Cost of carry refers to costs associated with the carrying value of an investment.
These costs can include financial costs, such as the interest costs on bonds, interest expenses on margin accounts, interest on loans used to make an investment, and any storage costs involved in holding a physical asset.
Cost of carry may also include opportunity costs associated with taking one position over another.
In the derivatives markets, cost of carry is an important factor for consideration when generating values associated with an asset’s future price.
Futures Cost of Carry Model
In the derivatives market for futures and forwards, cost of carry is a component of the calculation for the future price as notated below.
The cost of carry associated with a physical commodity generally involves expenses tied to all of the storage costs an investor foregoes over a period of time including things like cost of physical inventory storage, insurance, and any potential losses from obsolescence.
The futures market price calculation also takes into consideration convenience yield, which is a value benefit of actually holding the commodity.
F = Se ^ ((r + s – c) x t)
Where:
F = the future price of the commodity
S = the spot price of the commodity
e = the base of natural logs, approximated as 2.718
r = the risk-free interest rate
s = the storage cost, expressed as a percentage of the spot price
c = the convenience yield
t = time to delivery of the contract, expressed as a fraction of one year
Any derivative pricing model involving a future price for an underlying asset will incorporate some cost of carry factors if they exist.
Cost of carry is a factor in both direct investing and derivative markets.
Carrying costs detract from total return for direct investors.
In the derivative markets, carrying costs are a factor that influence derivative contract pricing.
Several cost-of-carry factors that investors should account for: Margin , Short Selling , Other Borrowings , Trading Commissions , Storage.
Expectancy model of futures pricing
It also argues that futures price is nothing but the expected spot price of an asset in the future.
According to this model, Futures can trade at a premium or discount to the spot price of underlying asset.
Futures price give market participants an indication of the expected direction of movement of the spot price in the future
If futures price is higher than spot price of an underlying asset, market participants may expect the spot price to go up in near future.
This expectedly rising market is called “Contango market”.
Similarly, if futures price are lower than spot price of an asset, market participants may expect the spot price to come down in future.
This expectedly falling market is called “Backwardation market”.
The pricing formula
Nifty Spot is at 8,845.5 whereas the corresponding current month contract is trading at 8,854.7, please refer to the snap shot below.
This difference in price between the futures price and the spot price is called the “basis or spread”.
In case of the Nifty example below, the spread is 9.2 points (8854.7 – 8845.5).
The difference in price is attributable to the ‘Spot – Future Parity’. The spot future parity the difference between the spot and futures price that arises due to variables such as interest rates, dividends, time to expiry etc.
