FNCE 4040 midterm 1 problems

1. You sell one December futures contracts when the futures price is $1,010 per unit. Each contract is on 100 units and the initial margin per contract that you provide is $2,000. The maintenance margin per contract is $1,500. During the next day the futures price rises to $1,012 per unit. What is the balance of your margin account at the end of the day? A. $1,800 B. $3,300 C. $2,200 D. $3,700

A. $1,800 expl: sell= short...gain =downward movement, x-y x= initial, y = futures initial margin: 2,000 day2: (1,010-1,012)*100= loss of $200 margin day 2= 2,000-200= $1800

1. On March 1 a commodity's spot price is $60 and its August futures price is $59. On July 1 the spot price is $64 and the August futures price is $63.50. A company entered into futures contracts on March 1 to hedge its purchase of the commodity on July 1. It closed out its position on July 1. What is the effective price (after taking account of hedging) paid by the company? A. $59.50 B. $60.50 C. $61.50 D. $63.50

A. $59.50 expl: purchase=buy= LONG--> effective price paid= NET AMOUNT PAID S2-(F2-F1)--> 64-(63.50-59)= $59.5

1. Futures contracts trade with every month end as a delivery month. A company is hedging the purchase of the underlying asset on June 15. Which futures contract should it use? A. The June contract B. The July contract C. The May contract D. The August contract

A. The June contract expl: always choose a date that is closest date after the close out date

1. Which of the following best describes the term "spot price"? A. The price for immediate delivery B. The price for delivery at a future time C. The price of an asset that has been damaged D. The price of renting an asset

A. The price for immediate delivery expl:is a contract of buying or selling a commodity, security or currency for immediate settlement on the spot date, which is normally two business days after the trade date.

1. A one-year forward contract is an agreement where A. One side has the right to buy an asset for a certain price in one year's time. B. One side has the obligation to buy an asset for a certain price in one year's time. C. One side has the obligation to buy an asset for a certain price at some time during the next year. D. One side has the obligation to buy an asset for the market price in one year's time.

B. One side has the obligation to buy an asset for a certain price in one year's time. explanation: futures and forwards have the OBLIGATION to buy/sell at a certain price

1. Which of the following is true about a long forward contract? A. The contract becomes more valuable as the price of the asset declines B. The contract becomes more valuable as the price of the asset rises C. The contract is worth zero if the price of the asset declines after the contract has been entered into D. The contract is worth zero if the price of the asset rises after the contract has been entered into

B. The contract becomes more valuable as the price of the asset rises expl: Long position (BUY) gains with an upward movement of a futures price x- initial $ y-futures $ gain= + (y-x)

1. An investor sells a futures contract of an asset when the futures price is $1,500. Each contract is on 100 units of the asset. The contract is closed out when the futures price is $1,540. Which of the following is true? A. The investor has made a gain of $4,000 B. The investor has made a loss of $4,000 C. The investor has made a gain of $2,000 D. The investor has made a loss of $2,000

B. The investor has made a loss of $4,000 expl: sells= SHORT... gain= downward movement of futures $... x- initial $ y- futures $ gain= +(x-y) (100*1500)-(1540*100)= -400= LOSS

1. A company will buy 1000 units of a certain commodity in one year. It decides to hedge 80% of its exposure using futures contracts. The spot price and the futures price are currently $100 and $90, respectively. The spot price and the futures price in one year turn out to be $112 and $110, respectively. What is the average price paid for the commodity?

Buy= LONG=effective purchase $-à net amount PAID Effective sales= S2 - (F2-F1)à HEDGED Where: S1= spot rate of date 1à$100 S2= spot rate of date 2à$112 F1= futures rate 1à$90 F2= futures rate 2à$110 Units= 1000 Hedged $= S2-(F2-F1)= 112-(110-90)= $92 Unhedged $= S2= 112 Weighted avg price: ($92*80%)+($112*20%)= $96

1. A company has a $36 million portfolio with a beta of 1.2. The futures price for a contract on an index is 900. Futures contracts on $250 times the index can be traded. What trade is necessary to increase beta to 1.8? A. Long 192 contracts B. Short 192 contracts C. Long 96 contracts D. Short 96 contracts

C. LONG 96 contracts expl: to INCREASE beta.... LONG! K*= (B0-B1)(Va/Vf) where K*= # of contacts B0= current beta B1= desired beta Va= value of current portfolio Vf= current value of one future contract -96= (1.2-1.8)(36M/{900*250})

1. A company enters into a short futures contract to sell 50,000 units of a commodity for 70 cents per unit. The initial margin is $4,000 and the maintenance margin is $3,000. What is the futures price per unit above which there will be a margin call? A. 78 cents B. 76 cents C. 74 cents D. 72 cents

