will occur in the near future. Zorn has decided to use S& 500 futures, currently trading at 1260, to reduce the portfolios systematic risk exposure by 30 percent. The multiplier is 250. What is the number of futures contracts, rounded up to the nearest whole number, that will be needed to achieve Zorns objective?

A) 182.

B) 169.

C) 176.

D) 191.

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Answer and Explanation

[$150,000,000/(250)(1260)](1.23)(0.30) = 175.71, rounded to 176.

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Michael Hallen, CFA, manages an equity portfolio with a current market value of $78 million and a beta of 0.95. Convinced the market is poised for a significant upward movement, Hallen would like to increase the beta of the portfolio by 40 percent, using S& 500 futures currently trading at 856. The multiplier is 250. What is the number of futures contracts, rounded up to the nearest whole number, that will be needed to achieve Hallens objective?

A) 139.

B) 143.

C) 127.

D) 144.

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Answer and Explanation

[$78,000,000/(250)(856)](0.95)(0.40) = 138.50, rounded to 139.

[$78,000,000/(250)(856)](0.95)(0.40) = 138.50, rounded to 139.

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A manager of a $10,000,000 portfolio wants to increase beta from the current value of 0.9 to 1.1. The beta on the futures contract is 1.2 and the futures price is $245,000. Using futures contracts, what strategy would be appropriate?

A) Short 7 contracts.

B) Long 11 contracts.

C) Long 7 contracts.

D) Short 11 contracts.

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Answer and Explanation

Number of contracts = 6.80 = (1.1-0.9)*($10,000,000)/(1.2*$245,000), and this rounds up to seven. Since the goal is to increase beta, the manager should go long.

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A manager of a $20,000,000 portfolio wants to decrease beta from the current value of 0.9 to 0.5. The beta on the futures contract is 1.1 and the futures price is $105,000. Using futures contracts, what strategy would be appropriate?

A) Short 69 contracts.

B) Long 69 contracts.

C) Long 19 contracts.

D) Short 19 contracts.

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Answer and Explanation

Number of contracts = -69.26 = (0.5-0.9)*($20,000,000)/(1.1*$105,000), and this rounds down to 69 (absolute value). Since the goal is to decrease beta, the manager should go short which is also indicated by the negative sign.

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If the value of a stock portfolio equals 16 times the futures price of the appropriate equity index contract and beta of the equity portfolio and futures price were equal, how many contracts would it take to reduce the beta of the equity index to zero?

A) A long position in 4 contracts.

B) A long position in 16 contracts.

C) A short position in 32 contracts.

D) A short position in 16 contracts.

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Answer and Explanation

Number of contracts = -16 = (0-beta)*(16*futures price)/(beta*futures price)

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The number of Treasury bond futures contracts that Kaufman would need to reduce the duration of the bonds in the portfolio is closest to:

A) buy 269 contracts.

B) sell 56 contracts.

C) sell 51 contracts.

D) buy 257 contracts.

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Answer and Explanation

Contracts = (Yield Beta) [(MD_Target MD_P)/MD_F][V_P/(P_f(Multiplier))]

Contracts = 1.1 × [(5 6.3)/4.2] × ($40,000,000/$245,000) = -55.59

To reduce the duration of the portfolio, take a short position in the futures contract. Note that we must round the number of contracts up to 56 since partial contracts cannot be traded.

Contracts = (Yield Beta) [(MD_Target MD_P)/MD_F][V_P/(P_f(Multiplier))]

Contracts = 1.1 × [(5 6.3)/4.2] × ($40,000,000/$245,000) = -55.59

To reduce the duration of the portfolio, take a short position in the futures contract. Note that we must round the number of contracts up to 56 since partial contracts cannot be traded.

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Kaufman is interested in increasing the beta of the equity portfolio to 1.4 for a brief period of time. Kaufman is expecting a(n):

A) increase in the market; a long position in approximately 27 contracts will accomplish this target.

B) decrease in the market; a short position in approximately 72 contracts will accomplish this target.

C) increase in the market; a long position in approximately 30 contracts will accomplish this target.

D) decrease in the market; a long position in approximately 45 contracts will accomplish this target.

