Question

Suppose a trader who owns 320,000 pounds of commodity A decides to hedge the value of her position with the futures contracts. One futures contract is for the delivery of 40,000 pounds of commodity B. The price of commodity A is $21.20 and the futures price is 18.30 (both dollars per pound). The correlation between the futures price and the price of commodity A is 0.92. The volatilities of commodity A and the futures are 0.31 and 0.38 per year, respectively. What is the optimal number of futures contracts with no tailing of the hedge?

	A.	7
	B.	6
	C.	8
	D.	9

Suppose a trader who owns 320,000 pounds of commodity A decides to hedge the value of her position with the futures contracts. One futures contract is for the delivery of 40,000 pounds of commodity B. The price of commodity A is $21.20 and the futures price is 18.30 (both dollars per pound). The correlation between the futures price and the price of commodity A is 0.92. The volatilities of commodity A and the futures are 0.31 and 0.38 per year, respectively. What is the optimal number of futures contracts with tailing of the hedge?

	A.	9
	B.	8
	C.	7
	D.	10

A fund manager of a $72 million equity portfolio with a beta of 0.9 considers changing the portfolio’s risk level using S&P 500 index futures. The S&P 500 index futures with the multiplier of 250 are trading at 3,359. What is the number of futures contracts necessary to increase beta to 1.25?

	A.	107
	B.	77
	C.	17
	D.	30

A fund manager of a $72 million equity portfolio with a beta of 0.9 considers changing the portfolio’s risk level using S&P 500 index futures. The S&P 500 index futures with the multiplier of 250 are trading at 3,359. Should the fund manager take a long or short futures position to increase beta to 1.25?

	A.	Short
	B.	Long

A fund manager of a $72 million equity portfolio with a beta of 0.9 considers changing the portfolio’s risk level using S&P 500 index futures. The S&P 500 index futures with the multiplier of 250 are trading at 3,359. What is the number of futures contracts necessary to completely hedge the portfolio’s market risk?

	A.	77
	B.	107
	C.	30
	D.	17

A fund manager of a $72 million equity portfolio with a beta of 0.9 considers changing the portfolio’s risk level using S&P 500 index futures. The S&P 500 index futures with the multiplier of 250 are trading at 3,359. Should the fund manager take a long or short futures position to completely hedge the portfolio’s market risk?

	A.	Short
	B.	Long

A fund manager of a $72 million equity portfolio with a beta of 0.9 considers changing the portfolio’s risk level using S&P 500 index futures. The S&P 500 index futures with the multiplier of 250 are trading at 3,359. Suppose that at the maturity of the futures contract, the future contract is trading at 3,305 and the portfolio has experienced a 1% decline in value. What is the net impact of the market decline on the completely hedged portfolio? In other words, what is the change in the value of the completely hedged portfolio?

	A.	-$706,500
	B.	$319,500
	C.	-$315,000
	D.	-$720,000

Answer 1

Q1-Suppose a trader who owns 320,000 pounds of commodity A decides to hedge the value of her position with the futures contracts. One futures contract is for the delivery of 40,000 pounds of commodity B. The price of commodity A is $21.20 and the futures price is 18.30 (both dollars per pound). The correlation between the futures price and the price of commodity A is 0.92. The volatilities of commodity A and the futures are 0.31 and 0.38 per year, respectively. What is the optimal number of futures contracts with no tailing of the hedge?

Answer-

Hedge Ratio =

where,

= Standard deviation or valatility of asset

=Standard deviation of Futures

r(A,F) = correlation between the futures price and the Asset price.

Hence hedge ratio =

optimal number of futures contracts = [(Hedge ratio* current Value of the asset)] / [Current value per contract]

=>[0.751* 320,000 pounds*$21.20 per pound] / [40,000 pounds* $18.30 per pound]

=> $5094784 / $732000 = 6.96 or 7 contract.

correct option- A.7 (SELL 7 CONTRACT)

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Q-2

Suppose a trader who owns 320,000 pounds of commodity A decides to hedge the value of her position with the futures contracts. One futures contract is for the delivery of 40,000 pounds of commodity B. The price of commodity A is $21.20 and the futures price is 18.30 (both dollars per pound). The correlation between the futures price and the price of commodity A is 0.92. The volatilities of commodity A and the futures are 0.31 and 0.38 per year, respectively. What is the optimal number of futures contracts with no tailing of the hedge?

Answer-

Hedge Ratio =

where,

= Standard deviation or valatility of asset

=Standard deviation of Futures

r(A,F) = correlation between the futures price and the Asset price.

Hence hedge ratio =

optimal number of futures contracts = [(Hedge ratio* current Value of the asset)] / [Current value per contract]

=>[0.751* 320,000 pounds*$21.20 per pound] / [40,000 pounds* $18.30 per pound]

=> $5094784 / $732000 = 6.96 or 7 contract.

correct option- C.7 (Sell 7 contract)

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Q-3.A fund manager of a $72 million equity portfolio with a beta of 0.9 considers changing the portfolio’s risk level using S&P 500 index futures. The S&P 500 index futures with the multiplier of 250 are trading at 3,359. What is the number of futures contracts necessary to increase beta to 1.25?

Number of Furures Contract Necessery=[ Value of portfolio*(New beta-Old beta)] / [value of one Index Futures]

=>[$72000000*(1.25-0.90)] / [ 250*3359]

=>30 contracts (Long or buy)

Correct Answer-D.30

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Q-4

A fund manager of a $72 million equity portfolio with a beta of 0.9 considers changing the portfolio’s risk level using S&P 500 index futures. The S&P 500 index futures with the multiplier of 250 are trading at 3,359. Should the fund manager take a long or short futures position to increase beta to 1.25?

Correct Answer. B . Take long position

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Q-5.A fund manager of a $72 million equity portfolio with a beta of 0.9 considers changing the portfolio’s risk level using S&P 500 index futures. The S&P 500 index futures with the multiplier of 250 are trading at 3,359. What is the number of futures contracts necessary to completely hedge the portfolio’s market risk?

Number of Furures Contract Necessery=[ Value of portfolio*(New beta-Old beta)] / [value of one Index Futures]

=>[$72000000*(0-0.90)] / [ 250*3359]

=> - 77.17 OR -77 Contract

(Negative means take Short Position).

Correct Answer-A.77

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Q-6A fund manager of a $72 million equity portfolio with a beta of 0.9 considers changing the portfolio’s risk level using S&P 500 index futures. The S&P 500 index futures with the multiplier of 250 are trading at 3,359. Should the fund manager take a long or short futures position to completely hedge the portfolio’s market risk?

Correct Answer-A-Take Short position

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Q-7

A fund manager of a $72 million equity portfolio with a beta of 0.9 considers changing the portfolio’s risk level using S&P 500 index futures. The S&P 500 index futures with the multiplier of 250 are trading at 3,359. Suppose that at the maturity of the futures contract, the future contract is trading at 3,305 and the portfolio has experienced a 1% decline in value. What is the net impact of the market decline on the completely hedged portfolio? In other words, what is the change in the value of the completely hedged portfolio?.

Ans-

Profit on Short position of 77 contract due to decrease in Index= (3359-3305)*250*77 = $1039500

Loss due to decline in Portfolio value = $72 million*1% = $720000

net profit = $1039500-$720000 = $319500

Correct answer-B -$319500