**Question 589** future, contango, market efficiency

In general, stock prices tend to rise. What does this mean for futures on equity?

Which of the following statements about futures contracts on shares is **NOT** correct, assuming that markets are efficient?

When an equity future is first negotiated (at t=0):

After doing extensive fundamental analysis of a company, you believe that their shares are overpriced and will soon fall significantly. The market believes that there will be no such fall.

Which of the following strategies is **NOT** a good idea, assuming that your prediction is true?

A trader **buys** one December futures contract on orange juice. Each contract is for the delivery of **10,000** pounds. The current futures price is $**1.20** per pound. The initial margin is $**5,000** per contract, and the maintenance margin is $**4,000** per contract.

What is the smallest price change would that would lead to a margin call for the buyer?

The price of gold is currently $**700** per ounce. The forward price for delivery in 1 year is $**800**. An arbitrageur can borrow money at **10**% per annum given as an effective discrete annual rate. Assume that gold is fairly priced and the cost of storing gold is zero.

What is the best way to conduct an arbitrage in this situation? The best arbitrage strategy requires zero capital, has zero risk and makes money straight away. An arbitrageur should **sell 1 forward** on gold and:

The current gold price is $**700**, gold storage costs are **2**% pa and the risk free rate is **10**% pa, both with **continuous compounding**.

What should be the **3** year gold futures price?

A **2**-year futures contract on a stock paying a continuous dividend yield of **3**% pa was bought when the underlying stock price was $**10** and the risk free rate was **10**% per annum with **continuous compounding**. Assume that investors are risk-neutral, so the stock's total required return is the risk free rate.

Find the forward price ##(F_2)## and value of the contract ##(V_0)## initially. Also find the value of the contract in 6 months ##(V_{0.5})## if the stock price rose to $**12**.

An equity index is currently at **5,000** points. The **2** year futures price is **5,400** points and the total required return is **8**% pa with continuous compounding. Each index point is worth $**25**.

What is the implied continuous dividend yield as a continuously compounded rate per annum?

A stock is expected to pay a dividend of $**5** per share in **1** month and $**5** again in **7** months.

The stock price is $**100**, and the risk-free rate of interest is **10**% per annum with continuous compounding. The yield curve is flat. Assume that investors are risk-neutral.

An investor has just taken a **short** position in a **one** year forward contract on the stock.

Find the forward price ##(F_1)## and value of the contract ##(V_0)## initially. Also find the value of the short futures contract in 6 months ##(V_\text{0.5, SF})## if the stock price fell to $**90**.

**Question 598** future, tailing the hedge, cross hedging

The standard deviation of monthly changes in the spot price of lamb is $**0.015** per pound. The standard deviation of monthly changes in the futures price of live cattle is $**0.012** per pound. The correlation between the spot price of lamb and the futures price of cattle is **0.4**.

It is now January. A lamb producer is committed to selling **1,000,000** pounds of lamb in May. The spot price of live cattle is $**0.30** per pound and the June futures price is $**0.32** per pound. The spot price of lamb is $**0.60** per pound.

The producer wants to use the June live cattle futures contracts to hedge his risk. Each futures contract is for the delivery of **50,000** pounds of cattle.

How many live cattle futures should the lamb farmer sell to hedge his risk? Round your answer to the nearest whole number of contracts.

Which one of the below option and futures contracts gives the possibility of potentially unlimited gains?

Which of the below formulas gives the payoff at maturity ##(f_T)## from being **long** a future? Let the underlying asset price at maturity be ##S_T## and the locked-in futures price be ##K_T##.

Which of the below formulas gives the payoff at maturity ##(f_T)## from being **short** a future? Let the underlying asset price at maturity be ##S_T## and the locked-in futures price be ##K_T##.

A trader **buys** one crude oil **futures** contract on the CME expiring in one year with a locked-in futures price of $38.94 per barrel. If the trader doesn’t close out her contract before expiry then in one year she will have the:

A trader **sells** one crude oil **futures** contract on the CME expiring in one year with a locked-in futures price of $38.94 per barrel. The crude oil spot price is $40.33. If the trader doesn’t close out her contract before expiry then in one year she will have the:

Alice, Bob, Chris and Delta are traders in the futures market. The following trades occur over a single day in a newly-opened equity index future that matures in one year which the exchange just made available.

