[金融市場與衍生性商品] HW1 & Quiz1

小考一的連結與解答：

https://drive.google.com/file/d/1V8QbkpNjStMCu_8BZfUQ_feYNQgGGiyf/view?usp=sharing

小考一為四題單選題，其實不難，可惜那時候有點緊張沒把題目看清楚一點，加上對margin account的概念還沒有完全搞清楚，把第一題臨時改掉就錯了...本來可以滿分的＠＠

作業ㄧ比較困難一點，半夜上ceiba網站才發現原來不是只有小考還有作業！

半夜大概花了兩個小時趕了作業這六題，沒有寫得很好那時候腦袋不清，但還是拿到平均的分數啦＠＠

平均分數80幾分超高，可能經濟系的同學有一起寫吧＠＠

外系生如我只能加油了！

1. Margin Requirement Suppose we sell a copper futures contract (25,000 pounds per contract), maturing in one month, at the forward price $1.5 per pound today. Suppose the initial margin is $4000 per contract and the maintenance margin is $3000. According to daily settlement requirement, and that the settlement price (or the closing forward price) for the next day rises to $1.55,

A. (6 points) Will the seller of the copper futures contract or the buyer of the copper futures contract lose and how much? B. (6 points) Will there be a margin call to us? If there is, what is the amount that we have to add to our margin account?

2. Basis Suppose that Delta Air Lines Inc will buy 60,000 lb oil in December 2006 and now the company buys a February 2007 oil futures (contract size 60,000 lb) to hedge. Now the oil futures price is 84.90 cents/lb.

Suppose that Marathon Oil Corp will sell 60,000 lb oil in December 2006 and now the company sells a February 2007 oil futures (contract size 60,000 lb) to hedge. Now the oil futures price is 84.90 cents/lb.

A. (6 points) What is the effective price paid by the Delta Air Lines Inc for the oil? (use notation for the answer, if needed) B. (6 points) Will Delta Air Lines Inc benefit for a smaller basis in December 2006? C. (6 points) What is the effective price received by the Marathon Oil Corp for the oil? (use notation for the answer, if needed) D. (6 points) Will Marathon Oil Corp benefit for a smaller basis in December 2006?

3. Forward and Futures Prices

You observe the following data on March 15: XYZ Index $125 September 15 XYZ Index forward price $123 Continuously compounding risk-free rate 7%

A. (12 points) Construct a replicating portfolio of the XYZ Index forward using XYZ Index stocks and risk-free bonds. What is the forward price? How much do you have to pay to enter the forward contract? Is there an arbitrage opportunity? How can you take advantage of it if there is one? B. (6 points) Notice that the XYZ Index forward price is below the spot quote of the XYZ Index on March 15. Does this immediately imply an arbitrage opportunity?

4. Forward and Futures Prices

A. (6 points) Suppose the stock price is $35 and the continuously compounded interest rate is 5%. What is the 6-month forward price, assuming dividends are zero?

B. (6 points) If the forward price is $35.50, what is the annualized continuous dividend yield?

5. Forward and Futures Prices

Suppose you are a market-maker in S&R index forward contracts. The S&R index spot price is 1100, the risk-free rate is 5%, and the dividend yield on the index is 0.

A. (6 points) What is the no-arbitrage forward price for delivery in 9 months?

B. (6 points) Suppose a customer wishes to enter a short index futures position. If you take the opposite position, demonstrate how you would hedge your resulting long position using the index and borrowing or lending.

C. (6 points) Suppose a customer wishes to enter a long index futures position. If you take the opposite position, demonstrate how you would hedge your resulting short position using the index and borrowing or lending.

6. Forward and Futures Prices (16 points)

Suppose the S&R index is 800, and that the dividend yield is 0. You are an arbitrageur with a continuously compounded borrowing rate of 5.5% and a continuously compounded lending rate of 5%.

Supposing that there are no transaction fees, show that a cash-and-carry arbitrage is not profitable if the 1-year forward price is less than 845.23, and that a reverse cash-and-carry arbitrage is not profitable if the 1-year forward price is greater than 841.02.

Answer: (我寫的加上後來訂正)

1. (這題跟小考第一題根本一樣，但我小考就是多疑啊)

A. (1.55-1.5)*25000=1250 so the seller lose 1250. B. yes, since 4000-1250=2750<3000, we need to add 1250 to our margin account.

簡單說就是都要補回initial margin account，因為那是基本的標準，低於maintenance margin會有margin call叫你補回到initial，不補的話就會幫你賣掉(斷頭)，高於maintenance margin但低於initial margin則不能交易，多出initial的部位可以提取。

2. A. -F(0,2007)+F(2006,2007)-S(2006)=-84.9+F(2006,2007)-S(2006) B. Basis=S(2006)-F(2006, 2007) so, yes, Delta Air Lines Inc will benefit for a smaller basis in December 2006. C. 84.9-F(2006,2007)+S(2006) D. No, Marathon Oil Corp will benefit for a larger basis in December 2006.

3.

A. Borrow $125 from bond market. Buy 1 XYZ Index sell XYZ Index on September 15 return $125*exp(0.5*0.07) = $129.45. So, the forward price is $129.45. And $123<$129.45. You don't pay any to enter the forward contract. If there is no premium, there is an arbitrage opportunity. We can buy actual forward contract and sell a synthetic forward.

B. No, since we use risk-free rate, but in reality there is risk and maybe the value of money will decrease.

4.

A. 35*exp(0.05*0.5)=35.886

B. (35.886/35.5)^2-1=2.186% (ans is 2.16% ?)

about dividend yield:

https://www.investopedia.com/terms/d/dividendyield.asp

5.

A. 1100*exp(0.05*0.75)=1142.0332

B. C.

題目很難懂，但我反覆讀了幾次之後，再看著答案想了一下，得到可能的答案：

B.題目是在說你現在是long position但你想要hedge你的position，所以你必須把asset 賣掉，

因此short-sell the index and after a while you buy the asset back and return.

C.則是要把保留index在手上，因此borrow money buy the index and after a while sell the index return the money.

6.

When cash-and-carry you full amount borrowed and buy the underlying asset and short the forward. So the price is 800*exp(0.055)=845.23. And when reverse cash-and-carry, you short sell the underlying asset and full invested. So the price is 800*exp(0.05)=841.02.