Cash and Carry Model for Futures Pricing
Cash and Carry model is also known as non -arbitrage model. This model assumes that in an efficient market, arbitrage opportunities cannot exist. In other words, the moment there is an opportunity to make money in the market due to mispricing in the asset price and its replicas, arbitrageurs will start trading to profit from these mispricing and thereby eliminating these opportunities. This trading continues until the prices are aligned across the products/ markets for replicating assets.
Let us understand the entire concept with the help of an example. Practically, forward/ futures position in a stock can be created in following manners:
Let us take an example from Bullion Market. The spot price of gold is Rs 15000 per 10 grams. The cost of financing, storage and insurance for carrying the gold for three months is Rs. 100 per 10 gram. Now you purchase 10 gram of gold from the market at Rs 15000 and hold it for three months. We may now say that the value of the gold after 3 months would be Rs 15100 per 10 gram. Assume the 3-month futures contract on gold is trading at Rs 15150 per 10 gram.
What should one do?
Apparently, one should attempt to exploit the arbitrage opportunity present in the gold market by buying gold in the cash market and sell 3-month gold futures simultaneously. We borrow money to take delivery of gold in cash market today, hold it for 3 months and deliver it in the futures market on the expiry of our futures contract. Amount received on honouring the futures contract would be used to repay the financier of our gold purchase. The net result will be a profit of Rs 50 without taking any risk. (In the entire process, we have not considered any transaction cost-brokerage etc.)
Because of this mispricing, as more and more people come to the cash market to buy gold and sell in futures market, spot gold price will go up and gold futures price will come down. This arbitrage opportunity continues until the prices between cash and futures markets are aligned.
Therefore, if futures price is more than the future fair price of asset/ synthetic futures price, it will trigger cash and carry arbitrage, which will continue until the prices in both the markets are aligned.
Price of acquiring the asset as on future date in both the cases should be same i.e. cost of synthetic forward/ futures contract (spot price + cost of carrying the asset from today to the future date) should be equivalent to the price of present forward/ futures contract. If prices are not same then it will trigger arbitrage and will continue until prices in both the markets are aligned.
Similarly, if futures prices is less than the future fair price of asset/ synthetic futures price, it will trigger reverse cash and carry arbitrage i.e. market participants start buying gold in futures markets and sell gold in cash market. Now people will borrow gold and deliver it to honour the contract in the cash market and earn interest on the cash market sales proceeds. After three months, they give gold back to the lender on receipt of the same in futures market. This reverse arbitrage will result in reduction of gold’s spot price and increase of its futures price, until these prices are aligned to leave no money on the table.
Assumptions in cash and carry model
Cash and carry model of futures pricing works under certain assumptions. The important assumptions are stated below:
- Underlying asset is available in abundance in cash market.
- Demand and supply in the underlying asset is not seasonal.
- Holding and maintaining of underlying asset is easy and feasible.
- Underlying asset can be sold short.
- No transaction costs.
- No taxes.
- No margin requirements.
The assumption that underlying asset is available in abundance in the cash market i.e. we can buy and/or sell as many units of the underlying assets as we want. This assumption does not work especially when underlying asset has seasonal pattern of demand and supply. The prices of seasonal assets (especially commodities) vary drastically in different demand-supply environments. When supplies arrive to the market place, prices are generally low whereas prices are generally high immediately before the supply of the underlying. When an underlying asset is not storable i.e. the asset is not easy to hold/maintain, then one cannot carry the asset to the future. The cash and carry model is not applicable to these types of underlying assets.
Expectancy Model of Future Pricing
According to the expectancy model, it is not the relationship between spot and futures prices but that of expected spot and futures prices, which moves the market, especially in cases when the asset cannot be sold short or cannot be stored. It also argues that futures price is nothing but the expected spot price of an asset in the future. This is why market participants would enter futures contract and price the futures based upon their estimates of the future spot prices of the underlying assets.
The Expectancy Model of futures pricing states that the futures price of an asset is basically what the spot price of the asset is expected to be in the future. This means, if the overall market sentiment leans towards a higher price for an asset in the future, the futures price of the asset will be positive. In the exact same way, a rise in bearish sentiments in the market would lead to a fall in the futures price of the asset. Unlike the Cost of Carry model, this model believes that there is no relationship between the present spot price of the asset and its futures price. What matters is only what the future spot price of the asset is expected to be. This is also why many stock market participants look to the trends in futures prices to anticipate the price fluctuation in the cash segment.
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.
For instance, 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”.
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