D. 72 cents expl: short=sell, want a downward movement...if it goes higher, then you are losing money short=x-y= daily gain/loss margin bal 0= 4,000 -->@72 cents= (.70-.72)*50,000= -1,000 margin bal 1= 4,000-1000= 3,000 -----since new margin bal is at 3,000, if the the futures price increased any higher the margin bal would fall below the maintenance margin and they would receive a margin call to increase bal to the initial margin

A company has a $20 million portfolio with a beta of 1.2. It would like to use futures contracts on a stock index to hedge its risk. The index futures is currently standing at 1080, and each contract is for delivery of $250 times the index. What is the hedge that minimizes risk? What should the company do if it wants to reduce the beta of the portfolio to 0.6?

HEDGE risk = SHORT K* = β (VA / VF) A) 1.2(20,000,000/{1080*250})= 89 contracts B) (1.2-.6) (20,000,000/{1080*250})= 44 contracts in the short position

A US company will pay £10 million for imports from a British supplier in 3 months and decides to enter into a long position of £ in a forward contract.

Hedger expl: already in business and using a supplier, using to minimize risk

(based on JH Problem 1.19) A trader enters into a short forward contract on 100 million yen. The forward exchange rate is $0.0090 per yen. How much does the trader gain or lose if the exchange rate at the end of the contract is (a) $0.0084 per yen; (b) $0.0101 per yen?

SHort= sell, downward movement wanted, X-Y= gain/loss a) (.009 * 100,000,000)- (.0084*100,000,000) = $60,000 gain b)(.009 * 100,000,000)- (.0101*100,000,000) = $110,000 loss

It is now March 1. A U.S. company expects to receive 50 million Japanese yen on July 31. The company wants to convert yen to USD on July 31.•Yen futures contracts have delivery months of March, June, September and December, and one contract is for 12.5 million yen.What should the company's futures position be? After the company receives 50 million yen on July 31, the company closes out its position.•Suppose F1 = 0.98 (¢/¥) S2 = 0.92 F2 = 0.925 What is the total amount of 50 million yen the company receives in $?

September--> Closest date AFTER close out SHORT--> selling yen to get USD Net amount received= S2 + (F1 - F2) = F1 + b2 .92+(.98-.925)= .975/Y *50M= $487,500

An investor with $4,000 to invest feels that Amazon.com's stock price will increase over the next 2 months and considers buying options. The current stock price is $40 and the price of a 2-month call option with a strike of 45 is $2.

Speculator expl: speculator bc in for a profit

An airline expects to purchase 2 million gallons of jet fuel in 1 month and decides to use heating oil futures for hedging. Given σS=0.0263, σF=0.0313, and ρ=0.928, A)What is the minimum variance hedge ratio?Each heating oil contract traded by the CME group is on 42,000 gallons. B)What is the optimal number of contracts? (in the nearest whole number)

purchase= long A) h* = ρ (σS / σF ) .928(.0263/.0313)= .779--> 78% percent exposure B) h* (NA / QF) .78(2,000,000/42,000)= 37 contracts

The std dev. of monthly changes in the spot price of live cattle is 1.2 (cents per pound). The std dev. of monthly changes in the futures price of live cattle for the closest contract is 1.4. The correlation between the futures price changes and the spot price changes is 0.7. It is now Oct 15. A beef producer is committed to purchasing 200,000 pounds of live cattle on Nov 15. The producer wants to use the Dec live-cattle futures contracts to hedge its risk. Each contract is for the delivery of 40,000 pounds of cattle.What strategy should the beef producer follow?

purchase= LONG Stdev S= 1.2/lbs stdev F= 1.4/lbs P= .7 units of asset: 200,000 lbs contract delivery: 40,000 lbs A) h* = ρ (σS / σF ) h*= .7(1.2/1.4)= .6 or 60% B) h* (NA / QF) k*= .6(200,000/40,000)= 3 contracts final answer= enter into 3 long position contracts

On March 1, the spot price of gold is $300 and the December futures price is $315. On November 1, the spot price of gold is $280 and the December futures price is $281. A gold producer entered into a December futures contract on March 1 to hedge the sale of gold on November 1. It closed out its position on November 1. What is the effective sales price received by the producer for the gold?

sale= SHORT= X-Y= downward Net amount received= S2 + (F1 - F2) = F1 + b2 280+(315-281)= 314 effective sales $

