Key Takeaways
- Interest rates, spot price, and storage costs increase futures prices, while dividend income and convenience yield decrease them.
- The futures price of a non-dividend and non-storable asset is influenced by the risk-free rate, spot price, and time to maturity.
- Rising interest rates generally lead to lower futures contract prices but can offer opportunities for anticipating traders.
- Storage costs added to futures prices compensate sellers for the cost of holding the asset until delivery.
- Convenience yield reflects the benefit of owning a physical asset, which can decrease futures prices.
Interest rates play a major role in financial markets and are a primary driver of future prices. Futures pricing is mainly influenced by the spot price, the risk-free interest rate, storage costs, and convenience yield, all of which are tied together through the no-arbitrage principle that keeps prices aligned with market opportunities. Understanding how these factors interact can help traders make more informed pricing and strategy decisions.
How Risk-Free Interest Rates Influence Futures Prices
If a trader buys a non-interest earning asset and immediately sells futures on it, because the futures cash flow is certain, the trader will have to discount it at a risk-free rate to find the present value of the asset. No-arbitrage conditions dictate that the result must be equal to the spot price of the asset. A trader can borrow and lend at the risk-free rate, and with no-arbitrage conditions, the price of futures with time to maturity of T will be equal to the following:
- F0,T=S0*er*T
Where:
- S0 is the spot price of the underlying at time 0.
- F0,T is the futures price of the underlying for a time horizon of T at time 0.
- R is the risk-free rate.
Thus, the futures price of a non-dividend-paying and a non-storable asset (an asset that does not need to be stored at a warehouse) is the function of the risk-free rate, spot price, and time to maturity.
If the underlying price of a non-dividend (interest) paying and a non-storable asset is S0 = $100, and the annual risk-free rate, r, is 5%, assuming that the one-year futures price is $107, we can show that this situation creates an arbitrage opportunity and the trader can use this to earn a risk-free profit. The trader can implement the following actions simultaneously:
- Borrow $100 at a risk-free rate of 5%.
- Buy the asset at spot market price by paying borrowed funds and hold.
- Sell one-year futures at $107.
After one year, at maturity, the trader will deliver the underlying earnings of $107, will repay the debt and interest of $105, and will net risk-free $2.
Suppose that everything else is the same as in the previous example, but the one-year futures price is $102. This situation again gives rise to an arbitrage opportunity, where traders can earn a profit without risking their capital, by implementing the following simultaneous actions:
- Short sell the asset at $100.
- Invest the proceeds of the short sell in the risk-free asset to earn 5%, which continues to be compounded on a continuous basis.
- Buy one-year futures on the asset at $102.
After one year the trader will receive $105.13 from their risk-free investment, pay $102 to accept the delivery through the futures contracts, and return the asset to the owner from which they borrowed for the short sell. The trader realizes a risk-free profit of $3.13 from these simultaneous positions.
These two examples show that the theoretical futures price of a non-interest paying and a non-storable asset must be equal to $105.13 (calculated based on continued compounded rates) in order to avoid the arbitrage opportunity.
Understanding How Interest Income Impacts Futures
If the asset is expected to provide an income, this will decrease the futures price of the asset. Suppose that the present value of the expected interest (or dividend) income of an asset is denoted as I, then the theoretical futures price is found as follows:
- F0,T=(S0 – I) erT
Or, given the known yield of the asset q, the futures price formula would be:
- F0,T=S0 e(r-q)T
The futures price decreases when there is a known interest income because the long side buying the futures does not own the asset and, thus, loses the interest benefit. Otherwise, the buyer would receive interest if they owned the asset. In the case of stock, the long side loses the opportunity to get dividends.
Important
Any asset that pays an income will reduce the price of a futures contract because the buying side does not own the asset and, therefore, loses out on receiving the interest income.
How Storage Costs Affect Futures Pricing
Certain assets such as crude oil and gold must be stored in order to trade or to use in the future. The owner holding the asset thus incurs storage costs, and these costs are added to the futures price if the asset is sold through the futures market. The long side does not incur any storage costs until it actually owns the asset. Therefore, the short side charges the long side for the compensation of storage costs and the futures price. This includes the storage cost, which has a present value of C as follows:
- F0,T=(S0 + C) erT
If the storage cost is expressed as a continuous compounding yield, c, then the formula would be:
- F0,T=S0 e(r+c)T
For an asset that provides interest income and also carries a storage cost, the general formula of the futures price would be:
- F0,T=S0 e(r-q+c)T or F0,T=(S0 – I + C)erT
The Role of Convenience Yield in Futures Markets
The effect of a convenience yield in futures prices is similar to that of interest income. Therefore, it decreases the futures prices.
A convenience yield indicates the benefit of owning some other asset rather than buying futures. A convenience yield can be observed particularly in futures on commodities because some traders find more benefit from ownership of the physical asset. For example, with an oil refinery, there is more benefit from owning the asset in a warehouse than in expecting the delivery through the futures because the inventory can be put immediately into production and can respond to the increased demand in the markets. Overall, consider convenience yield, y:
- F0,T=S0 e(r-q+c-y)T
The last formula shows that three components (spot price, risk-free interest rate, and storage cost) out of five are positively correlated with futures prices.
For example, if we take a historical look to see the correlation between the futures price change and risk-free interest rates demonstrated, one can estimate the correlation coefficient between the June 2015 S&P 500 Index futures price change and the 10-year U.S. Treasury bond yields on a historical sample data for the whole year of 2014.
The result is a coefficient of 0.44. The correlation is positive but the reason why it may not seem that strong could be because the total effect of the futures price change is distributed among many variables, which include spot price, risk-free rate, and dividend income. (The S&P 500 should include no storage cost and a very small convenience yield.)
Are Rising Interest Rates Good or Bad for Futures Traders?
Rising interest rates are generally bad for futures traders because they can lead to lower contract prices. However, traders who anticipate these rate increases may profit from short positions in certain futures contracts.
Why Are Interest Rates Important for Hedging with Futures Contracts?
Interest rate futures provide a means for hedging interest rate risk. For example, a borrower might use futures to lock in a fixed interest rate, protecting against future rate increases, which could make borrowing more expensive. Alternatively, speculators can use interest rate hedges to capture variable rates that may yield profit opportunities.
How Do Long-Term and Short-Term Interest Rates Differ in Futures Trading?
Short-term interest rates primarily influence the front end of the yield curve, including contracts with shorter maturities, while long-term rates affect the back end of the curve and contracts with longer maturities.
What Is the Role of Inflation in Interest Rate Futures Markets?
Inflation expectations are a crucial factor in interest rate futures markets. Higher expected inflation can lead to rising interest rates, as the Federal Reserve may try to cool the economy by making capital more difficult to obtain. Alternatively, as inflation dissipates, the Federal Reverse may be more inclined to reduce interest rates, boosting the economy and encouraging economic activity.
The Bottom Line
Under the no-arbitrage assumption that guides efficient markets, futures prices change based on several core factors, including the spot price, the risk-free interest rate, interest income, storage costs, and convenience yield. Spot prices, risk-free rates, and storage costs generally have a positive correlation with futures prices, while interest income and convenience yield tend to have a negative correlation.