Class #5: Futures, page 1
Class Currency FuturesCh 8
Introduction...... 1
Comparison between Futures and Forward contracts:...... 2
Example of Daily Cash Flows...... 2
Link between currency futures and forward markets...... 2
Margins and Maintenance Level...... 4
Example of margin and maintenance level...... 4
Hedging with futures: Application...... 4
Basis...... 4
Definition...... 4
Basis Risk...... 5
Example of hedging with futures and basis risk...... 5
Example of hedging with futures & cost of borrowing...... 5
Introduction
Currency futures are another type of financial instrument, one that is different from fwd contracts and options. Currency futures are , however, very similar to commodity futures.
Currency futures are usually traded in a formal market place, like the International Monetary Market (IMM) of the Chicago Mercantile Exchange or the London International Financial Futures Exchange (LIFFE).
Unlike fwd contracts which are written for amounts and dates to suit the convenience of each customer, future contracts are relatively homogeneous, that is, the contracts are only for a limited number of dates (four dates, the 3rd Wednesday of March, June, September and December) and for fixed amounts. Here are some examples:
ContractFace Amount
£ (IMM, LIFFE)62,500
DM ( )125,000
Can$ (1MM)100,000
Another major difference is that while a fwd contract requires cash flows only on the maturity date, future contracts (may) require daily cash flows to maintain your margin at the required level.
Thus, it should be obvious that futures are less flexible than fwd contracts. Thus, they are, in most cases, less useful for hedging fx risk and more useful for speculating.
Comparison between Futures and Forward contracts:
FuturesForward
• Daily cash flow (see example)Single CF at maturity
(Therefore time pattern of CFs and roi become important)
• Futures are traded only in standardized amts;Fwds any
• Futures have fixed maturity (only 4) dates; Fwds don't
• Futures are traded in central mkts; Fwds in OTC markets
• Futures have daily price limits; Fwds do not
Example of Daily Cash Flows
Suppose that you go long a £25,000 futures contract at P0 = $1.45/£ and the settlement prices for the next two days are : P1 = $1.4460/£ and P2 = $1.4510/£.
Then the cash flows are the following:
Day 1 : +(P1- P0 ) *£25,000 = ($1.4460/£ - $1.45/£)= - $100
Day 2 : +(P2- P1 ) *£25,000 = ($1.451/£ - $1.1.446/£)= +$125
Would you prefer this pattern of cash flows or would you prefer to receive +$125 on the first day and -$100 on the second day? Prefer to receive $125 on day 1 and pay out $100 on day 2 - because of the time value of money. Lt us study this in greater detail.
Link between currency futures and forward markets
It should be clear to all of you that since the fwd and futures contracts are similar in so many ways there should be a relation between their prices. If the price of the forward varied a lot from the price of the futures there would be an arbitrage opportunity.
Can you guess what the relationship betwen the forward and the futures price is if the interest rate is positively related to the futures price?
Answer: G > F, that is the futures is more costly than the forward. The reson for this is, that since the futures price is positively correlated with the interest rate, gains on the (long) futures position are made when the interest rate is high, and losses are made when the interest rate is low, and hence are cheaper to finance. Got it?
To understand this let us look at a simple example, with only three dates: t= 0, t = 1, and t= 2, the maturity date.
Suppose you buy the £ fwd today, for the maturity of date of t = 2. Then, the gain/loss on the fwd contract will be the difference between the fwd price paid and the spot rate at t = 2.
For a futures contract purchased for the same maturity, the gain/loss will also depend on what happens at t = 1. There are two possibilities:
Either, at t = 1, the $ futures price of the £ is above the original value and the buyer of the futures contract will pocket a gain at this time, which he can invest for the maturity of t = 1 to t = 2, thereby generating an extra gain over and above the difference between the original futures price and the spot price at t = 2;
Or, the futures price is below its original price, and the loss has to be made good, by borrowing at the interest rate prevailing at t = 1, and thus there is a a loss at maturity over and above the difference between the original futures price and the spot price at t = 2;
If the interim interest rate at t=1 were certain (or independent of the futures price) then the investment/financing of the interim cash flow would be done at the same interest rate (disregarding bid-ask spreads), and the prospect of the the extra gain would actuarially cancel out the prospect of the extra loss. But if there is a probabilistic tendency for the interim gains to be invested at an interest rate higher than the one at which the interim losses are financed (positive correlation), it is clear that buying the futures offers an advantage over buying the forward contract. Hence, for the case of positive correlation, the futures price will be above the forward price.
Note, however, that the prices of the two need not be identical, for while forward contract requires only a single cash flow at maturity, the futures contract may require daily cash flows and hence we must take into account risk considerations arising from uncertainty about the roi prevailing during the life of a futures contract.
If the roi was non-stochastic then the futures price would be exactly equal the forward price. However, even when the roi is stochastic, the price difference between the forward and the future is very small and therefore we will not go into the gory details of this (till C 478).
Margins and Maintenance Level
When one opens a futures contract, one is required pay a fee to the broker and to post a margin. The margin is posted to ensure that deals are honored. When the equity position falls, then this margin must be supplemented by additional cash to bring it up to the maintenance level.