One orange juice future contract is on 15,000 pounds of frozen concentrate. Suppose that in September 2014 a company sells a March 2016 orange juice futures contract for 120 cents per pound. In December 2014 the futures price is 140 cents; in December 2015 the futures price is 110 cents; and in February 2016 it is closed out at 125 cents.-What is the company's profit or loss on the contract?

sells= Short= x-y (120-125)* 15,000= -750 --> LOSS

(based on JH Problem 2.23)Suppose that on October 24, 2015, a company sells one April 2016 live-cattle futures contracts. It closes out its position on January 21, 2016. The futures price (per pound) is 121.20 cents when it enters into the contract, 118.30 cents when it closes out its position, and 118.80 cents at the end of December 2015. One contract is for the delivery of 40,000 pounds of cattle. What is the total profit? How is it taxed if the company is (a) a hedger and (b) a speculator? Assume that the company has a December 31 year end.

sells= short= X-Y= downward 1 contract= 40,0000 lbs cattle futures price= 121.2 cents /lbs--> selling price spot rate= 118.3 cents/lbs---> buying price futures price 2= 118.8 cents/lbs 1) total profit= X-Y= Contract size *(Selling Price-Buying price) = 40,000*(121.2-118.3)= $116,000 a) hedger pays ordinary income tax on the entire gain of %116,000 for the year end of 2016 b) a speculator gets taxed on capital gains for short term capital gain and long term capital gain based on when the gain or loss was realized 2015: 40,000*(121.2-$118.8)= $96,000 short term cap gain 2016: 40,000*($118.8-118.3)= $20,000 short term cap gain

A trader enters into a short cotton futures contract when the futures price is 50 cents per pound. The contract is for the delivery of 50,000 pounds. How much does the trader gain or lose if the cotton price at the end of the contract is (a) 48.20 cents per pound; (b) 51.30 cents per pound?

short, sell, want a downward price, a gain/loss = X-Y A) (.5*50,000)-(.482*50000) = $900 gain B) (.5*50000)-(.513*50000)= -$650 loss

1. A company enters into a long futures contract to buy 1,000 units of a commodity for $60 per unit. The initial margin is $6,000 and the maintenance margin is $4,000. What futures price will allow $2,000 to be withdrawn from the margin account? A. $58 B. $62 C. $64 D. $66

B. $62 expl: long= buy= y-x for gain/loss...need an upward price movement for gain initial margin= 6,000 maint marg= 4,000 --> if you take 2,000 out of margin now, youll get a maint call... so need the price to increase @62-->(62-60)*1000= 2,000 gain --->now 8,000 in margin bal and can withdraw 2000+

1. Margin accounts have the effect of A. Reducing the risk of one party regretting the deal and backing out B. Ensuring funds are available to pay traders when they make a profit C. Reducing systemic risk due to collapse of futures markets D. All of the above

D. All of the above expl: minimize the possibility of a loss through default of contract, minimizes the possibility that a counterparty doesnt pay when you get the profit,

1. On March 1, the spot price of gold is $300 and the December futures price is $315. On November 1, the spot price of gold is $280 and the December futures price is $281. A gold producer entered into a December futures contract on March 1 to hedge the sale of gold on November 1. It closed out its position on November 1. What is the effective sales price received by the producer for the gold?

Gold producer= sell= SHORT.... Effective sales received= net amount Received Effective sales= S2 + (F1-F2) Where: S2= spot rate of date 2à$280 F1= futures rate 1à$315 F2= futures rate 2à$281 = 280 +(315-281)= $314

Suppose that in September 2015 a company takes a long position in a contract on May 2016 crude oil futures. It closes out its position in March 2016. The futures price (per barrel) is $88.30 when it enters into the contract, $90.50 when it closes out its position, and $89.10 at the end of December 2015. One contact is for the delivery is 1,000 barrels. -What is the company's total profit? -When is it realized?-How is it taxed?

LONG= BUY= Y-X hedger: profits realized when position is closed Mach 2016 total profit realized= (90.50-88.30)*1000= 2200---> taxed like ordinary income for 2016 speculator: profits realized at end of december 2015 then end of march 2016 December: (89.10-88.30)*1000= 800 december march: (90.50-89.1) *1000= 1400 march = 2,200 total but taxed and realized in diff years

On a particular day, there were 2,000 trades in a particular futures contract. This means that there were 2,000 buyers (going long) and 2,000 sellers (going short). What is the impact of the day's trading on open interest? -Of the 2,000 buyers, 1,400 were closing out positions and 600 were entering into new positions. -Of the 2,000 sellers, 1,200 were closing out positions and 800 were entering into new positions.

