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Sem 5 Prep
← Money & BankingForwards, futures and margin

Formulas for this chapter

Forward payoff

Long: profit per unit = S(T) - F(0,T) Short: profit per unit = F(0,T) - S(T) Total = profit per unit x quantity

Any forward or futures profit question. Decide your side first: buying forward makes you the long, selling forward the short.

S(T)
Spot price of the asset at delivery
F(0,T)
Forward price agreed at the start, for delivery at T

Default-risk exposure on a forward

Exposure at time t = PV{ |F(0,T) - F(t,T)| }, 0 < t < T

When a question asks who has the incentive to default and how much is at stake. The defaulting party is the one for whom the contract is a liability.

F(t,T)
Today's forward price for delivery on the original delivery date T
PV
Present value, discounting from T back to t at the rate for that tenor

Margin account, one day at a time

Contract value = lot size x number of lots x price Initial margin = margin % x contract value MTM (long) = (today - yesterday) x quantity MTM (short) = (yesterday - today) x quantity Equity = previous equity + MTM + variation margin Call fires when equity < maintenance margin Variation margin = initial margin - equity

Every mark-to-market table. Work one row at a time and never skip the equity line, because the call is tested on equity, not on the price.

quantity
Units controlled: lot size times number of lots
maintenance margin
Minimum equity that must be kept in the account
variation margin
Top-up called for, sized to restore equity to the initial margin

Price move that triggers the first call

Cushion = initial margin - maintenance margin Adverse move allowed per unit = cushion / quantity

When asked how far the price can go before a margin call. Convert the equity cushion into a price move using the number of units, never the number of lots.

cushion
Equity available above the maintenance level
Step 3 of 29
The real wordsTheory

The long and the short

Every forward has exactly two counterparties, and the slide names both.

The shortThe seller. Commits to deliver the asset at the specified forward price.
The longThe buyer. Commits to take delivery of the asset at the specified forward price.

At delivery, cash is exchanged for the asset. Remember the direction of the bet: the long is betting the price will go up, the short that it will go down.

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