FIN470 Exam 1
The standard deviation of monthly changes in the (log) spot price of live cattle is (in cents per pound) 1.2. The standard deviation of monthly changes in the (log) futures price of live cattle for the closest contract is 1.4. The correlation between the futures returns and the spot returns is 0.7. It is now October 15. A beef producer is committed to purchasing 200,000 pounds of live cattle on November 15. The producer wants to use the December live-cattle futures contracts to hedge its risk. Each contract is for the delivery of 40,000 pounds of cattle. Suppose the price per pound of cattle is 100 cents. What is the optimal (minimum variance) hedge ratio? What position should the beef producer take?
0.7(1.2/1.4)=0.60*5= 3 200,000/40000=5 A1: hedge ratio = 0.6 A2: position is 3 contracts long
On July 1, an investor holds a portfolio worth $1,500,000. 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 futures price is currently 1,500 and one contract is for delivery of $50 times the index. The beta of the portfolio is 1.3 with an R2 of 70%. What position should the investor take to hedge his position? Will the hedge be effective? Explain.
1.3*(1,500,000/(1500*50))= 26 shortA1: 26 contracts short.
1.1. What is the difference between a long futures position and a short futures position?
A trader who enters into a long futures position is agreeing to buy the underlying asset for a certain price at a certain time in the future. A trader who enters into a short futures position is agreeing to sell the underlying asset for a certain price at a certain time in the future.
Suppose a company takes a long position in 20 December oil futures contracts on June 8 when the futures price is $58. It closes out its position on November 10. The spot price and futures price at this time are $65 and $62. The company is hedging 20,000 barrels, and uses a hedge ratio of 0.8. Each contract is for 1,000 bbl.Q1: How many futures contracts should the firm hedge? Q2: What is the dollar change in the value of their futures position?Q3: What is cash flow (i.e., negative cost) to purchase the oil on the spot market? What is the net cash flow, after figuring the gain in the futures position?
A1: N* = 0.8*20k/1k = 16 contracts A2: (62-58).8-65= 61.80 Total Cash Flow: 3.20* 2000= $64,000 A3: Net cost is = $1,300,000 + 64,000= 61.80
An airline executive has argued: "There is no point in our using oil futures. There is just as much chance that the price of oil in the future will be less than the futures price as there is that it will be greater than this price." Discuss the executive's viewpoint.
A: hedging will reduce volatility of earnings. Will not always make money on the hedge, only make money half the time, takes away some risk for investors
Basis Risk
Basis = Futures price − Spot price An increase in the basis is referred to as a strengthening of the basis and a decrease in the basis is referred to as a weakening of the basis basis is positive prior to expiration of the futures contract.
Cross Hedging
Cross hedging occurs when the two assets are different. For example, an airline that is concerned about the future price of jet fuel. Since jet fuel futures are not actively traded, it might choose to use heating oil futures contracts to hedge its exposure.
Market-if-touched order (MIT)
Is executed at the best available price after a trade occurs at a specified price or at a price more favorable than the specified price. In effect, an MIT becomes a market order once the specified price has been hit. An MIT is also known as a board order. A market-if-touched order is designed to ensure that profits are taken if sufficiently favorable price movements occur.
Strike price/ Exercise price
The price at which the asset may be bought or sold in an option contract. Also called the exercise price
A company enters a short position in 4 e-mini S&P500 futures contracts. The index futures price is currently $1,615 and the mini S&P500 index futures have a multiplier of 50. The initial margin is $6,400 and the maintenance margin is $5,800 per contract. At what index futures price will there be a margin call? (Type just the number to zero decimal places, without symbols. For example, if your answer is "-$1,425.237" then enter "-1425").
a. Initial Margin: $6400* 4= 25,600 Nominal value: (1615*50)*4= 323,000 Maintenance margin (5800*4)= 23,200 (25,600-23,200)=2,400+ 323,000= Nominal value $325,400 325,400/(4*50)= $1627
1.2. Explain carefully the difference between (a) hedging, (b) speculation, and (c) arbitrage.
A company is hedging when it has an exposure to the price of an asset and takes a position in futures or options markets to offset the exposure. In a speculation the company has no exposure to offset. It is betting on the future movements in the price of the asset. Arbitrage involves taking a position in two or more different markets to lock in a profit.
