Amaranth Advisors L.L.C. was a hedge fund that, as of September 2006, massively invested in energy derivatives. The fund held very large positions in natural gas futures. The trades consisted mainly of buying and selling natural gas futures contracts with a variety of maturity dates, setting up what is called a calendar spread.

The fund had positions on most of the futures contracts available, covering almost any month between September 2006 and December 2011. We will consider the positions in two of these many contracts to get a practical understanding of what happened in September 2006.

Suppose that, as of August 31^st 2006, Amaranths book (i.e., portfolio) was constituted as follows:

Contract expiration	Number of contracts	Futures price, $
Nov. 06	59,247 long	$8.23
Apr. 07	(77,527) (short)	$8.34

The Excel file Amaranth.xls contains daily futures prices of the two contracts between August 31^st 2006 and September 21^st 2006. Using these prices, and bearing in mind that the size of one Natural Gas futures contract is 10,000 MMBtu (millions of British Thermal Units, a unit of measure for gas), compute:

The daily and cumulative Profit and Loss (P&L) from the strategy.

The value of the portfolio (constituted of the two futures position) between August 31^st and September 21^st 2006, assuming that the portfolio was initiated on August 31^st 2006.

The cumulative cash required by the strategy, knowing that NYMEX (i.e., the exchange) requires $5,400 initial margin and $2,700 maintenance margin per contract. Assume that the cash in excess of the initial margin (if any) is withdrawn from the account daily and margin calls result in full replenishment of the margin account (i.e., up to the initial margin).

If you wish to read more about Amaranth Advisors, the link below contains some references: https://en.wikipedia.org/wiki/Amaranth_Advisors

	Futures price per MMBtu, USD
Day	NOV. 06	APR. 07
31-Aug	8.23	8.34
1-Sep	8.06	8.38
5-Sep	8.08	8.46
6-Sep	8.02	8.43
7-Sep	7.61	8.15
8-Sep	7.61	8.14
11-Sep	7.26	7.91
12-Sep	7.27	7.75
13-Sep	7.08	7.58
14-Sep	6.47	7.15
15-Sep	6.36	7.31
18-Sep	6.26	7.51
19-Sep	6.20	7.49
20-Sep	6.02	7.33
21-Sep	6.01	7.17