Long open interest = open interest + new long - long closing out X+600-1200= X-600 Short open interest = open interest +new short- short closing out X+800-1400 = x-600 --> open interest decreased by 600. remember closing out is the opposite position

S&P 500 futures price is 1,000.The size of one future contract is 250.Value of a portfolio is $5 million.Beta of the portfolio is 1.5.What position in futures contracts on the S&P 500 is necessary to change the portfolio's beta to 0.75.?

REDUCING BETA= HEDGE SHORT K* = (β - β') (VA / VF) = (1.5-.075)(5,000,000/1,000*250) = 15 contracts short position

S&P 500 futures price is 1,000.The size of one future contract is 250.Value of a portfolio is $5 million.Beta of the portfolio is 1.5.What position in futures contracts on the S&P 500 is necessary to hedge the portfolio completely (beta=0)?

TO REDUCE BETA= SHORT/HEDGING K* = β (VA / VF) Va= value of current portfolio Vf= value of 1 future contract 1.5*(5,000,000/{1,000*250}) = 30 contracts entered in the short position

•Is there an arbitrage opportunity? Suppose that -The spot price of a non-dividend paying stock is $40. -The 3-month forward price is $38. -The 1-year USD interest rate is 5% per annum.

Yes. Short-sell the share, Invest $40, and Long the forward.

•Is there an arbitrage opportunity? Suppose that -The spot price of a non-dividend paying stock is $40. -The 3-month forward price is $43. -The 1-year USD interest rate is 5% per annum.

Yes. Borrow $40, Buy the share, and Short the forward.

1. Suppose that the minimum variance hedge ratio (h*) of corn futures is calculated as 0.6. A corn farmer wants to hedge corn price risk by entering into the closest corn futures contracts. He expects his crops will be 100,000 bushels. If the size of futures contract is 5,000 bushels, what would be his optimal number and position of futures contracts?

Answer: 12 contracts in the short position The corn farmer wants to sell his crops of corn, so he takes a short futures position. The optimal number of contracts (K*) is the bushels of corn futures needed (NF*) divided by the size of corn futures (QF*). The bushels of corn futures needed (NF*) is 0.6´100,000 bushels=60,000 bushels. Therefore, the optimal number of contracts is 60,000 bushels / 5,000 bushels=12.

1. A company has a $36 million portfolio with a beta of 1.2. The futures price for a contract on an index is 900. Futures contracts on $250 times the index can be traded. What trade is necessary to reduce beta to 0.9? A. Long 192 contracts B. Short 192 contracts C. Long 48 contracts D. Short 48 contracts

D. Short 48 contracts expl: to REDUCE beta.... SHORT! K*= (B0-B1)(Va/Vf) where K*= # of contacts B0= current beta B1= desired beta Va= value of current portfolio Vf= current value of one future contract 48= (1.2-.9)(36M/{900*250})

(based on JH Problem 3.30)It is July 16. A company has a portfolio of stocks worth $100 million. The beta of the portfolio is 1.2. The company would like to use the December futures contract on a stock index to change beta of the portfolio to 0.5 during the period July 16 to November 16. The index is currently 1,000, and each contract is on $250 times the index.a) What position should the company take?b) Suppose that the company changes its mind and decides to increase the beta of the portfolio from 1.2 to 1.5. What position in futures contracts should it take?

Equity Portfolio Hedging - Change the beta from --β to β' -----K* = (β - β') (VA /VF) K*: the number of index futures contracts - VA: current value of the portfolio - VF: current value of the future contract (futures price x contract size) a) What position should the company take?--> to reduce beta SHORT a futures contract (1.2-.5)((100,000,000/{1,000*250})= 280 short futures contracts b) Suppose that the company changes its mind and decides to increase the beta of the portfolio from 1.2 to 1.5. What position in futures contracts should it take?---> to INCREASE beta, but enter the LONG postion (1.2-1.5)((100,000,000/{1,000*250})= 120 futures contracts

(based on JH Problem 3.18)On July 1, an investor holds 50,000 shares of a certain stock. The market price is $30 per share. The investor is interested in hedging against movements in the market over the next month and decides to use the September Mini S&P 500 futures contract. The index is currently 1,500 and one contract is for delivery of $50 times the index. The beta of the stock is 1.3. What strategy should the investor follow?