2.2. What is the difference between a local and a futures commission merchant?
A futures commission merchant trades on behalf of a client and charges a commission. A local trades on his or her own behalf.
3.4. Under what circumstances does a minimum variance hedge portfolio lead to no hedging at all?
A minimum variance hedge leads to no hedging when the coefficient of correlation between changes in the futures price and changes in the price of the asset being hedged is zero.
3.3. Explain what is meant by a perfect hedge. Does a perfect hedge always lead to a better outcome than an imperfect hedge? Explain your answer.
A perfect hedge is one that completely eliminates the hedger's risk. A perfect hedge does not always lead to a better outcome than an imperfect hedge. It just leads to a more certain outcome. Consider a company that hedges its exposure to the price of an asset. Suppose the asset's price movements prove to be favorable to the company. A perfect hedge totally neutralizes the company's gain from these favorable price movements. An imperfect hedge, which only partially neutralizes the gains, might well give a better outcome.
3.1. Under what circumstances are (a) a short hedge and (b) a long hedge appropriate?
A short hedge is appropriate when a company owns an asset and expects to sell that asset in the future. It can also be used when the company does not currently own the asset but expects to do so at some time in the future. A long hedge is appropriate when a company knows it will have to purchase an asset in the future. It can also be used to offset the risk from an existing short position.
Index Futures
A stock index tracks changes in the value of a hypothetical portfolio of stocks. The weight of a stock in the portfolio at a particular time equals the proportion of the hypothetical portfolio invested in the stock at that time. The percentage increase in the stock index over a small interval of time is set equal to the percentage increase in the value of the hypothetical portfolio. Dividends are usually not included in the calculation, so that the index tracks the capital gain/loss from investing in the portfolio If the hypothetical portfolio of stocks remains fixed, the weights assigned to individual stocks in the portfolio do not remain fixed. When the price of one particular stock in the portfolio rises more sharply than others, more weight is automatically given to that stock The weights assigned to the stocks are then proportional to their market prices, with adjustments being made when there are stock splits. Other indices are constructed so that weights are proportional to market capitalization (stock price* number of shares outstanding)
What does a stop order to sell at $2 mean? When might it be used? What does a limit order to sell at $2 mean? When might it be used?
A stop order to sell at $2 is an order to sell at the best available price once a price of $2 or less is reached. It could be used to limit the losses from an existing long position. A limit order to sell at $2 is an order to sell at a price of $2 or more. It could be used to instruct a broker that a short position should be taken, providing it can be done at a price more favorable than $2.
A cattle farmer expects to have 120,000 pounds of live cattle to sell in three months. The live-cattle futures contract on the Chicago Mercantile Exchange is for the delivery of 40,000 pounds of cattle. How can the farmer use the contract for hedging? From the farmer's viewpoint, what are the pros and cons of hedging?
A: Farmer could short 3 (120,000/40,000) contracts. The Farmer could hedge against lower prices for his cattle, hedging would allow him to sell his cattle for a fixed price and that would benefit him if prices were to drop but hurt him if prices rose and he wouldn't make as much money. Deliver the cattle at a fixed price. Hedge ratio of 1. Dollar price exposure will offset.
It is July 2016. A mining company has just discovered a small deposit of gold. It will take six months to construct the mine. The gold will then be extracted on a more or less continuous basis for one year. Futures contracts on gold are available on the New York Mercantile Exchange. There are delivery months every two months from August to December next year. Each contract is for the delivery of 100 ounces. Discuss how the mining company might use futures markets for hedging.
