1) The worlds most actively traded commodity is crude oil. New York Mercantile Exchange (NYMEX) is the largest market for future oil contracts, both light sweet and brent. Contracts are traded in units of 1000 barrels. Currently, non-member initial margin is $4,725 per contract. The Maintenance requirement is $3,500. Suppose you long 10 September 05 contracts with the exercise price of $62.25 per barrel.

Number of contracts = 10
Size of each contract= 1000 barrels

a) suppose price of oil in the spot market drops to $60.25. What will be the balance of your margin account?

Number of contracts = 10
Size of each contract= 1000 barrels

Initial Margin = $4,725 per contract
Exercise price= $62.25 per barrel
If the price falls below the exercise price there is a loss
Price= $60.25
Loss per barrel= $2.00 =62.25-60.25
Loss per contract= $2,000 =1000x2
Margin account per contract= $2,725 =4725-2000
Balance in margin account since there are 10 contracts= $27,250 =10x2725

Answer: Balance in margin account= $27,250

Note: Actually the price of future contract should change for changes in balance account. Spot price changes will cause changes in futures price but futures price must be mentioned for calculations to be made. Here I have assumed that the future prices are changing and made calculations accordingly

b) Suppose price of oil jumps to $65.10. What will be the balance of your margin account?

Initial Margin = $4,725 per contract
Exercise price= $62.25 per barrel
If the price rises above the exercise price there is a gain
Price= $65.10
Gain per barrel= $2.85 =62.25-65.1
Gain per contract= $2,850 =1000x2.85
Margin account per contract= $7,575 =4725+2850
Balance in margin account since there are 10 contracts= $75,750 =10x7575

Answer: Balance in margin account= $75,750

c) What price triggers a margin call?

Initial Margin = $4,725 per contract
Maintenance margin= $3,500 per contract
Exercise price= $62.25 per barrel
If the price falls below the exercise price there is a loss
For a margin call the amount should fall below $3,500 per contract
Difference per contract= $1,225 =4725-3500
Size of each contract= 1000 barrels
Difference per barrel= $1.225 =1225/1000

Therefore, price that triggers a margin call = $61.025 =62.25-1.225

Answer: $61.03

d) What price triggers a $20,000 margin call?

Number of contracts = 10
Size of each contract= 1000 barrels

Initial Margin = $4,725 per contract
Maintenance margin= $3,500 per contract

When thae amount falls below the maintenance margin, it has to be topped, i.e. brought to the level of initial margin
A $20,000 margin call = $2,000 per contract

Exercise price= $62.25 per barrel
Difference per contract= $2,000 =4725-3500
Size of each contract= 1000 barrels
Difference per barrel= $2.000 =2000/1000

Therefore, price that triggers a $20,000 margin call = $60.25 =62.25-2

Answer: $60.25

2)Assume DJIA records the changes in prices of 4 stocks. Assume initially the prices of these stocks are $40. $20, $60. and $80. What is the DJIA? Suppose the 4th company declares a 4-for-1 stock splits. If after the split the closing prices of stocks happen to be $39, $21.50 $63 and $19 respectively, what is the new DJIA? Now assume that the first two companies merge. The editorial board of WSJ adds a new corporation to the list. This company's share closes t $20 the day before it is added to DJIA. If the closing price of stocks of the 4 companies are $50,$61,$19, $22, what is the new DJIA?

DJIA is a price weighted index

A price-weighted average is calculated by adding up the prices of the index constituents and dividing by a divisor.
The divisor begins as the number of constituents, but will change over time (to maintain price continuity)

Stocks Prices
1 $40
2 $20
3 $60
4 $80
Total= $200

DJIA= 50 =200/4 (as the initial divisor is 4)

For the split we need to find the new divisor

Stocks Prices
1 $40
2 $20
3 $60
4 $20 =80/4
Total= $140

DJIA= 50 =140/x
or x= 2.80

After the split

Stocks Prices
1 $39.00
2 $21.50
3 $63.00
4 $19.00
Total= $142.50

DJIA= 50.89 =142.5/2.8

After merger and addition of new companies

Find the new divisor

Stocks Prices
1&2 $60.50 =39+21.5
3 $63.00
4 $19.00
5 $20.00
$162.50

DJIA= 50.89 =162.5/ x
or x= 3.1930

Stocks Prices
1&2 $50.00
3 $61.00
4 $19.00
5 $22.00
Total= $152.00

DJIA= 47.60 =152/3.193