6.3. EFFECT OF MARKING TO MARKET ON FUTURES PRICES 235
- In the third case you still like the zero-rate loan, but the gain is lower: at time
2 you make just 8% on the 5, or 0.40. Likewise you still mind the forced deposit
at zero percent, but now you lose 0.60 time value on it since the interest rate is
higher, 12%. And if,ex ante, the up- and down-scenarios are equally probable, a
risk-neutral agent now dislikes the zero-rate operations: the expected time value
effect is now negative. It follows that the conjectureF=fis no longer acceptable
when the risk-free rate is higher in the down-state.
The example is quite special, but the basic logic holds under very general cir-
cumstances as it is based on a simple syllogism:
Fact 1 Unexpectedly low interest rates tend to go with rising asset prices, while
unexpectedly high interest rates tend to go with falling prices.
Fact 2 To the futures buyer, rising prices are like receiving a zero-interest loan,
relative to a forward contract, while falling prices mean zero-interest lending
(you have to pay money to the clearing house).
Therefore the time-value game is not fair: you get the free loan when rates tend
to be low, while you are forced to lend for free when rates tend to be high.
Stated differently, money received from marking to market is, more often than not,
reinvested at low rates, while intermediate losses are, on average, financed at high
rates. Thus, the financing or reinvestment of intermediary cash flows is not an
actuarially fair game. If futures and forward prices were identical, a buyer of a
futures contract would, therefore, be worse off than a buyer of a forward contract.
It follows that, to induce investors to hold futures contracts, futures prices must be
lower than forward prices.^4
The above argument is irrefutable, and contradicts the gut feeling of the 1800s
that discounting or not made no difference, on average. But how important is
the effect? In practice, the empirical relationship between exchange rates and short-
term interest rates is not very strong. Moreover, simulations by, for example, French
(1983) and Cornell and Reinganum (1981) have shown that even when the interest
rate is negatively correlated with the futures price, the price difference between the
forward and the theoretical futures price remains very small—at least for short-term
contracts on assets other than T-bills and bonds. Thus, for practical purposes, one
can determine prices of futures contracts almost as if they were forward contracts.
Note that what is called the spot-forward swap rate in forward markets tends to
be called thebasiswhen we deal with futures:
basis :=ft,T−St. (6.1)(^4) If the correlation were positive rather than negative, then marking to market would be an
advantage to the buyer of a futures contract; as a result, the buyer would bid up the futures price
above the forward price. Finally, if the correlation would be zero, futures and forward prices would
be the same.