A: Short futures according to schedule. Hedge against lower prices of gold. "Strip Hedge". If it was 10-20 years out you would use a "Stack and roll" method
convergence of futures price to spot price
As the delivery period for a futures contract is approached, the futures price converges to the spot price of the underlying asset. When the delivery period is reached, the futures price equals, or is very close to the spot price. The futures price is very close to the spot price during the delivery period
3.2. Explain what is meant by basis risk when futures contracts are used for hedging.
Basis risk arises from the hedger's uncertainty as to the difference between the spot price and futures price at the expiration of the hedge.
Long futures position
Buyer
"If the minimum-variance hedge ratio is calculated as 1.0, the hedge must be perfect." Is this statement true? Explain your answer.
FALSE, knowing the hedge ratio alone does not tell if the hedge will be effective
A comparison of Forward and Option contracts
Forward contracts are designed to neutralize risk by fixing the price that the hedger will pay or receive for the underlying asset. Option contracts, by contrast, provide insurance. They offer a way for investors to protect themselves against adverse price movements in the future while still allowing them to benefit from favorable price movements. Unlike forwards, options involve the payment of an up-front fee.
3.5. Give three reasons why the treasurer of a company might not hedge the company's exposure to a particular risk.
If the company's competitors are not hedging, the treasurer might feel that the company will experience less risk if it does not hedge The shareholders might not want the company to hedge. If there is a loss on the hedge and a gain from the company's exposure to the underlying asset, the treasurer might feel that he or she will have difficulty justifying the hedging to other executives within the organization.
1.3. What is the difference between (a) entering into a long futures contract when the futures price is $50 and (b) taking a long position in a call option with a strike price of
In (a) the investor is obligated to buy the asset for $50 and does not have a choice. In (b) the investor has the option to buy the asset for $50 but does not have to exercise the option.
2.7. What differences exist in the way prices are quoted in the foreign exchange futures market, the foreign exchange spot market, and the foreign exchange forward market?
In futures markets prices are quoted as the number of U.S. dollars per unit of foreign currency. Spot and forward rates are quoted in this way for the British pound, euro, Australian dollar, and New Zealand dollar. For other major currencies, spot and forward rates are quoted as the number of units of foreign currency per U.S. dollar.
A trader buys (goes long) two July futures contracts on frozen orange juice. Each contract is for the delivery of 15,000 pounds. The current futures price is 120 cents per pound, the initial margin is $6,000 per contract, and the maintenance margin is $4,500 per contract. What price would lead to a margin call? Under what circumstances (i.e., the price) could $2,000 be withdrawn from the margin account?
Initial margin: 6000*2= 12,000 Notional value= 1.20*15000*2= 36,000 Maintenance margin= 4,500*2= 9,000 What price would lead to a margin call? 12,000-9000= 3,000 36,000-3000= 33,000/(15,000*2)= $1.10 A1: F1 = $1.10/lbs Under what circumstances (i.e., the price) could $2,000 be withdrawn from the margin account? 36,000+2,000=38,000/(15000*2)= A2: F1 = $1.267/lbs
A company enters into a short futures contract to sell 5,000 bushels of wheat for 2.50 cents per bushel. The initial margin is $3,000, and the maintenance margin is $2,000. At what price would there be a margin call? Under what circumstances (or price) could $1,500 be withdrawn from the margin account?
