Spot-Futures Price Relationship: Interest Rate & Income

Let’s explore the fascinating connection between today’s price of a financial asset, what we call the spot price, and its price for delivery at a future date, known as the futures price. This relationship isn’t arbitrary; it’s actually quite logical and heavily influenced by two key factors: the risk-free interest rate and any income the asset might generate.

Think of it like this: imagine you want to own some gold. You have two options. You could buy the gold right now at today’s spot price and store it safely. Alternatively, you could enter into a futures contract. This is essentially an agreement to buy the same amount of gold at a specific future date, at a price agreed upon today, the futures price.

Now, why would these two prices be different? And how do interest rates play a role? Let’s consider the cost of carrying the gold. If you buy gold today at the spot price, you incur several potential costs. First, you have the cost of storage. You need to keep it secure, perhaps in a vault. Second, and more importantly in our discussion, you are tying up your money. If you hadn’t bought the gold, you could have invested that money in a risk-free investment, like a government bond, and earned interest. This foregone interest is what we call the opportunity cost.

The risk-free interest rate represents the return you could expect from the safest possible investment. It serves as a benchmark. When considering futures prices, this interest rate becomes crucial. Imagine you are deciding whether to buy gold now at the spot price or buy a futures contract. If you buy the gold now, you incur the storage and opportunity cost. If you buy a futures contract, you defer the purchase to the future, effectively deferring these costs as well.

Therefore, in a simplified world without any income from the asset, the futures price tends to be higher than the spot price. Why? Because the futures price must compensate for the cost of carrying the asset until the future delivery date. This cost of carry is directly related to the risk-free interest rate. The higher the interest rate, the more expensive it is to hold the asset today instead of buying it in the future. Consequently, the futures price will be higher relative to the spot price when interest rates are higher. You can think of it as the futures price being the spot price plus the cost of financing the asset until the delivery date, at the risk-free interest rate.

Now, let’s introduce the second factor: income generated by the asset. Some assets, like stocks, pay dividends. Other assets, like rental properties, generate rental income. This income is a benefit of owning the asset. If an asset generates income while you hold it, this income effectively offsets some of the cost of carrying it.

Consider stocks that pay dividends. If you buy a stock today at the spot price, you will receive any dividends paid out between now and the futures contract’s delivery date. However, if you buy a futures contract, you don’t own the stock yet and therefore do not receive these dividends. Because the holder of the spot asset receives this income, the futures price will be adjusted downwards to reflect this benefit. The income from the asset reduces the net cost of carry.

So, when an asset generates income, the relationship between spot and futures prices changes. The futures price will still be influenced by the risk-free interest rate, but it will be reduced by the present value of any income expected to be generated by the asset between now and the futures contract’s delivery date.

In summary, the futures price of a financial asset is generally determined by the spot price, adjusted for the cost of carry. The risk-free interest rate increases the cost of carry, tending to make futures prices higher than spot prices. Conversely, any income generated by the asset reduces the cost of carry, tending to make futures prices lower relative to spot prices. The interplay of these two factors, interest rates and asset income, shapes the dynamic relationship between spot and futures prices in the financial markets.