Futures & Forwards
Part of the the investment sequenceA derivative Derivative (finance) is a contract whose value is derived by the underlying assets or benchmarks. There are many derivatives, but three of the most common types are discussed here: futures, calls, and puts.
Forwards and Futures
Forward contracts Forward contract are among the oldest and most common derivatives. For example, a forward is simply an agreement between Alice and Bob where Alice agrees to buy an asset from Bob for a specified price ("delivery price") on a specified date. Historically, this has been a common way for farmers to reduce their financial risk by ensuring the ability to sell crops at a profitable price - even if market prices fall considerably in the interim.
Note, while forwards can be useful for farmers, there are two significant issues with using it as an investor:
- At the end of the contract, you actually have to provide or receive the good.
- There can be significant risk that the buyer or seller will renege.
The solution to the first problem is to just require that each party send cash equal to the difference between the market price and the price in the contract. Such a contract is called a cash-settled forward.
The solution to the second problem is the the futures contract Futures contract.
In a futures contract, Alice and Bob both go to a trusted third-party: Carol.
Every day, Carol will require Alice and Bob to update their margins based on price moves (a "margin call"). For instance, if the asset's price goes down 1%, Alice will be required to pony up cash equal to the price change, while Bob will receive it. In this way, by the time the contract expires, Carol can simply refund the remaining margin to both parties and the forward contract will have been replicated.
There still exists counterparty risk in a futures contract, but they are seriously mitigated:
- Carol will go bankrupt for other reasons, skip town, etc. This risk is minimal since large financial institutions are used to facilitate these transactions. In any case, because of daily rebalancing, even if Carol does turn out to be untrustworthy, only the margin amount will be lost.
- The price will move more in a single day than the margin size. This gives either Alice or Bob the motive to skip town. This risk is reduced by (1) the requirement of the margin call and (2) the fact that in real life Carol has information about both parties like their social security numbers, which opens up the reneging party to civil lawsuits and reputational repurcussions.
Finally, it's worth mentioning some nomenclature: the person who agrees to buy the security in the future for the specified price is said to "be long" because if the security increases in price, they gain money - similar to holding the actual asset. The person who agrees to sell is said to "be short" for the same reason.
Risk-Free, Cashless Portfolios
Suppose we have a security with both its own markets and its own futures markets. Now let's add two assumptions:
- The markets are efficient (not this implicitly implies 0 transaction costs)
- The markets prices are continuous over time
Assumption 2 implies that the party managing the margins can instantaneously make margin calls, and this with assumption 3 implies that amount of margin required is infinitesimal.
The efficiency assumption also implies that every cashless, risk-free portfolio must earn the risk-free interest rate.
To see why, suppose you had such a portfolio that earned more than the risk-free interest rate - this would violate the EMH (why would anyone buy the risk-free interest rate if a strictly superior alternative existed?). Likewise, suppose a cashless, risk-free portfolio earned less than the risk-free interest rate - then we could just invert it to beat the risk-free interest rate, which would likewise violate the EMH.
Futures Pricing
A futures contract doesn't have a market price (like stocks) or interest rate (like bonds) as a market mechanism to ensure demand equals supply. Instead, this rationing occurs via changes in the delivery price.
This delivery price has some economic theory behind it Forward price, and we'll discuss a special case now: where the asset in question pays no dividends. One such asset (historically) was AMZN stock.
Let
- $r$ - risk-free interest rate
- $x$ - the price of AMZN now
- $y$ - the price of AMZN in one year
If I have $x$ dollars, I can choose to buy one AMZN stock. This will yield an eventual profit of $y - x$.
I can then go short on a futures contract of AMZN with delivery price $f$, which yields a profit of
$$ f - y $$Note the return from this overall portfolio is
$$ \left( y - x \right) + \left( f - y \right) $$which just equals
$$ f - x $$Note this is a risk-free, cashless portfolio that started with $x$ dollars, so we know it must earn the risk free interest rate of $r x$, so
$$ f - x = r x $$thus
$$ f = (1+r) x $$The formula can be generalized if the asset pays dividends (like most stocks) or costs money to store (like most commodities), but the general notion that forward prices reflect risk free returns holds Forward price.
I just want to note one little irony here: since the delivery price is merely the spot price and the risk-free interest rate, it is actually impossible (at least in academic theory) to predict changes in the underlying security via analysis of its futures.
A Wrinkle
The above analysis is literally "textbook". Textbooks will also add that things get more complicated in reality. For instance, if there are storage costs (e.g. for oil futures) or the underlying security pays dividends (e.g. stocks). However, the above model can be elegantly modified to accommodate such changes.
Where things get really interesting is markets where you can't buy-and-hold the underlying security in the first place. In those markets, the simple math proof above can't be completed, because you don't have access to buy or short the underlying security, and so there is no way to construct a risk-free portfolio if the delivery price is more or less than the spot price plus the risk-free interest rate.
A pure example of such a market is the market for weather futures Weather Products. Other nearly-pure examples include futures markets for the Case-Shiller home price index CME Metro Area Housing Index: Futures and the future markets for electricity prices Products - Futures & Options (batteries are negligible for investment purposes).
Given that above, what is the appropriate delivery price for such futures contracts?
Since the arbitrage lens is now useless to us, we need to choose a different one. The obvious choice of new lens is the Capital Asset Pricing Model. Suppose the weather is independent of the overall market (i.e. beta=0). By the CAPM, the investing in weather futures can yield at most the risk-free interest rate. However, futures don't (in academic theory) require cash to invest in, so, in fact, weather futures must return an expected value of zero. Therefore, if the expected temperature in 12 months is 40˚, the delivery price must be equivalent to 40˚.
While my use of the CAPM model for the above analysis is, as far as I know, novel - the conclusion is not: experts broadly expect the future prices to predict the underlying variable Ritchken, though with some nuanced warnings:
If there is terrific uncertainty about the futures price, then the speculator may not purchase the futures contract, even if its price is below the expected futures price. If, for example, the futures price were \$99, then speculators may not pursue the \$1 expected profit. Indeed, to entice speculators to bear the risk of a position in the futures, they must be compensated with an appropriate risk premium. As a result, a simple relationship between futures prices and expected future spot prices may not exist.
Ironic, isn't it? It is only when we remove the ability to arbitrage that we can use futures to accurately forecast the future.
Under the CAPM, the only risk worth thinking about is beta. Under this model, then we need to add a correction term to subtract the "equity premium" from the expected value in the future to bring it back into accordance with the CAPM. For instance, if the risk-free interest rate is 4%, the S&P 500 has an expected return of 10%, then the premium for an asset with beta=1 is 6%. So, if future predicts the Case-Shiller index futures "predicts" a 10% increase in home prices, but the index has a beta of 0.5, then the unbiased prediction is 7% (10% - 0.5 * 6%).
Obviously, CAPM is only a model, and risk other than beta exist in practice (e.g. liquidity risk, adverse selection, etc.)