Initial margin= 3000 Notional margin= 5,000*2.50=12,500 Maintenance call= 2000 At what price would there be a margin call? 3000-2000= 1000 12500-1000= 13,500/5000=2.70 Under what circumstances (or price) could $1,500 be withdrawn from the margin account? 12500-1500=11,000/5000=2.20
Basis Risk in a long Hedge
It is June 8. A company knows that it will need to purchase 20,000 barrels of crude oil some time in October or November. The current December oil futures price is $58.00 per barrel. Its hedging strategy is as follows: 1) Take a long position in 20 December oil futures contracts on June 8 at a futures price of $58 2) Close out the contract when ready to purchase the oil One possible outcome is: Company is ready to purchase oil on November 10 Spot price on November 10= $65 December futures price on November10= $62 Basis on November 10= $3 Spot price Nov 10- Gain on Futures= $65-$4= $61 Or Futures price June 8th+ Basis on Nov 10= $58+$3= $61
Basis risk in a short hedge Example
It is March 1. A U.S. company expects to receive 50 million Japanese yen at the end of July. The September futures price for the yen is currently 0.8800 cents per yen. Its hedging strategy is as follows: 1) Short four September yen futures contracts on March 1 at a futures price of 0.8800 2) Close out the contract when the yen arrive at the end of July One possible outcome is: spot price at end of July= 0.82 September futures price at end of July= .8250 Basis at end of July =-0.0050 There are two ways of calculating the net exchange rate after hedging: Spot price in July+gain on futures= .82+0.0550= 0.8750 or futures price in march+ Basis in July = 0.88-0.005=0.8750
Hedging with options
It is May. An investor who owns 1,000 shares of a company and wants protection against a possible decline in the share price over the next two months. Market quotes are as follows: Current share price: $28 July 27.50 put price: $1 The investor buys 10 put option contracts for a total cost of $1000( 1000 shares *$1 put price). This gives the investor the right to sell 1,000 shares for a strike price of $27.50 per share during the next two months.
market order
It is a request that a trade be carried out immediately at the best price available in the market
"When a futures contract is traded on the floor of the exchange, it may be the case that the open interest increases by one, stays the same, or decreases by one." Explain this statement.
Must always be even long needs a short
Optimal number of contracts
N*= h*Qa/ Qf Qa= size of position being hedged (units) Qf=size of one futures contract (units)
Hedging with Forward contracts
Note that a company might do better if it chooses not to hedge than if it chooses to hedge. Alternatively, it might do worse. Consider ImportCo. If the exchange rate is 1.5000 on August 13 and the company has not hedged, the £10million that it has to pay will cost $15,000,000, which is less than $15,742,000. On the other hand, if the exchange rate is 1.6000, the £10million will cost $16,000,000 —and the company will wish it had hedged! The position of ExportCo if it does not hedge is the reverse. If the exchange rate in August proves to be less than 1.5736, the company will wish it had hedged; if the rate is greater than 1.5736, it will be pleased it has not done so.
1.6. You would like to speculate on a rise in the price of a certain stock. The current stock price is $29 and a three-month call with a strike price of $30 costs $2.90. You have $5800 to invest. Identify two alternative strategies. Briefly outline the advantages and disadvantages of each.
One strategy is to buy 200 shares. Another is to buy 2,000 options (20 contracts). If the share price does well, the second strategy will give rise to greater gains. For example, if the share price goes up to $40, you gain [2000×($40−$30)]−$5800=$14200 from the second strategy and only 200×($40$29)=$2200 from the first strategy. However, if the share price does badly, the second strategy yields greater losses. For example, if the share price goes down to $25, the first strategy leads to a loss of 200×($29−$25)=$800 whereas the second strategy leads to a loss of the entire $5800 investment.
If more people with to buy September corn than to sell September corn
Price goes up
Explain how margin accounts protect against default.
Prices are marked to market daily, protect against a couple days variation. Margin is like a down payment against a larger value of a commodity
Short futures position
Seller Chooses when delivery is made
Speculation in futures markets is pure gambling, which is not in the public interest. Discuss.
Speculators add liquidity, compensated on risk exposure
On the floor of a futures exchange, one futures contract is traded where the long party closes out and short party are opens a new position. What is the resulting change in open interest?
Stays the Same
3.7. A company has a $20 million portfolio with a beta of 1.2. It would like to use futures contracts on a well-diversified stock index to hedge its risk. The index futures price is currently 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?
The formula for the number of contracts that should be shorted gives: 1.2* (20,000,000/(1080*250)= 88.9 Rounding to the nearest whole number, 89 contracts should be shorted. To reduce the beta to 0.6, half of this position, or a short position in 44 contracts, is required.