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Answer and Explanation

Number of Contracts = (Target Beta Portfolio Beta/Beta on Futures) × (Value of the portfolio/Price of the futures x the multiplier).

Number of Contracts = [(1.4 1.25)/0.90] × ($60,000,000/$335,000) = 29.85 contracts. 

The positive sign indicates that we should take a long position in the futures to leverage up the position. If that is Kaufmans goal, he must be expecting an increase in the market.

Number of Contracts = [(1.4 1.25)/0.90] × ($60,000,000/$335,000) = 29.85 contracts. 

The positive sign indicates that we should take a long position in the futures to leverage up the position. If that is Kaufmans goal, he must be expecting an increase in the market.

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How many S& index futures contracts would Kaufman need to buy or sell to create a six-month synthetic cash position?

A) Buy approximately 121 contracts.

B) Sell approximately 400 contracts.

C) Buy approximately 400 contracts.

D) Sell approximately 121 contracts.

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Answer and Explanation

[$60,000,000 × (1.02)^0.50]/(2000 × $250) = 121.19 contracts

Kaufman would need to sell the contracts to create the synthetic cash (zero equity) position. If he were converting cash to a synthetic equity position, he would of course buy contracts.

Kaufman would need to sell the contracts to create the synthetic cash (zero equity) position. If he were converting cash to a synthetic equity position, he would of course buy contracts.

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The most appropriate strategy to pre-invest the anticipated $6 million inflow would be to:

A) buy 22 bond futures contracts and sell 13 stock futures contracts.

B) buy 21 bond futures contracts and buy 35 stock futures contracts.

C) buy 22 bond futures contracts and buy 13 stock futures contracts.

D) sell 21 bond futures contracts and buy 13 stock futures contracts.

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Answer and Explanation

Take the existing portfolio weights, 40% debt and 60% equity and apply them to the new money that is coming in. Also, mirror the duration and beta of the original portfolios.

Number of bond futures = 1.05 × [(6.3-0)/6.2] × [(6,000,000 × 0.40)/115,460] = 22.18 contracts

Number of stock futures = [(1.25 0)/1.10] × [(6,000,000 × 0.60)/315,650] = 12.96

Kaufman Co. would take a long position in both the stock index and bond futures contracts because it is synthetically creating an existing portfolio until the actual $6 million is received and can be invested.

Take the existing portfolio weights, 40% debt and 60% equity and apply them to the new money that is coming in. Also, mirror the duration and beta of the original portfolios.

Number of bond futures = 1.05 × [(6.3-0)/6.2] × [(6,000,000 × 0.40)/115,460] = 22.18 contracts

Number of stock futures = [(1.25 0)/1.10] × [(6,000,000 × 0.60)/315,650] = 12.96

Kaufman Co. would take a long position in both the stock index and bond futures contracts because it is synthetically creating an existing portfolio until the actual $6 million is received and can be invested.

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Tom Corser is the manager of the $140,000,000 Intrepid Growth Fund. Corsers long-term view of the equity market is negative, and as a result, his portfolio is allocated defensively with a beta of 0.85. Despite his negative long-term outlook, Corser thinks the market is temporarily mispriced, and could rise significantly over the next few weeks. Corser has implemented tactical asset allocation measures in his fund sporadically over the years, and thinks now is another time to do so. Because he likes his long-term holdings, he decides to use a futures overlay rather than trading assets to implement his view of the market. Corser decides he wants to increase the beta of his portfolio to 1.25. The appropriate futures contract has a beta of 1.03 and the total futures price is $310,000. What is the appropriate tactical allocation strategy for Corser to accomplish his objective?

A) Buy 175 equity futures contracts.

B) Buy 373 equity futures contracts.

C) Sell 175 equity futures contracts.

D) Sell 373 equity futures contracts.

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Answer and Explanation

NOTE on the exam, it is very likely for material on tactical asset allocation to be tested in conjunction with material from derivatives as tactical asset allocation can be accomplished by selling assets, or with a derivative overlay. Because Corser wants to increase the beta of his portfolio, he should buy futures contracts. The appropriate number of contracts to buy is calculated as:

[(1.25 0.85) / 1.03] × ($140,000,000 / $310,000) = 175.38 ≈ 175 contracts.