1. Alice buys a future from Bob.

2. Chris buys a future from Delta.

3. Delta buys a future from Alice.

These were the only trades made in this equity index future. What was the trading volume and what is the open interest?

Alice, Bob, Chris and Delta are traders in the futures market. The following trades occur over a single day in a newly-opened equity index future that matures in one year which the exchange just made available.

1. Alice buys a future from Bob.

2. Chris buys a future from Delta.

3. Delta buys a future from Bob.

These were the only trades made in this equity index future. What was the trading volume and what is the open interest?

A trader **buys** a one year futures contract on crude oil. The contract is for the delivery of 1,000 barrels. The current futures price is $38.94 per barrel. The initial margin is $3,410 per contract, and the maintenance margin is $3,100 per contract.

What is the smallest price change that would lead to a margin call for the buyer?

A trader **sells** a one year futures contract on crude oil. The contract is for the delivery of 1,000 barrels. The current futures price is $38.94 per barrel. The initial margin is $3,410 per contract, and the maintenance margin is $3,100 per contract.

What is the smallest price change that would lead to a margin call for the seller?

In February a company sold one December 40,000 pound (about 18 metric tons) lean hog futures contract. It closed out its position in May.

The spot price was $**0.68** per pound in February. The December futures price was $**0.70** per pound when the trader entered into the contract in February, $**0.60** when he closed out his position in May, and $**0.55** when the contract matured in December.

What was the total profit?

An equity index is currently at **5,200** points. The **6** month futures price is **5,300** points and the total required return is **6**% pa with continuous compounding. Each index point is worth $25.

What is the implied dividend yield as a continuously compounded rate per annum?

An equity index is currently at **4,800** points. The **1.5** year futures price is **5,100** points and the total required return is **6**% pa with continuous compounding. Each index point is worth $25.

What is the implied dividend yield as a continuously compounded rate per annum?

Which of the following statements about futures and forward contracts is **NOT** correct?

Alice, Bob, Chris and Delta are traders in the futures market. The following trades occur over a single day in a newly-opened equity index future that matures in one year which the exchange just made available.

1. Alice buys a future from Bob.

2. Chris buys a future from Delta.

3. Bob buys a future from Chris.

These were the only trades made in this equity index future. What was the trading volume and what is the open interest?

1. Alice buys a future from Bob.

2. Chris buys a future from Delta.

3. Alice buys a future from Chris.

An equity index stands at **100** points and the one year equity futures price is **102**.

The equity index is expected to have a dividend yield of **4**% pa. Assume that investors are risk-neutral so their total required return on the shares is the same as the risk free Treasury bond yield which is **10**% pa. Both are given as discrete effective annual rates.

Assuming that the equity index is fairly priced, an arbitrageur would recognise that the equity futures are:

An equity index stands at **100** points and the one year equity futures price is **107**.

The equity index is expected to have a dividend yield of **3**% pa. Assume that investors are risk-neutral so their total required return on the shares is the same as the risk free Treasury bond yield which is **10**% pa. Both are given as discrete effective annual rates.

Assuming that the equity index is fairly priced, an arbitrageur would recognise that the equity futures are:

A pig farmer in the US is worried about the price of hogs falling and wants to lock in a price now. In one year the pig farmer intends to sell **1,000,000** pounds of hogs. Luckily, one year CME lean hog futures expire on the exact day that he wishes to sell his pigs. The futures have a notional principal of **40,000** pounds (about 18 metric tons) and currently trade at a price of **63.85** cents per pound. The underlying lean hogs spot price is **77.15** cents per pound. The correlation between the futures price and the underlying hogs price is **one** and the standard deviations are both **4** cents per pound. The initial margin is USD**1,500** and the maintenance margin is USD**1,200** per futures contract.

Which of the below statements is **NOT** correct?

An equity index fund manager controls a USD**1 billion** diversified equity portfolio with a beta of **1.3**. The equity manager fears that a global recession will begin in the next year, causing equity prices to tumble. The market does not think that this will happen. If the fund manager wishes to reduce her portfolio beta to **0.5**, how many S&P500 futures should she sell?