1.4. An investor enters into a short forward contract to sell 100,000 British pounds for U.S. dollars at an exchange rate of 1.5000 U.S. dollars per pound. How much does the investor gain or lose if the exchange rate at the end of the contract is (a) 1.4900 and (b) 1.5200?
The investor is obligated to sell pounds for 1.5000 when they are worth 1.4900. The gain is (1.5000−1.4900)×100,000=$1000. The investor is obligated to sell pounds for 1.4000 when they are worth 1.4200. The loss is (1.5200-1.5000)*100,000= $2,000
2.6. What is the difference between the operation of the margin accounts administered by a clearing house and those administered by a broker?
The margin account administered by the clearinghouse is marked to market daily, and the clearinghouse member is required to bring the account back up to the prescribed level daily. The margin account administered by the broker is also marked to market daily. However, the account does not have to be brought up to the initial margin level on a daily basis. It has to be brought up to the initial margin level when the balance in the account falls below the maintenance margin level. The maintenance margin is usually about 75% of the initial margin.
2.1. Distinguish between the terms open interest and trading volume.
The open interest of a futures contract at a particular time is the total number of long positions outstanding. (Equivalently, it is the total number of short positions outstanding.) The trading volume during a certain period of time is the number of contracts traded during this period.
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?
The optimal hedge ratio is: 0.8*(0.65/0.81)= 0.642 This means that the size of the futures position should be 64.2% of the size of the company's exposure in a three-month hedge.
1.7. What is the difference between the over-the-counter and the exchange-traded market? What are the bid and offer quotes of a market maker in the over-the-counter market?
The over-the-counter market is a telephone- and computer-linked network of financial institutions, fund managers, and corporate treasurers where two participants can enter into any mutually acceptable contract. An exchange-traded market is a market organized by an exchange where traders either meet physically or communicate electronically and the contracts that can be traded have been defined by the exchange. When a market maker quotes a bid and an offer, the bid is the price at which the market maker is prepared to buy and the offer is the price at which the market maker is prepared to sell.
Suppose that in September 2016 a company takes a long position in a contract on May 2017 crude oil futures. It closes out its position in March 2017. The futures price (per barrel) is $58.30 when it enters into the contract, $60.50 when it closes out the position, and $59.10 at the end of December 2016. One contract is for the delivery of 1,000 barrels. What is the company's profit? When is it realized? How is it taxed if it is (a) a hedger and (b) a speculator? Assume that the company has a December 31 year end.
The total profit is ($60.50-58.30)*1000=$2,200 Of this (59.10-58.30)*1000= $800 is realized on a day-by-day basis between September 2016 and December 31, 2016. A further (60.50-59.10)*1000= $1400 is realized on a day-by-day basis between January 1, 2017, and March 2017. A hedger would be taxed on the whole profit of $2,200 in 2017. A speculator would be taxed on $800 in 2016 and $1,400 in 2017.
2.3. Suppose that you enter into a short futures contract to sell July silver for $27.20 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?
There will be a margin call when $1,000 has been lost from the margin account. This will occur when the price of silver increases by 1,000/5,000=$0.20. The price of silver must therefore rise to $27.40 per ounce for there to be a margin call. If the margin call is not met, your broker closes out your position.
In some years an oversupply situation of corn may create favorable prices; in other years scarcity may cause the prices to be exorbitant. It can make sense for the farmer and the company to get together in June (or even earlier) and agree on a price for the farmer's estimated production of corn in September.
This involves them negotiating a type of futures contract. The contract provides a way for each side to eliminate the risk it faces because of the uncertain future price of corn.
Maintenance Margin
To ensure that the balance in the margin account never becomes negative, a maintenance margin, which is somewhat lower than the initial margin, is set. If the balance in the margin account falls below the maintenance margin, the investor receives a margin call and is expected to top up the margin account to the initial margin level the next day. The extra funds deposited are known as a variation margin. If the investor does not provide the variation margin, the broker closes out the position.
