# Meaning of Cash Future Arbitrage

## Cash futures arbitrage example

Consider stock X on January 1, 2020. Its cash market price for the stock is Rs 150, and its May futures price is Rs 152. The multiplier of the contract would be 100 shares. Imagine there is a cost to carry. This is 8% per annum or 0.75 percent per month. The fair price can be calculated by using the formula F = S*exp (rT), where S is the spot price, and r is the cost per month of carry. T is the time until expiration in years. In this example, 150*exp(0.0075*5/12) is the fair price. This gives us a number 150.469. This means it is an overvalued forwards contract (market price at Rs 152). You go long in cash and short in futures.

A trader would have 100 shares of the stock if the stock price rises to Rs 155. The profit would be between 155 and 150x100, or Rs 500. Futures would cost you Rs 300. The arbitrage costs the trader Rs 200. This arbitrage costs Rs 0.469 for 100 shares. Your total gain would be Rs 200-Rs 26.9. This would amount to Rs 153.1

If you consider that the Rs 150 stockX falls to Rs 148, it would be a different scenario. For 100 shares, this would mean that the loss on the underlying asset would amount to Rs 200. For 100 shares, the futures profit would be Rs 400 (152-148). Arbitrage would net you Rs 200. To reduce the cost of carry, you would need to subtract Rs 46.9 from Rs 200. This would give you Rs 153.1. This cash futures arbitrage example demonstrates the simplicity of the trading strategy.

## Summarising

This cash futures arbitrage example demonstrates that futures offer traders the opportunity to leverage pricing differences and make a profit in a relatively riskless manner. The cash to future arbitrage strategy is simple.

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