Equity Portfolio Hedging - K* = β (VA /VF) K*: the number of index futures contracts VA: current value of the portfolio - (50,000*30)= 1,500,000 VF: current value of the future contract (futures price x contract size) = (1,500*50)=75000 beta= 1.3 K*= 1.3(1,500,000/75000)= 26 contracts ---> hedging is ALWAYS short

(based on JH Problem 2.11)A trader buys two July futures contracts on frozen orange juice. Each contract is for the delivery of 15,000 pounds. The current futures price is 160 cents per pound, the initial margin is $6,000 per contract, and the maintenance margin is $4,500 per contract. What price change would lead to a margin call? Under what circumstances could $2,000 be withdrawn from the margin account?

buys= long= upward movement= Y-X for gain initial margin= 6000 A) = can only lose 1500 before needing to add to initial margin day 1 margin= (Y*15,000)- (1.60*15,000)= -1500 Y= $1.50 or the price could not decrease more than 150 cents per pound B) change in $= *2 contracts= 1,000 amount to withdraw day 1 margin= (Y*15,000)- (1.60*15,000)= 1000 Y= if the price increased to 166 cents per pound, you would gain 500, enough to withdraw 2000 from the margin accnt

if investor was in the short position of corn futures contract @day1 and closes out on day 5...

enters a long position of a corn futures contract on day 5 with price at day 5

(based on JH Problem 3.27)A company wishes to hedge its exposure to a new fuel whose price changes have a 0.6 correlation with gasoline futures price changes. The company will lose $1 million for each 1 cent increase in the price per gallon of the new fuel over the next three months. The new fuel's price change has a standard deviation that is 50% greater than price changes in gasoline futures prices. If gasoline futures are used to hedge the exposure what should the hedge ratio be? What is the company's exposure measured in gallons of the new fuel? What position measured in gallons should the company take in gasoline futures? How many gasoline futures contracts should be traded? Each contract is on 42,000 gallons.

h* = ρ (σS / σF ) P= .6 h* = ρ (σS / σF ) The new fuel's price change has a standard deviation that is 50% greater than price changes in gasoline futures prices=1.5 h*= .6*1.5= .9 a) hedge ratio = .9--> .9* 100 million gallons = 90 million gallons in gasoline futures = exposure in fuel b)= h* (NA / QF)--> NA: units of an asset to be hedged - NF*: units of the asset in futures contract number of futures contracts= (90,0000/42,000) = 2143 gas futures contract

(based on JH Problem 3.6)Suppose that the standard deviation of quarterly changes in the prices of a commodity is $0.65, the standard deviation of quarterly changes in a futures price on the commodity is $0.81, and the coefficient of correlation between the two changes is 0.8. What is the optimal hedge ratio for a three-month contract? What does it mean?

h* = ρ (σS / σF ) ρ : correlation between ΔS and ΔF--> .8 ΔS, ΔF: changes in prices of the asset to be hedged and the asset in futures contract σS, σF : standard deviations of ΔS and ΔF--> .65, .81 h*= .6419 expl: in a 3 month hedge, the optimal size of the future position should be 64% of the optimal size of the companies exposure... it measures the relationship between change in commodity spot prices and change in future prices

Suppose that the minimum variance hedge ratio (h*) of corn futures is calculated as 0.6. A corn farmer wants to hedge corn price risk by entering into the closest corn futures contracts. He expects his crops will be 100,000 bushels. If the size of futures contract is 5,000 bushels, what would be his optimal number and position of futures contracts?

hedge= short B) h* (NA / QF) .6(100,000/5,000) =12 contract in the short position

(based on JH Problem 2.30)A company enters into a short futures contract to sell 5,000 bushels of wheat for 750 cents per bushel. The initial margin is $3,000 and the maintenance margin is $2,000. What price change would lead to a margin call? Under what circumstances could $1,500 be withdrawn from the margin account?

short= sell= X-Y= downward margin call= -1000 loss in daily day1= (7.5*5000)-(Y* 5000)= -1000 A) Y= 7.7--> if price increase to 770 cents per bushell you would need a margin call B) change in $= (Amount to withdraw/contract size) (1,500/5,000) = .30 ----> 750-30= 720 cents OR margin call= 1500 + in daily gain day1= (7.5*5000)-(Y* 5000)= 1500 Y= if price decreased to 720 cents per bushell you could withdraw 1500 from the margin account

(based on JH Problem 2.3)Suppose that you enter into a short futures contract to sell July silver for $17.20 per ounce. The size of the contract is 5,000 ounces. The initial margin is $4,000, and the maintenance margin is $3,000. What change in the futures price will lead to a margin call? What happens if you do not meet the margin call?

short= sell= downward= x-y day one margin= 4,000 cannot lose more than 1000 or will lead to a margin call day 1= ($17.20/oz*5,000)-(X*5000) = -1000 x= $17.4--> if price increases to $17.4 or more, then you will receive a margin call if you do not meet the margin call you can continue to trade without having to add more money into your margin account