The relation between Future price and Spot price of an Index or a Stock is a widely discussed subject in derivatives trading. The terms Premium, Discount, Cost of Carry (CoC), etc are being used frequently. Let us discuss these in the perspective of derivatives trading.

The Spot and Future Price are related as follows:

Future Price = Spot Price + Cost of Carry

Suppose shares of Reliance are trading at Rs. 851.30 on February 6, 2015 and on the same day Reliance Future of February Series (expiry 26th Feb) are trading at 854.70. If an investor is bullish on Reliance and can borrow unlimited money at, say, 6% p.a., should he buy in cash markets or futures markets (assume no margin payments)?

If the investor were to buy in cash market and make payment by borrowing at 6% for 20 days (Feb 6 to Feb 26), the interest cost would be 851.30 x 6 x 20/365 i.e, Rs.2.80. The total acquisition cost would thus be Rs. 851.30 + Rs. 2.80 = Rs. 854.10

Now if the Future is available at a price lower than Rs. 854.10 then it would make sense to buy Reliance in the Futures Market. The price Rs. 854.10 is therefore ‘No Arbitrage Price’ or ‘Equilibrium Price’.

The Risk Free rate of interest that equates the Spot price to the Future price is the Cost of Carry. The formula for determining cost of carry is as follows

FP = S* (1+r)t

Where FP = Future Price, e.g 854.70

S= Spot price, e.g, 851.30

t = Number of days e.g, 20/365

r = Cost of carry

Substituting the previous values of Reliance Spot Price & futures Price, we get r = 7.55

Therefore, Cost of carry is the cost incurred on holding positions in the underlying security till the expiry of future.  The cost includes the risk free interest rate and excludes any dividend pay out from the underlying security.

Determining Stock Future price without Dividend

Suppose shares of Reliance are trading at Rs. 851.30, if Cost of carry is 6% p.a., what would be the calculated price of Reliance Future?

Using the same formula, FP = S* (1+r)t, we get FP = 854.10. This is No Arbitrage Price where investor is neutral between buying in the cash or futures market. If the actual price differs from this calculated price, arbitrage opportunity arises.

Determining Stock Future price with Dividend

In the above example let us now assume that Reliance is expected to give a dividend of Re. 1 per share in 12 days.

An investor holding the underlying share will receive dividends but the holder of Reliance future will not be entitled to dividend. The present value of dividend (PVD) will have to be subtracted from the spot price.

PVD = Re 1 / (1+6%)12/365 = 0.998

Now FP = (S0 – PVD) * (1+r)t = Rs. 853.05

From the above discussion, we see that normally the Future Price is higher than the Spot price, due to Cost of Carry factor. This situation is called as Contango. In some cases, Future price is lower than the spot price; either due to dividend or some other factors, the situation is called as Backwardation. Backwardationis more commonlyobserved in Commodity. On the expiry day, Future price converges with the Spot price.

When the future price is lower than the Spot price without any valid reason, arbitrage opportunity arises (reverse cash and carry) and generally traders take the opportunity by buying Futures and selling spot of the same underlying at the same time. For the purpose of selling spot, demand arises in SLBM segment.

Interpretation of Cost of Carry (CoC)

Traders often use CoC to gauge the market sentiment. We saw earlier that CoC is actually the cost a trader is willing to pay to hold the position. NSE website displays CoC of the Stock futures and Index Futures. What do we conclude from the price, open interest (OI) and CoC trend?

Change in CoC seen along with open interest shapes a clear picture of the broader sentiment for the stock or index. Open interest is the total number of open positions in a contract. For a rising OI, an increase in CoC indicates accumulation of long (or bullish) positions, while an accompanied fall in the CoC indicates addition of short positions and bearishness. Likewise, a fall in OI, accompanied with a rise in CoC, indicates closure of short positions. Whereas, both falling OI and CoC indicates that traders are closing long positions.

Analysts also observe changes in CoC at the expiry of derivatives contract. If a significant number of positions are rolled over with a higher cost of carry, it implies a bullish trend.

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