The US market equity index is the S&P500. One year CME futures on the S&P500 currently trade at **2,062** points and the spot price is **2,091** points. Each point is worth $**250**. How many one year S&P500 futures contracts should the fund manager sell?

The standard deviation of monthly changes in the spot price of corn is **50** cents per bushel. The standard deviation of monthly changes in the futures price of corn is **40** cents per bushel. The correlation between the spot price of corn and the futures price of corn is **0.9**.

It is now March. A corn chip manufacturer is committed to buying **250,000** bushels of corn in May. The spot price of corn is **381** cents per bushel and the June futures price is **399** cents per bushel.

The corn chip manufacturer wants to use the June corn futures contracts to hedge his risk. Each futures contract is for the delivery of **5,000** bushels of corn. One bushel is about 127 metric tons.

How many corn futures should the corn chip manufacturer buy to hedge his risk? Round your answer to the nearest whole number of contracts. Remember to tail the hedge.

1. Alice buys 2 futures from Bob.

2. Chris buys 3 futures from Delta.

3. Delta buys 5 futures from Alice.

Which of the following statements is **NOT** correct?

Which derivatives position has the possibility of unlimited potential gains?

What derivative position are you exposed to if you have the **obligation** to **sell** the underlying asset at maturity, so you will definitely be forced to sell the underlying asset?

**Question 825** future, hedging, tailing the hedge, speculation, no explanation

An equity index fund manager controls a USD**500** million diversified equity portfolio with a beta of **0.9**. The equity manager expects a significant rally in equity prices next year. The market does not think that this will happen. If the fund manager wishes to increase his portfolio beta to **1.5**, how many S&P500 futures should he buy?

The US market equity index is the S&P500. One year CME futures on the S&P500 currently trade at **2,155** points and the spot price is **2,180** points. Each point is worth $**250**.

The number of one year S&P500 futures contracts that the fund manager should buy is:

On **1 February** 2016 you were told that your refinery company will need to purchase oil on **1 July** 2016. You were afraid of the oil price rising between now and then so you bought some **August** 2016 futures contracts on 1 February 2016 to hedge against changes in the oil price. On 1 February 2016 the oil price was $**40** and the August 2016 futures price was $**43**.

It's now **1 July** 2016 and oil price is $**45** and the August 2016 futures price is $**46**. You bought the spot oil and closed out your futures position on **1 July** 2016.

What was the effective price paid for the oil, taking into account basis risk? All spot and futures oil prices quoted above and below are per barrel.

You intend to use futures on oil to hedge the risk of purchasing oil. There is no cross-hedging risk. Oil pays no dividends but it’s costly to store. Which of the following statements about basis risk in this scenario is **NOT** correct?

You **bought** a **1.5** year (18 month) futures contract on oil. Oil storage costs are **4**% pa continuously compounded and oil pays no dividends. The futures contract is entered into when the oil price is $**40** per barrel and the risk-free rate of interest is **10**% per annum with continuous compounding.

Which of the following statements is **NOT** correct?

**Question 829** option, future, delta, gamma, theta, no explanation

Below are some statements about futures and European-style options on non-dividend paying stocks. Assume that the risk free rate is always positive. Which of these statements is **NOT** correct? All other things remaining equal:

A stock is expected to pay its semi-annual dividend of $1 per share for the foreseeable future. The current stock price is $**40** and the continuously compounded risk free rate is **3**% pa for all maturities. An investor has just taken a **long** position in a **12**-month futures contract on the stock. The last dividend payment was exactly 4 months ago. Therefore the next $**1** dividend is in **2** months, and the $**1** dividend after is **8** months from now. Which of the following statements about this scenario is **NOT** correct?

A non-dividend paying stock has a current price of $**20**.

The risk free rate is **5**% pa given as a continuously compounded rate.

A **2** year futures contract on the stock has a futures price of $**24**.

You suspect that the futures contract is mis-priced and would like to conduct a risk-free arbitrage that requires zero capital. Which of the following steps about arbitraging the situation is **NOT** correct?