Hedgers
Type of trader who use futures, forwards, and options to reduce the risk that they face from potential future movements in a market variable
Suppose that a futures contract with four months to maturity is used to hedge the value of a portfolio over the next three months in the following situation: Index level= 1,000 Index futures price= 1,010 value of portfolio= %5,050,000 Risk-free interest rate= 4% per annum Dividend yield on on index= !% per annum Beta of portfolio= 1.5 Futures contract is for deliver of $250 times the index.
Vf= 250*1010= 252,500 1.5*(5,050,000/252500)= 30 Suppose the index turns out to be 900 in three months, and the futures price is 902. The gain from the Short futures position is then 30*(1,010-902)*250= $810,000 The loss on the index is 10% (900-1000)/1000 The index pays a dividend of 1% per annum or 0.25% per three months. When dividends are taken into account, an investor in the index would therefore earn -9.75% (10%-.25%) over the three-month period. Expected return on portfolio= Risk-free interest rate (1.0) + (Beta (1.5)*( return on index (-9.75)- risk free interest (1.0))= -15.125% Expected value of the portfolio at the end of the three months is, therefore = 5,050,000*(1-0.15125)= $4,286,187 The expected value of the hedger's positon, including the gain on the hedge, is: 4,286,187+ 810,000= $5,096,187
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 the beta of the portfolio to 0.5 during the period July 16 to November 16. The index futures price is 2,000 and each contract is on $250 times the index. What position should the company take? 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?
What position should the company take? |1.2-0.5| 100,000,000/(2000*250)= A1: 140 contracts short or -140 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? A2: 60 contracts long
1.5. Suppose that you write a put contract with a strike price of $40 and an expiration date in three months. The current stock price is $41 and one put option contract is on 100 shares. What have you committed yourself to? How much could you gain or lose?
You have sold a put option. You have agreed to buy 100 shares for $40 per share if the party on the other side of the contract chooses to exercise the right to sell for this price. The option will be exercised only when the price of stock is below $40. Suppose, for example, that the option is exercised when the price is $30. You have to buy at $40shares that are worth $30; you lose $10 per share, or $1000 in total. If the option is exercised when the price is $20, you lose $20 per share, or $2000 in total. The worst that can happen is that the price of the stock declines to almost zero during the three-month period. This highly unlikely event would cost you $4000. In return for the possible future losses, you receive the price of the option from the purchaser.
Short Hedge
a hedge, such as the one just described, that involves a short position in futures contracts. A short hedge is appropriate when the hedger already owns an asset and expects to sell it at some time in the future.
A company enters into long futures contract to buy 8,000 barrels of oil for a futures price of $115.25 per barrel. The initial margin is $6,000 and the maintenance margin is $4,000 per contract. Each contract is for 1,000 barrels. What oil futures price (per barrel) will allow $3,000 to be withdrawn from the margin account? (Type just the number to two decimal places, without symbols. For example, if your answer is "-$1,425.237" then enter "-1425.24").
a. Initial Margin= 6,000*8= 48,000 Notional value= 115.25*1,000*8 contracts= 922,000 Margin is 48,000+3000= 51,000 Notional value = 922,000+3000= 925,000 925,000/(8*1000)= $115.625
A company enters into long position in a futures contract for 3,000 barrels of oil for a futures price of $50.11 per barrel. The initial margin is $6,000 and the maintenance margin is $4,000 per contract. Each contract is for 1,000 barrels. At what oil futures price (per barrel) will there be a margin call? (Type just the number to two decimal places, without symbols. For example, if your answer is "-$1,425.237" then enter "-1425.24").
a. Initial margin = $6,000*3= 18,000 Notional value= 50.11*1,000*3 contracts= 150,330 A margin call would be at 4,000*3 contracts= 12,000 18,000-12,000=6000 150,330-6000= 144330/3000= a price of $48.11
A company enters into short futures contract to deliver 5,000 barrels of oil for a futures price of $59.04 per barrel. The initial margin is $6,000 and the maintenance margin is $4,000 per contract. Each contract is for 1,000 barrels. What oil futures price (per barrel) will allow $5,000 to be withdrawn from the margin account? (Type just the number to two decimal place, without symbols. For example, if your answer is "-$1,425.237" then enter "-1425.24").
