A company runs a number of slaughterhouses which supply hamburger meat to McDonalds. The company is afraid that live cattle prices will increase over the next year, even though there is widespread belief in the market that they will be stable. What can the company do to hedge against the risk of increasing live cattle prices? Which statement(s) are correct?

(i) buy call options on live cattle.

(ii) buy put options on live cattle.

(iii) sell call options on live cattle.

Select the most correct response:

You operate a cattle farm that supplies hamburger meat to the big fast food chains. You buy a lot of grain to feed your cattle, and you sell the fully grown cattle on the livestock market.

You're afraid of adverse movements in grain and livestock prices. What options should you buy to hedge your exposures in the grain and cattle livestock markets?

Select the most correct response:

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.

**Question 793** option, hedging, delta hedging, gamma hedging, gamma, Black-Scholes-Merton option pricing

A bank buys **1000** European put options on a $10 non-dividend paying stock at a strike of $12. The bank wishes to hedge this exposure. The bank can trade the underlying stocks and European call options with a strike price of 7 on the same stock with the same maturity. Details of the call and put options are given in the table below. Each call and put option is on a single stock.

European Options on a Non-dividend Paying Stock |
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Description |
Symbol |
Put Values |
Call Values |

Spot price ($) | ##S_0## | 10 | 10 |

Strike price ($) | ##K_T## | 12 |
7 |

Risk free cont. comp. rate (pa) | ##r## | 0.05 | 0.05 |

Standard deviation of the stock's cont. comp. returns (pa) | ##\sigma## | 0.4 | 0.4 |

Option maturity (years) | ##T## | 1 | 1 |

Option price ($) | ##p_0## or ##c_0## | 2.495350486 | 3.601466138 |

##N[d_1]## | ##\partial c/\partial S## | 0.888138405 | |

##N[d_2]## | ##N[d_2]## | 0.792946442 | |

##-N[-d_1]## | ##\partial p/\partial S## | -0.552034778 | |

##N[-d_2]## | ##N[-d_2]## | 0.207053558 | |

Gamma | ##\Gamma = \partial^2 c/\partial S^2## or ##\partial^2 p/\partial S^2## | 0.098885989 | 0.047577422 |

Theta | ##\Theta = \partial c/\partial T## or ##\partial p/\partial T## | 0.348152078 | 0.672379961 |

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

**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.

**Question 860** idiom, hedging, speculation, arbitrage, market making, insider trading, no explanation

Which class of derivatives market trader is **NOT** principally focused on ‘buying low and selling high’?

**Question 956** option, Black-Scholes-Merton option pricing, delta hedging, hedging

A bank sells a European call option on a non-dividend paying stock and delta hedges on a daily basis. Below is the result of their hedging, with columns representing consecutive days. Assume that there are 365 days per year and interest is paid daily in arrears.

Delta Hedging a Short Call using Stocks and Debt |
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Description |
Symbol |
Days to maturity (T in days) |
|||||

60 |
59 |
58 |
57 |
56 |
55 |
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Spot price ($) | S | 10000 | 10125 | 9800 | 9675 | 10000 | 10000 |

Strike price ($) | K | 10000 | 10000 | 10000 | 10000 | 10000 | 10000 |

Risk free cont. comp. rate (pa) | r | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 | 0.05 |

Standard deviation of the stock's cont. comp. returns (pa) | σ | 0.4 | 0.4 | 0.4 | 0.4 | 0.4 | 0.4 |

Option maturity (years) | T | 0.164384 | 0.161644 | 0.158904 | 0.156164 | 0.153425 | 0.150685 |

Delta | N[d1] = dc/dS | 0.552416 | 0.582351 | 0.501138 | 0.467885 | 0.550649 | 0.550197 |

Probability that S > K at maturity in risk neutral world | N[d2] | 0.487871 | 0.51878 | 0.437781 | 0.405685 | 0.488282 | 0.488387 |

Call option price ($) | c | 685.391158 | 750.26411 | 567.990995 | 501.487157 | 660.982878 | ? |

Stock investment value ($) | N[d1]*S | 5524.164129 | 5896.301781 | 4911.152036 | 4526.788065 | 5506.488143 | ? |

Borrowing which partly funds stock investment ($) | N[d2]*K/e^(r*T) | 4838.772971 | 5146.037671 | 4343.161041 | 4025.300909 | 4845.505265 | ? |

Interest expense from borrowing paid in arrears ($) | r*N[d2]*K/e^(r*T) | 0.662891 | 0.704985 | 0.594994 | 0.551449 | ? | |

Gain on stock ($) | N[d1]*(SNew - SOld) | 69.052052 | -189.264008 | -62.642245 | 152.062648 | ? | |

Gain on short call option ($) | -1*(cNew - cOld) | -64.872952 | 182.273114 | 66.503839 | -159.495721 | ? | |

Net gain ($) | Gains - InterestExpense | 3.516209 | -7.695878 | 3.266599 | -7.984522 | ? | |

Gamma | Γ = d^2c/dS^2 | 0.000244 | 0.00024 | 0.000255 | 0.00026 | 0.000253 | 0.000255 |

Theta | θ = dc/dT | 2196.873429 | 2227.881353 | 2182.174706 | 2151.539751 | 2266.589184 | 2285.1895 |

In the last column when there are 55 days left to maturity there are missing values. Which of the following statements about those missing values is **NOT** correct?