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Calendar arbitrage, Part 1

Calendar arbitrage is a strategy that profits same instruments’ but different expiry dates futures contracts. Calendar arbitrage works as follows: if spread between two contracts grows, nearby contract is bought, next one is sold, if the spread is narrowing - the opposite, selling nearby contract and buying next futures. The attractiveness of this strategy is high potential returns while maintaining low risk, because the position always remains neutral to the market, or delta-neutral. In this article, we will cover some theoretical aspects of calendar arbitrage as well as show a real example of calendar arbitrage using Megatrader (part 2).

Let’s first have a look at the theoretical background of calendar arbitrage. It is known that in normal circumstances the futures price exceeds the asset’s price by a little, as additional income of futures contract (futures needs much less margin to buy than spot asset) is already included in contract’s price. It is obvious that amount of extra income decreases over time depending on the number of days remaining until expiration. Thus, if interest rate remains the same, we can assume that spread between futures and spot decreases linearly with time and becomes zero at the time of expiration. If having two futures - with near and far expiration dates, with unchanged expectations of interest rate, spread between two has to be constant as shown in the following picture:

However, in practice, due to the differences of investors' interest rates and spot prices expectations as well as due to differences in speculative activity in nearby and next contracts, the spread between the nearby and next futures constantly varies, thus creating lots of arbitrage opportunities.

Note that the calendar arbitrage has some significant advantages over classical spot-futures arbitrage. First, much less margin is needed to open a position as calendar spreads when trading on most exchanges require margin on only one side of spread. Second, commissions are less in calendar arbitrage than in classical (futures commissions tend to be lower than forex or equities’ commissions). These advantages, coupled with low risk, make calendar arbitrage so compelling to traders.

However, in practice, traders using calendar arbitrage strategy face a number of pitfalls that limit the period of this strategy effectiveness to a few months of the year. First is low liquidity on next futures contract which only begins to increase with the approach of nearby contract’s expiration date when investors are beginning to shift their positions from the near to far contracts. Second, competition among traders using arbitrage increases every day and reaches a peak in the last couple of weeks before expiration. As a result of high competition amplitude of the spread oscillations decreases and slippage when opening and closing orders increases, which significantly reduces the efficiency of the trading strategy.

In our experience, the best time to use calendar arbitrage is the period beginning approximately two months and ending about two weeks before the expiry date of nearby futures contract. During this period, the next futures, as a rule, already gather up enough liquidity to trade freely, while arbitrageurs’ activity has not yet reached its limit, when competition between them begins to seriously hinder the strategy’s effectiveness and profitability.

As an example, here is a chart of a calendar spread between the futures on Gazprom shares (GZU2 - GZM2) from 15 March to 14 May 2012:

Calendar spread

As it can be seen from the chart, spread between futures fluctuates near a constant level, providing a lot of arbitrage opportunities.

What is the potential profitability of this strategy? It largely depends on the amount of money involved in trading. It is because of the lack of liquidity in next futures, so smal-cap traders, as opposed to large ones, have a relatively easy time fully using their capital in arbitrage. Therefore, ROI of small investors using calendar arbitrage may be several times larger than ROI of large investors trying to involve large amounts of funds.

Judging by our experience in 2012, we can say that for small accounts (up to 3000$) calendar arbitrage yields an average of 30-40% per trading period. Accordingly, given that the futures expire four times a year, the performance of strategy may well reach 150% per year. Of course, it will be much harder to get such a ROI with larger deposit.

In part 2 we will show you an example of calendar arbitrage robot we use to trade on live accounts with Megatrader.