# Cost of carry relationship definition math

### Arbitraging futures contract (video) | Khan Academy

The cost of carry or carrying charge is cost of storing a physical commodity, such as grain or metals, over a period of time. The carrying charge includes. In financial mathematics, put–call parity defines a relationship between the price of a European .. Parity of implied volatility: In the absence of dividends or other costs of carry (such as when a stock is difficult to borrow or sell short), the implied . standard theories of forward and futures pricing, namely, the Cost-of-Carry and the Risk modelled the relationship between spot and forwardafutures prices either through . account of computation costs, Telser claims that the best mathematical form for Using Working's definition of the price spread, written solely.

It can also be defined as the difference between the interest generated on a cash asset and the cost of funds to finance that instrument. In the commodity market, it is the cost of holding an asset in physical form, including insurance payments.

In the derivatives market, it includes interest expenses on margin accounts, which is the cost incurred on an underlying security or index until the expiry of the futures contract. The cost also includes economic costs, such as the opportunity costs associated with taking the initial position. Theoretically, the price of a futures contract is the sum of the prevailing spot price and the cost of carry. See formula But the actual price of futures contract also depends on the demand and supply of the underlying stock.

Suppose the spot price of scrip X is Rs 1, and the prevailing interest rate is 7 per cent per annum.

### Relationship between Futures Price and Cost of Carry | Anilkumar G Garag - pugliablog.info

Futures price of one-month contract would therefore be: When making an informed investment decision, consideration must be given to all potential costs associated with taking a position.

A longer position on margin attracts higher interest payment. Buying of more futures as opposed to cash generally raises the cost of carry, as it is an annualised premium of the futures to cash.

The higher the absolute price difference between futures and cash, higher is the cost of carry. Meanwhile, the term is used to interpret market sentiment for a stock or index, as higher values of cost of carry along with the build-up of open interest indicates that traders are bullish and willing to pay more for holding futures. The opposite is true for falling cost of carry. Sometimes, futures trade at a discount to the price of the underlying, which makes the cost of carry negative.

This usually happens when the stock is expected to pay a dividend, or when traders execute a reverse-arbitrage strategy that involves buying in spot market and selling futures. If storage costs, borrowing costs and income accrue at the same time, the whole net cost of carry can be treated as an annual rate and if continuous compounding is assumed then the equation 3. After calculating the cost of carry, does this cost of carry have any significant relation with the futures price of the contracts?

If the cost of carry goes increases, does the futures price also increase? Does the change in cost of carry bring about a corresponding change in the futures price?

**Costs of Production- Microeconomics 3.3 (Part 1)**

These are the questions that are attempted to be answered in the following paragraphs. The futures prices for the months of the contract expiring in July to June were considered for computing the cost of carry in the stock on a daily basis. The data was available on an average for about 90 days per contract, from the day of introduction of the contract to the expiry of the contract.

## Cost of carry

It was observed that these contracts were traded thinly until they became near-month contracts. Therefore only the data pertaining to the near month contracts was selected and a single data set of near month contract prices was prepared for each of these stocks.

The data for the day of expiry was omitted and data for the next contract was included for the day of contract expiry as the cost of carry is expected to be zero on the contract expiry date for a specific contract. The stocks selected were: Hero Honda Motors Ltd. The underlying dynamics of the economy were changing fast and the popularity of futures trading were just picking up in these years and therefore this study would at best describe the phase of evolution of futures market in India.

The study aims to find out whether cost of carry and the change in change in cost of carry in a stock futures contract and index contract have any effect on the change in the prices of the contract.

Since the cost of carry equation is a proven theory and has been the cornerstone of all the research on futures contracts and derivatives in general it is not an attempt to prove or disprove a theory. This is attempt to find out how much truth is there in the market perception that futures prices behave according to the behaviour of the cost of carry. The futures Price data collected from the NSE website www. Data for each stock was contained in a contract-wise file making it up to 48 files per stock.

These 48 files were further pruned to one month or near month contract data and then merged into a single data set containing the one month or near month contract price data for the period of 28 June to 29 June The spot prices for all the stocks for the period from 28 June to 29 june were downloaded from the NSE website and placed alongside the futures data for the purpose of consolidation.

Thus each data set had the following fields: The population parameter is denoted by the Greek letter rho and the sample statistic is denoted by the roman letter r and is given by the equation 1. Ft is the closing futures price of the day. Ft-1 is the closing futures price of the previous day. We determine change in Futures Price y as given by equation 5.

For each of the stocks we have x as change in Cost of Carry and y as change in Futures price We determine coefficient of correlation r using equation 3.

- Species–area relationship
- Cost Of Carry
- Put–call parity

A T-test to confirm our observations also yields the same results that the correlation between eh change in futures price and the change in cost of carry is near ZERO.

This leads us to the conclusion that the change in futures price cannot be explained by the change in cost of carry at all. This also means that popular conception that futures prices vary with the change in cost of carry is not true.

The chart below describes the distribution of correlation.

## Arbitraging futures contract

This leads us to conclude that the variables are not related to each other and they are independent of each other. There is a strong and positive correlation between the change in futures price and the change in cost of carry in single stock futures.

The hypothesis is rejected as the correlation coefficient hovers around ZERO.