Example of margin and maintenance level
Suppose the margin on a futures contract on the £ is $3000 and the maintenance level is $2500. Then as long as the the decline in the futures position is less than $500 you need not take any action, but once the futures position declines by more than $500 you need to post additional margin equal to the full decline in value in the futures position.
Hedging with futures: Application
Suppose you have exported goods to the UK and expect to receive £ in the future. Thus, you have a long position in the £. To hedge this, you wish to take such a position in the futures that when your original position loses money, the position in the futures should gain money.
The whole point of the story that I am going to tell you, and the example that we will do, is that to be hedged PERFECTLY the value of your position in futures should change exactly one-for-one (and in the opposite direction) for a change in the value of the underlying original position. That is, the futures price should move one-for-one with the price of the underlying position. And this may not happen all the time.
Let,
S = change in the spot position
G = change in the futures position
Then since we are long in the spot position and short the futures, the total change in the position, T is:
T = S - G (negative sign on F because we are short Fut
Now, as long as G=S exactly, T = 0 and the hedge is perfect. However, if G is not equal to S then you are not hedged perfectly, and you may end up making or losing some money.
Basis
Definition
The basis is the difference between the spot price and the futures price.
Bt = Gt - St
If the movement in the spot price and the futures price is one-for-one, then the basis is constant.
Basis Risk
When you hedge with futures there is always a risk that the movement in the spot and the futures price will not be one-for-one. This is called the basis risk.
Hedging with futures will never eliminate ALL the risk. There will always be some basis risk. The important point to remember is that, normally, the basis risk is much smaller than the risk of an open position, that is if you did not hedge at all.
Let us now look at a numerical example to make sense of this all.
Example of hedging with futures and basis risk
Suppose your original position is long £25,000 and you wish to hedge this by going SHORT one futures contract.
St = $1.1545/£;Gt= $1.1620/£
St+1= $1.1350/£;Gt+1= $1.1460/£
Q1. Calculate the basis today and the basis after a month?
Q2. Calculate the net gain/loss on the hedged position?
Q3. Compare the net gain/loss of the hedged position to that of the unhedged position?
A1.Basist = St - Futt = - 0.0075
Basist+1 = St+1 - Futt+1 = - 0.0110
A2. Spot position: +$/£(1.1350 - 1.1545)*£25,000= -$487.50
Fut position: (-)$/£(1.146 - 1.162)*£25,000= +$400.00
NET Loss = - $87.50
Alternate way of calculating:
Change in basis = (-0.0110) - (-0.0075)*£25,000 = - $87.50
A3. The loss on the unhedged position is -487.50
The loss on the hedged position is -87.50
Obviously, hedging was a good idea.
Example of hedging with futures & cost of borrowing
On March 31, a Canadian firm borrows DM 2 m for 3 months at 6% p.a. in Germany. Since the firm needs the money in Canada, it hedges against exchange risk. On March 31, the spot rate $ .50/DM, the 90-day forward rate is $ .51/DM and the DM June futures is $ .51. At the end of June, the spot rate is $ .48 . Assume the firm hedges only the principal and not the interest payments.
(a) What is the effective cost of borrowing (in percent p. a.) if the firm hedges in the forward market?
(b) What is the effective cost of borrowing (in percent p. a.) if the firm hedges in the futures market? Assume that the margin is $3000 per contract (remember, each contract is for DM 125,000), that the firm liquidates the futures contracts at a price of $ .48 at the end of June, and that the firm borrows $ at 14% in order to pay for the margins.
Ans. To calculate the effective rate of interest we need to find out how much we are receiving today, and how much we are paying at the end of 3 months; and we need to look at these amounts in Can$ terms.
The amount that is received today is DM 2m ($0.50/DM) = $1m
First, let us calculate the interest on this loan:
DM interest on the loan is DM 2m (1.06)1/4 = DM 0.029348m
Since we do not hedge this, the $ value of this (at St+1) is
= DM 0.029348 (DM 0.48/$) = $0.014087m
(a) Now let us look at the forward hedge calculations:
(1) Buy DM 2m fwd, @ $0.51/DM to hedge the principal payment = - $1.02m
(2) Add the interest payment amount = - $0.014087m
(3) Total amount to be paid back is (1) +(2) = - $1.034087m
Thus, the effective rate of interest is = 1.0340874 - 1 = 0.14347% pa
(b)The calculations for the case where we hedge with futures:
(1) The interest payment amount = - $0.014087m
(2) Add the interest payment on the margins = - $3000 (16) (1.141/4 - 1) = - $0.001598m
(3) Change in value of underlying position = - DM2m ($/DM 0.48 - 0.50)
= + $0.4m
(4) Change in value of futures position = + DM2m ($/DM 0.48 - 0.51)
= - $0.6m
(5) Total amount to be paid back is (1) +(2) + (3) +(4) - $1m = - $1.035587
Thus, the effective rate of interest is = 1.0355874 - 1 = 0.1505% pa
Thus, it was cheaper to hedge with forwards, ex post.