a. Initial margin: 6000*5 contracts= 30,000 Notional value: 59.04*1000* 5= 295,200 The Notional value has to go down by 5,000: 295,200-5000= 290,200 30,000-5000= 25,000 290,200/(5*1000)= 58.04
Suppose you are managing an equity portfolio with a beta of 0.6 and $16M in assets. S&P 500 index futures with a multiplier of 250 (not the e-mini futures) are currently priced at 1386, and the index is also 1,386. What position in index futures is necessary to increase the portfolio beta to 1.3? (For this problem, respond with a numerical value rounded to one decimal place. For example, if your answer is "short 25.46 contracts", then enter "-25.5")
a. Long N*= | 0.60-1.3| 16,000,000/(250*1386)= 32.32 contracts If beta goes up then it is long
Suppose you are managing an equity portfolio with a beta of 1.8 and $125M in assets. S&P 500 index futures (with a multiplier of 250) are currently priced at 2017, and the index is also 2,017. What position in index futures is necessary to hedge the equity portfolio beta to 0? (For this problem, respond with a numerical value rounded to one decimal place. For example, if your answer is "short 25.46 contracts", then enter "-25.5")
a. Short N*= |1.8-0| 125,000,000/(250*2017)= -446.20 Beta goes down so it is short
Agricultural futures contracts are carefully designed to specify the commodity being delivered. Sometimes the price is adjusted based on the quality of commodity delivered. The reason for this price adjustment is to
a. To minimize the risks of a short squeeze. As the shorts scramble to buy back and cover their losses, upward momentum can build on itself, causing the stock to move sharply higher
stop order or stop-loss order
also specifies a particular price. The order is executed at the best available price once a bid or offer is made at that particular price or a less-favorable price. Suppose a stop order to sell at $30 is issued when the market price is $35. It becomes an order to sell when and if the price falls to $30. In effect, a stop order becomes a market order as soon as the specified price has been hit. The purpose of a stop order is usually to close out a position if unfavorable price movements take place.
fill-or-kill order
as its name implies, must be executed immediately on receipt or not at all.
The minimum Variance hedge ratio
depends on the relationship between changes in the spot price and changes in the futures price. Define: h* is the slope of the best-fit line from a linear regression of Change in S (spot price) against Change in F (futures price). We would expect h* to be the ratio of the average change in S for a particular change in F. h*= Coefficient of Correlation *(Standard dev of change in S/ Standard dev of change in F)
How Margin accounts work!
for example, that by the end of the first day the futures price has dropped from $1,250 (current futures price) to $1,241. The investor has a loss of $1,800(=200(investor has contracted to buy a total of 200 ounces) ×$9(difference between 1250-1241)), because the 200 ounces of December gold, which the investor contracted to buy at $1,250, can now be sold for only $1,241. The balance in the margin account would therefore be reduced by $1,800 to $10,200(12,000 initial margin that is given- 1800). Similarly, if the price of December gold rose to $1,259 by the end of the first day, the balance in the margin account would be increased by $1,800 to $13,800 (12,000+1800).
Call option
gives the holder the right to buy an asset by a certain date for a certain price. Price of a call option decreases as the strike price increases. In our example, the trader has obtained at a cost of $2900 the right to buy 100 Google shares for $550 each. If the price of Google does not not rise above $550.00 by December 18, 2015, the option is not exercised and the trader loses $2900. But if Google does well and the option is exercised when the bid price for the stock is $650 the trader is able to buy 100 shares at $550 and immediately sell them for $650 for a profit of $10000—or $7100 when the initial cost of the options is taken into account.
