Futures: Arbitrage & its meaning.

ARBITRAGE

Buying in one market (say, spot market) and simultaneously selling in another market (say, futures market) to make risk free profits when there is substantial mismatch between two prices is called arbitrage. Arbitrage is described as risk free because participants are not speculating on market movements. Instead, they bet on the mis-pricing of a share/asset that has happened between to related markets.

In short, when you earn by selling and buying same security at different rates in different markets, it is called Arbitrage. It is a highly technical field. Market’s mis-pricing is taken advantage by traders to make risk free gains.

Mispricing? How?

The futures price has a definite relationship with the spot price. In normal market conditions, futures price would be greater than the spot price because of the effect of cost of carry and it moves in tandem with the price of the underlying asset. So, broadly we can say that if the spot price of the share moves up by Rs 5, the futures position would also have made a profit of Rs 5.  The correlation is not very accurate but, almost so.

Thus, based on the cost of carry principle, if the spot price of a share on a given day is ‘x’ then, the futures price on that day would be ‘x’ + the interest for holding the spot to the duration of futures contract ( minus) any dividend accrued on the spot.

So, to compute the cost of carry accurately a participant needs accurate information on interest rates and expected dividends. However, futures market is not so perfect where all the requisite information is readily available to all. Imperfections are common and that results in a mismatch between spot and futures price based on the cost of carry principle.

When the relationship between spot and futures does not hold, the futures are incorrectly priced and that results in arbitrage opportunities.

Example-1

AT THE GOLD SOUK.

Gold coins sell at Rs 2500 for a gram right now. 1 year gold futures are available at Rs 3750 for a gram. (I.e. Gold coins deliverable after one year from now). Let’s also assume that personal loan interest rates are 15%.

Given the above situation, is there a way to make some guaranteed profits? The answer is ‘yes’. Let’s see how.

You borrow Rs 2500 at 15% interest for a year and buy in the spot market. At the same time, you’d also sell futures at Rs 3750. A year later, to fulfill the futures contract ( remember, you were the seller of futures contract) you deliver the gold for Rs 3750 and out of the proceeds, you pay back your loan of Rs 2500 with interest which works out to Rs 2875. Net of Rs 875 (3750-2875) is your guaranteed profit, whatever may come. What you’ve done is technically called – arbitrage.

You made money because; the futures were priced illogically higher than the spot price. The actual fair price of the futures should have been Rs 2875 (spot + cost of carry). But since futures were priced higher, you got the opportunity to make money.

Example 2.

The risk free interest rate is 6% right now. Shares of Toobler Ltd are available in the cash market for Rs 2000 whereas the futures contract of Toobler due for expiry in 3 months from now is available at Rs 2030 which is a 1.50% premium over cash market. This 1.50% works out to an annual risk free cost of 6% based on cost of carry principle. There is no arbitrage opportunity right now as the relationship is theoretically correct. Opportunities arise when the market over reacts to some news or events disturbing this equilibrium.

For instance, let’s assume that the government raises the interest rates to 8% and Toobler Ltd’s share price in cash market slumps to Rs 1970. The futures of Toobler Ltd, which is traded by speculators, may fall 3% to Rs 1969. You might get an arbitrage opportunity here since the theoretical spread between spot and futures has to be maintained by the market. Either the spot market has to fall or the futures price has to rise thereby maintaining the spread between the two. Here, if you buy futures and sell spot, you may make some risk free profits when the market comes back to normalcy.

THE TWO RULES OF ARBITRAGE.

We sum up the two rules of arbitrage.

Rule 1. Buy spot and sell futures – if the actual futures price is greater than the theoretical futures price.

Rule 2. Buy futures and sell spot- If the actual futures price is lower than the theoretical futures price.

Example 3

The shares of Toobler Ltd are quoted at Rs 2000 in the spot market. The risk free interest rate 12% per annum continuously compounded. Toobler is certain to pay a dividend of Rs 125 per share 3 months from now. 3 month Toobler future contracts are available. What would be the value of futures? If Toobler’s futures are available at Rs 2100, what would be your strategy to make risk free profits?

Fair futures price:

The present value of divided to be declared 3 months from now would be

  • Rs 125 x E -(0.12 x .25)
  • Rs 125 x E –(0.03) = Rs 125 x 0.97045 = Rs 121.30

Therefore, adjusted spot market price would be Rs 2000 – 121.30 = Rs 1,878.70.

Fair value of futures would be

  • Rs 1878.70 x E ( R x T)
  • Rs 1878.70 x 1.30345 = Rs 1935.
  • Since the futures are over valued at Rs 2100, you should sell futures and buy spot. (Rule 1)

Example 4.

If we assume that Toobler Ltd’s futures are available for Rs 1800. What would be the strategy to make risk free gains?

Since futures are undervalued at Rs 1800, we apply Rule 2. You should buy futures and sell spot.

You may like these posts:

  1. Futures: Principles of pricing.
  2. Futures: Understanding the basic terms
  3. Futures: Types of contracts

1 Response to “Futures: Arbitrage & its meaning.”

Twinkle

August 20, 2016 at 1:22 am

Great work…this post clears my all confusion…thankx alot..

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