Economy is coherent, it has structure to it. The discipline of the clearing constraint that forces people, whether they want to or not, to pay attention to their little place in the larger system. The money rate of interest is a symptom of the state of the larger system.
There’s another way in which people are forced to pay attention to their role in the system. That is through forward-looking financial markets. That are always looking into the future and valuing future production. These are capital assets: the stock market, the bond market, etc. The prices in these markets fluctuate, and are supposed to be guiding people’s investments and so forth. Because when these prices change, cash flows happen, so the survival constraint kicks in.
- If they’re positive cash flows, the survival constraint weakens, and you’re freer.
- If they’re negative cash flows, then the survival constraint tightens, you are forced to do something.
The survival constraint influences behavior by monkeying with money market prices, with short-term interest rates and things like that. And so it changes behavior, not just through asset prices, but also money market prices.
Forwards can be seen as relationships between a bank and a firm that we can spell out as swap of IOUs today that locks in 3-month loan 3 months from now, that is the forward contract. The bank is locking in a 3-month interest rate three months ahead by doing this swap of IOUs.
The interest on that loan is F0(3,6), which is defined by the Forward Interest Parity.
[1 + R(0,3)] × [1 + F0(3,6)] = [1 + R(0,6)]| Firm A Assets | Liabilities | Bank Assets | Liabilities | Firm B Assets | Liabilities |
| Deposit (3-month) | Loan (6-month) | Loan (6-month) Deposit (3-month) | Deposit (3-month) Loan (6-month) Futures | Loan (6-month) | Deposit (3-month) |
The bank could possibly hedge this by finding somebody else who wants exactly the opposite, say Firm B, who is looking to lock in an interest rate for a deposit that they’re going to make three months from now.
This bank is matched book, they’re just taking money and they’re funneling it through. The bank has cleared the whole thing all ready. There will be a bid-ask spread for the bank to make some money. But it won’t be necessarily to push around prices very much in the money market. Moreover, it is not reasonable to expect there are equal number of people on both sides. So, matched book is too good to be true.
The economics of the dealer function says, when there’s an inequality, it’s going to push prices around until dealer will be willing to take that price risk under their own balance sheet. Banks act as dealers. The bank system as a whole is taking as much risk as they want. But when banks really can’t take on any more risk, They go and they find hedge funds or private speculators who are willing to take some of this risk from them, and that involves the futures market.
| Speculator Assets | Liabilities |
| Futures |
The hedging transaction sequence among firms, banks, speculators involve a range of different kinds of instruments:
- Firms want lock in a loan, at forward rate
F0(3,6) - Banks (dealers) hedge their position with others in forward rate agreements
- Speculators at futures exchange
- At the spot money market, there are realized interest rate
R(3,6)
What we know for sure is that the forward rate F0(3,6) is not an unbiased expectation of the futures spot rate R(3,6). One possible reason is because of mismatch book and the forward market are pushing prices around, pushing the forward rate F0(3,6) away from the expected spot rate R(3,6), because you got to give dealers some incentive to take this risk on their own balance sheet.
The hedging transaction sequence is only making sense if forward rate F0(3,6) is greater than the futures rate, which is greater than the expected spot rate R(3,6):
F0(3,6) > Futures rate > E[R(3,6)]The difference between forwards and futures is cash flow:
| Forward agreements | cause no cash flow except at maturity. |
| Futures agreements | cause cash flow everyday. |
Forward Contracts
Forward contracts are promises to deliver goods at a futures time T at a given price K:
K = S0 erT
where
K: Forward price
S0: Spot price
r: interest rate
T: time periodThe forward price K is established at the moment that you do the contract and then it stays the same, even though everything else is changing. That means the value of the forward contract changes over time.
The value of the forward contract
ft = St - S0
= St - K e-r(T-t)
where
St: Spot price which changes over timeSo the things that cause the value of the forward contract to are changes in the spot rate St, and changes in the term that is left to go (T-t). Note at the beginning of the contract t=0, the value of the contract is zero ft = 0. When the contract matures t=T, fT = ST - K, the long side (bank) wins. There is no cash flows until t=T.
Just by manipulating the definition in discrete time, what we see here is that the forward rate at maturity is exactly equal to the spot rate: F3(3,6) = R(3,6).
Forward price K = Spot price S0 × Interest rate over next few periods
t=0: 1/[1 + F0(3,6)] = 1/[1 + R(0,6)] × [1 + R(0,3)]
t=1: 1/[1 + F1(3,6)] = 1/[1 + R(1,6)] × [1 + R(1,3)]
t=2: 1/[1 + F2(3,6)] = 1/[1 + R(2,6)] × [1 + R(2,3)]
t=3: 1/[1 + F3(3,6)] = 1/[1 + R(3,6)] × [1 + R(3,3)]
⟹ 1/[1 + F3(3,6)] = 1/[1 + R(3,6)]So there is convergence happens during the period of forwards contract. The value of this forwards contract between the Firm A and the Bank changes over its lifetime:
- At the beginning of the transaction’s value is zero, since there was only IOU, there was no cash flow.
- Then the contract is NOT zero value at all. One side wins and the other side loses.
This is a zero-sum transaction, in general the Bank wins, because the Bank has locked in a lending rate that’s greater than the expected spot rate.
Futures Contracts
Futures contract works exactly like forward contracts, except that every period the value is set to zero again, by changing the futures price. So instead of fixing the K forever for the lifetime, we change it every day to get back to a contract that has zero value.
The value of the forward contract is set to zero
ft = St - S0 = 0
= St - K e-r(T-t) = 0
⟹ Ft = K = St er(T-t)
where
St: Spot price which changes over timeFutures price Ft changes over time, and at the time we change this price of this contract, we move cash from the losers to the winners. So the big difference between forwards and futures from the point of view of money and banking, is cash flow.
| Forwards | The only cash that changes hands is at the very end, where one side ultimately wins. |
| Futures | There could be very large cash flows before the end. |
If you’re entering into a futures contract, you have to be prepared to absorb those kinds of cash flow fluctuations. There’s liquidity risk involved in a futures contract that is not involved in a forward contract.
The spot price St is an asset’s price. Asset prices can fluctuate all over the place, so the futures price Ft can fluctuate a lot, and whenever it does, a payment has to be made. Remember banks are using the futures to hedge forward positions. In general the banks have long forward positions that they’re looking to hedge, from their point of view the futures price fluctuations are just equal and opposite of some fluctuation in the forward market. There is naked speculators on the other side somewhere who is being paid to take this position and they have to come up with margin. Somebody has to be unhedged.
What the bank is not hedged against is this liquidity risk. But the bank is a bank. The bank is hedged in liquidity risk in the sense that it has access to the discount window, inter-bank relationships that allow it to borrow more readily than a regular speculator. The speculators are, are facing this liquidity risk and they are getting paid the term premium (the difference between forward rate and the expected spot rate) for it.
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For more on Forwards and Futures, please refer to the wonderful course here https://www.coursera.org/learn/money-banking
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