1.) The futures contracts on the SPX (S&P 500 Index) has a value of $250X the cu
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Question
1.) The futures contracts on the SPX (S&P 500 Index) has a value of $250X the current index value. Today, the index is at 2630 so the futures contracts has a value of $657,500. Explain, with a numerical example, how does futures contract could be used by both a hedger any speculator. Make whatever assumptions you need to you about your portfolio size for the example to work. It does not have to match up perfectly to the side of your portfolio. See my current margin requirement for $30,000.
2.) Margin requirements for hedgers are lower than they are for speculators. Why?
Explanation / Answer
Hedging
Let total portfolio value be $ 1315000 which is the amount that needs to be hedged. Also hedging of portfolio using index futures would involve selling a requisite number of futures now and buying them to square off the futures position at maturity.
Therefore, Number of Futures Contract required to be sold = 1315000 / (250 x 2630) = 2
We would analyse hedging using a 10% rise in index value and a 10% fall in index value between now and the time at which futures mature. It is also assumed that your portfolio has a beta of 1 which implies that a 10% rise/fall in index value changes portfolio value by an equal amount in the same direction as that of the index movement.
10% rise in index value
Current Portfolio Value = $ 1315000
Portfolio Value after rise = $ 1446500
Profit in Portfolio Position = $ 131500
Index Value at Present = 2630 , Index Vaue at futures maturity = 2630 x 1.1 = 2893
Value of 2 futures sold now = 2 x 250 x 2630 = $1315000
Value of 2 futures bought at maturity = 2 x 250 x 2893 = - $1446500
Therefore, Loss in Futures Position = - $1446500 + $1315000 = - $ 131500
Therefore, the gain in the portfolio (underlying asset) position is equalized by loss in the futures position. However, there is a margin requirement of $30000 for the futures positon. A price rise in case of a short futures position erodes the margin.
Current Margin Requirment = Change in Index Value x 250 x number of contracts
Therefore, Change in Index Value = 30000 / ( 250 x 2) = 60. If the index value changes by more than 60 then margins get eroded and the same has to be replenished. Since,index value changes from 2630 to 2893 the margin of $30000 needs to be replenished.
10% fall in index value
Current Portfolio Value = $ 1315000
Portfolio Value after rise = $ 1183500
Loss in Portfolio Position = $ -131500
Index Value at Present = 2630 , Index Vaue at futures maturity = 2630 x 0.9 = 2367
Value of 2 futures sold now = 2 x 250 x 2630 = $1315000
Value of 2 futures bought at maturity = 2 x 250 x 2367 = - $1183500
Therefore, Loss in Futures Position = - $1183500 + $1315000 = $ 131500
Therefore, loss in the portfolio position is equalized(hedged) by the gain in the futures position.
A margin requirement in this case(price fall) would actually accumulate to the hedger. Thereby allowing the hedger a smal profit.
Speculation
Calculation of Percentage Margin Requirement :
Margin Required = Contract value x number of contracts x % margin required
30000 = (2630 x 250) x 2 x % margin required
% margin required = 30000 / 1315000 (in decimal)
Now assume that an investor has $ 1315000 to invest. If the entire amount is invested in the portfolio then a 10%rise/fall increases/decreases portfolio value by 10% of $ 1315000 = $ 131500.
However, a riskier bet would be taking a position in the futures market.
Suppose the investor is extremely sure about a 10% rise in the market.
Then, the investor would purchase (and not sell) futures.
Value of each future = 250 x 2630 = $ 657500. However, futures purchase would just require the current margin.
Therefore, margin requirement per contract = 657500 x (30000 / 1315000) = $15000
Number of contracts purchasable at margin requirement = 1315000 / 15000 = 87.66 OR 88
If market rises by 10%, index value goes up from 2630 to 2893
Purchase Price of per contract = 250 x 2630 = $ 657500
Sale Price per contract = 250 x 2893 = $ 723250
Profit per contract = $65750
Therefore, total profit = Number of contract x profit per contract = $ 5786000
If market falls by 10%, then index value drops from 2630 to 2367
Purchase Price of contract = 250 x 2630 = $ 657500
Sale Price of contract = 250 x 2367 = $ 591750
Loss per contract = $ -65750
Therefore, Total Loss = 88 x - 65750 = - $ 5786000
Therefore, profit and loss is greatly increased by speculation through just margin requirement deposit.
The same procedure would inverse loss and profit if futures are sold first and bough later.
NOTE: Please raise a separate query for the second question
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