Explore key concepts, practical strategies, and in-depth examples of forward and futures contract valuation, including the cost-of-carry model, marking to market, arbitrage, and real-world applications.
If you’ve ever wished you could “lock in” a future price to protect yourself from fluctuating market conditions, you’ve tapped into the essential spirit of forward and futures contracts. I remember the first time I heard about these contracts, I was lying awake at night worrying about how coffee bean prices might shoot up by the time I’d saved enough money to open a quaint coffee cart. A friend casually mentioned a “forward contract” on commodities. My reaction was something like “Wait, you can actually fix the price now and buy coffee beans in six months?” That’s exactly their point. Now, let’s dig into the essential building blocks of forward and futures contract valuation in a way that connects the intuition, the math, and the practice.
A forward contract is a private agreement between two parties to buy or sell an underlying asset (like a commodity, bond, or currency) at some future date for a price decided right now. Because forwards are often customized (e.g., quantity, quality, delivery date, etc.), they aren’t typically traded on an exchange—think of them as tailor-made suits in a world of typical off-the-rack offerings.
On the other hand, a futures contract is an exchange-traded instrument with standardized terms (quantity, quality, delivery location, and date). The exchange’s clearinghouse stands between buyers and sellers, mitigating counterparty (or credit) risk by guaranteeing trades. With futures, you can be fairly relaxed about default concerns because the clearinghouse effectively replaces the original counterparty’s obligations. Even so, you’ll still encounter daily gains or losses from marking to market (we’ll get to that soon).
Both contracts let you hedge or speculate. If you’re a wheat farmer worried about next season’s wheat prices cratering, you can lock in a favorable price using a forward/futures contract. If you’re a portfolio manager who expects equity prices to rise, you might take a speculative long position in stock index futures.
In forward/futures valuation, we rely heavily on the cost-of-carry model, which basically says: “What does it cost me to buy the underlying asset now and hold it until the delivery date?” Then it takes into account financing costs (like interest), storage costs (if we’re dealing with commodities), and any income from the asset (like dividends).
In the simplest case for a non-income-producing asset, the no-arbitrage relationship is given by:
$$ F_0 = S_0 \times e^{rT}, $$
where
This equation is sometimes read as: “Forward Price = Spot Price Grown at the Risk-Free Rate.” It’s the bedrock of forward pricing in a frictionless, perfect-market scenario where the underlying doesn’t pay any income and there are no storage costs.
If the underlying produces some regular income or yield (like dividends on stocks or coupon payments on bonds), the forward or futures price is typically lower than \( S_0 e^{rT} \). The reason? You effectively “lose out” on the yield if you hold the forward instead of holding the asset. For stocks, we incorporate an expected dividend yield \( q \) like so:
$$ F_0 = S_0 e^{(r - q)T}. $$
For commodities, you might face storage costs \( u \) (e.g., paying for a warehouse to store barrels of oil), which pushes the forward price upward. If there’s a convenience yield \( y \) for physically holding the commodity (like a refinancial firm might have an incentive to keep some supply on hand), it can push the forward price downward. Combined in one expression, these adjustments can look a bit like:
$$ F_0 = S_0 e^{(r + u - q - y)T}. $$
(In practice, you’ll frequently see these broken out or combined differently, depending on the specific exam reading or real-life application.)
There’s a wonderful notion called convergence in futures and forwards: as expiration approaches, the forward/futures price converges to the spot price. If not, we’d have an arbitrage opportunity. Arbitrage—profiting with zero net investment and no risk—keeps markets in check.
If the forward price is way too high compared to its “fair value,” arbitrageurs will do something like short the forward (agree to sell at an artificially high forward price) and buy the underlying asset in the spot market, pocketing a near-riskless profit. Conversely, if the forward price is oddly low, they’ll do the reverse. Over time, these trades push the forward/futures price back to where they “should be” per the cost-of-carry model.
Futures contracts come with a daily “marking to market” feature that can feel a bit jarring if you’re used to the more straightforward hold-’til-expiration approach of forwards. Basically, your gains or losses on a futures contract are realized each trading day based on the settlement price. If you’re on the winning side of the price movement, your broker credits your account. If you’re on the losing side, your broker debits it. This daily settlement reduces the chance that you or the other party can build up huge potential losses and default at maturity.
Because of marking to market, you need an initial margin—a relatively small deposit that ensures you have “skin in the game.” There is also a maintenance margin. If your losses build up and your margin balance dips below this maintenance level, you’ll get a margin call, requiring you to top up your account. If you fail to do so, the broker can close out your position. This system keeps the futures market robust, but it introduces a bit of day-to-day volatility in your cash balance—unlike forward contracts, which settle only at maturity.
Forwards are like having a tailor measure you for a custom suit—quantity, quality, delivery date, and location are all negotiated. Futures are the “one-size-fits-all” approach (or maybe “select-from-a-few-common-sizes”). They’re standardized, so you get set contract sizes and designated expiration dates.
Forwards directly link two parties, so they each hold the other’s credit risk. Meanwhile, futures are backstopped by an exchange’s clearinghouse, drastically reducing counterparty risk. This difference can matter a lot if you’re dealing in huge notional amounts or if partner default is a serious worry.
Futures typically have higher liquidity because they’re traded on organized exchanges with many participants. Forwards, anchored in the over-the-counter (OTC) market, rely on direct negotiation between counterparties. Liquidity is relatively lower. That said, forwards make sense for specialized deals (like hedging the sale price of some extremely niche commodity).
