InvestorQ : How exactly do the interest rates impact the futures price at which to sell over spot?

# How exactly do the interest rates impact the futures price at which to sell over spot?

2 years ago
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Unlike options, that are just a right without an obligation, the futures are a right and an obligation. Futures are symmetric products as the buyer and the seller have the same set of rights and obligations. But how is the futures price determined and how do you decide at what futures you should put in your trade. That depends on the rate of interest and the time to expiry. Let us consider some situations to understand the interest point by starting off with our base case scenario.

 Futures Price Determination Basic equation for the future's price without cash flows during maturity F = future's price 100.99 S = spot price 100.00 r 12.00% (continuous) T-t = days to maturity 30 (365 days in year)

In the above illustration, if the spot price is Rs.100 and if you are looking at a 1-month future, then for a return of 12% annualized you need to sell the futures at a price of Rs.100.99. Of course, there is brokerage and statutory costs and that will impact but for now let us leave that out for simplicity. Let us only focus on the interest rates only. What if the above conditions pertained lower or higher return requirements? What happens then? Check the calculation below when the required rate of return on futures goes down from 12% to just 10%.

 Futures Price Determination Basic equation for the future's price without cash flows during maturity F = future's price 100.83 S = spot price 100.00 r 10.00% (continuous) T-t = days to maturity 30 (365 days in year)

Clearly, the futures price at which the futures should be sold comes down as you now require a lower spread over the spot price. That explains why the futures price has come down. This is one of the reasons why the cash-futures spread in the market tends to come down when the interest rates in the markets come down. But what happens to the futures price if the interest rates go up or the required return for the trader goes up? Check the illustration below:

 Futures Price Determination Basic equation for the future's price without cash flows during maturity F = future's price 101.16 S = spot price 100.00 R 14.00% (continuous) T-t = days to maturity 30 (365 days in year)

Clearly, the futures price at which the futures should be sold goes up further as you now require a higher spread over the spot price. That explains why the futures price has gone up. This is one of the reasons why the cash-futures spread in the market tends to increase when the interest rates in the markets move up. This relationship between time to expiry, interest rates and the spot price determines the price of futures.

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