Put option
gives the holder the right to sell an asset by a certain date for a certain price. Price of a put option increases as the strike price increases. An alternative trade would be to sell one September put option contract with a strike price of $525 at the bid price of $22.40.This would lead to an immediate cash inflow of 100×22.40=$2240. If the Google stock price stays above $525 this option is not exercised and the trader makes a profit of this amount. However, if stock price falls and the option is exercised when the stock price is, say, $480 there is a loss. The trader must buy 100 shares at $525when they are worth only $480. This leads to a loss of $4500 or $2260 when the initial amount received for the option contract is taken into account.
spot price
immediate, or almost immediate delivery. (like the market price right NOW)
stop-Limit order
is a combination of a stop order and a limit order. The order becomes a limit order as soon as a bid or offer is made at a price equal to or less favorable than the stop price. Two prices must be specified in a stop-limit order: the stop price and the limit price. Suppose that, at the time the market price is $35, a stop-limit order to buy is issued with a stop price of $40 and a limit price of $41. As soon as there is a bid or offer at $40, the stop-limit becomes a limit order at $41
Limit Move
is a move in either direction equal to the daily price limit. Normally, trading ceases for the day once the contract is limit up or limit down
Futures contract
is an agreement to buy or sell an asset at a certain time in the future for a certain price. Traded on exchanges. Settled daily
Long Hedge
is appropriate when a company knows it will have to purchase a certain asset in the future and wants to lock in a price now.
open order or good-till-canceled order
is in effect until executed or until the end of trading in the particular contract
Forward Contract
is similar to a futures contracts in that it is an agreement to buy or sell an asset at a certain time in the future for a certain price. But, whereas futures contracts are traded on exchanges, forward contracts trade in the over-the-counter market. Settled at the END of its life
Hedge ratio
is the ratio of the size of the position taken in futures contracts to the size of the exposure. When the asset underlying the futures contract is the same as the asset being hedged it is natural to use a hedge ratio of 1.0. When cross hedging is used, setting the hedge ratio equal to 1.0 is not always optimal. The hedger should choose a value for the hedge ratio that minimizes the variance of the value of the hedged position.
Discretionary Order
or market-not-held order is traded as a market order except that execution may be delayed at the broker's discretion in an attempt to get a better price
Time-of day order
specifies a particular period of time during the day when the order can be executed
Limit Order
specifies a particular price. The order can be executed only at this price or at one more favorable to the investor. Thus, if the limit price is $30 for an investor wanting to buy, the order will be executed only at a price of $30 or less.
position limits
the maximum number of contracts that a speculator may hold.
Basis Risk Example
we will consider the case where the spot and futures prices at the time the hedge is initiated are $2.50 and $2.20, respectively, and that at the time the hedge is closed out they are $2.00 and $1.90. This means that S1= 2.50, F1= 2.20, S2=2.00, and F2= 1.90. Basis 1= S1-F1 (2.50-2.20)= .30 Basis 2= S2-F2(2.00-1.90)= .10 Consider first the situation of a hedger who knows that the asset will be sol at time t2 and takes a short futures position at time t1. The price realized for the asset is S2 and the profit on the futures positon is F1-F2. The effective price obtained for the asset with hedging is therefore: S2+F1-F2= F1+b2 (2.00+2.20-1.90)=2.30 Next consider a situaation where a company knows if will buy the asset at time t2 and initiates a long hedge at time t1. The price paid for the asset is S2 and the loss on the hedge is F1-F2. The effective price paid with hedging is therefore. S2+F1-F2=F1+B2 which again is 2.30, b2 represent s basis risk short hedge because it plans to sell the asset. If the basis strengthens (i.e., increases) unexpectedly, the company's position improves because it will get a higher price for the asset after futures gains or losses are considered; if the basis weakens (i.e., decreases) unexpectedly, the company's position worsens. For a company using a long hedge because it plans to buy the asset, the reverse holds. If the basis strengthens unexpectedly, the company's position worsens because it will pay a higher price for the asset after futures gains and losses are considered; if the basis weakens unexpectedly, the company's position improves.