Since futures are marked to market daily, interest rate movements can introduce subtle differences in pricing compared to an equivalent forward. In stable rate environments, the difference might be negligible, but it can become noticeable when interest rates flutter around a lot.
Forward Rate Agreements (FRAs) might sound fancy, but in essence, they let you fix an interest rate you’ll pay or receive on a notional for a specified future period. Suppose you need to borrow $10 million for three months, beginning in six months. You’re nervous that interest rates might jump by then, so you’d go long an FRA that locks in the borrowing rate. At the end of the FRA period, you’ll settle the difference between the FRA’s “contract rate” and the actual reference rate (often SOFR nowadays, historically LIBOR). This approach effectively pegs your borrowing cost.
FRAs are popular among financial institutions, corporations, and anyone with big interest rate exposures. They can also be used to speculate on future rate movements, though that’s riskier if your rate view is incorrect.
Some futures physically deliver the underlying asset at expiration—think wheat, crude oil, or live cattle. These are deliverable futures. Others are purely cash-settled, meaning there’s no actual exchange of the physical commodity or financial instrument. Instead, final profits or losses are settled in cash. Stock index futures (like the S&P 500 or S&P/TSX Composite) and interest rate futures often fall into this category. It’s much more straightforward to settle in cash for an index than to deliver a basket of hundreds of stocks.
Imagine you manage a portfolio of Canadian equities and are bullish on the broad Canadian market for the next quarter. Instead of rebalancing your entire portfolio to add more equities, you can buy S&P/TSX Composite futures for a cost-effective, leveraged approach to increasing market exposure.
The cost-of-carry model for equity index futures includes adjustments for the expected dividend yield of the index:
$$ F_0 = S_0 e^{(r - q)T}, $$
where \( q \) is the continuous dividend yield. If the index yield is large, your futures price is lower than \( S_0 e^{rT} \). In practice, you’d keep a watchful eye on the real dividend feed from the underlying stocks, short-term interest rates, and your trading costs.
This approach can help you quickly adapt to market outlook changes without drastically overhauling your entire holdings. But remember, with futures, you’ll face daily margin calls if the market moves against you.
Below is a simple Mermaid diagram illustrating the broad process of entering, holding, and eventually closing or delivering a futures contract.
flowchart LR
A["Identify Hedging/Speculative Need"] --> B["Select Underlying Futures"]
B["Select Underlying Futures"] --> C["Post Initial Margin With Broker"]
C["Post Initial Margin With Broker"] --> D["Daily Marking to Market <br/> (Profits or Losses)"]
D["Daily Marking to Market <br/> (Profits or Losses)"] --> E["Futures Contract Expiration <br/> or Position Closed"]
• Forward Price: The contractually agreed-upon price in a forward contract, set at inception.
• Initial Margin (Futures): The collateral deposit required to open a futures position.
• Maintenance Margin (Futures): The minimum margin balance you must maintain before topping up is required.
• Cost of Carry: The net effect of all costs (financing, storage) and benefits (dividends, convenience yield) associated with holding the underlying over the contract’s life.
• Marking to Market: The daily settling of gains or losses based on the new market price of the futures contract.
• Convergence: The process of futures (or forward) prices moving toward the spot price as expiration nears.
• Carry Arbitrage: A strategy that exploits mispricing between the spot asset and forward/futures prices by simultaneously taking positions in the underlying and the derivative.
• Forward Rate Agreement (FRA): A forward contract on short-term interest rates.
• Always consider transaction costs and the cost of capital. Simple formulas assume frictionless markets.
• Understand your margin obligations for futures. The daily “cash in or out” can cause operational headaches if not planned for.
• For deliverable commodity contracts, the possibility of physical delivery is real. If you can’t handle receiving 1,000 barrels of oil at your doorstep, you should close your position before expiration or carefully choose financial settlement.
• Watch out for credit risk in forwards. If you’re dealing with an OTC contract, confirm the creditworthiness of your counterparty or structure collateral agreements.
• Be mindful of interest rate and dividend changes in equity index futures. These can nudge your implied cost of carry up or down, sometimes unexpectedly.
It’s tempting to see these formulas and think it’s all mechanical—plug in numbers and go. In reality, successful forward/futures trading or hedging demands close attention to market conditions, interest rates, liquidity, credit risk, and the big picture of your portfolio’s exposures. Think about how changes in any of these variables alter the forward price or your strategy’s viability. Maybe you’re short a futures contract but local interest rates just pivoted upward; that shift might adjust the shape of your daily margin flows.
Forward and futures contracts are essential in modern finance for hedging and speculation. Understanding how to price them using cost-of-carry, deal with the daily marking-to-market in futures, and exploit or avoid arbitrage opportunities underpins much of what you’ll do as a risk manager or investments professional.
In exam scenarios, you’ll see vignette-style questions that require:
• Quick recall of the forward/futures price formulas (with or without dividends, storage costs, etc.).
• Clarification on daily settlements, margin calls, and the net effect on your cash flows.
• Understanding subtle differences between forward and futures pricing in different interest rate environments.
• Possibly employing a “cash-and-carry” or “reverse cash-and-carry” example to find mispriced markets.
Stay disciplined with formula application. Show each step clearly. And if the question references an asset with known yield or storage costs, incorporate those adjustments. Remember that the exam might throw real-world quirks like convenience yield or extremely high storage costs at you.
• Hull, John. “Options, Futures, and Other Derivatives.” Pearson.
• CFA Institute Level II Curriculum, Derivatives Readings and Practice Problems.
• Pirrong, Craig. “The Economics of Commodity Markets: Exercises and Case Studies.”
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