Concept of Convergence

Convergence is the movement of the price of a futures contract toward the spot price of the underlying cash commodity as the delivery date approaches. It simply means that, on the last day that a futures contract can be delivered to fulfill the terms of the contract, the price of the futures and the price of the underlying commodity will be nearly equal. The two prices must converge. If not, an arbitrage opportunity exists and the possibility for a risk-free profit.

Convergence happens because the market will not allow the same commodity to trade at two different prices at the same place at the same time. For example, you rarely see two gasoline stations on the same block with two very different prices for gas at the pump. Car owners will simply drive to the place with the lower price.

In the world of futures and commodities trading, big differences between the futures contract (near the delivery date) and the price of the actual commodity are illogical and contrary to the idea that the market is efficient with intelligent buyers and sellers. If significant price differences did exist on the delivery date, there would be an arbitrage opportunity and the potential for profits with zero risk.

Arbitrage

The idea that the spot price of a commodity should equal the futures price on the delivery date is straightforward. Purchasing the commodity outright on Day X (paying the spot price) and purchasing a contract that requires delivery of the commodity on Day X (paying the futures price) are essentially the same thing. Buying the futures contract adds an extra step to the process: step one is to buy the futures contract, and step two is to take delivery of the commodity. Still, the futures contract should trade at or near the price of the actual commodity on the delivery date.

If these prices somehow diverged on the delivery date, there is probably an opportunity for arbitrage. That is, there is the potential to make a functionally risk-free profit by purchasing the lower-priced commodity and selling the higher-priced futures contract assuming the market is in contango. It would be the opposite if the market were in backwardation.

• Convergence is the movement in the price of a futures contract toward the spot or cash price of the underlying commodity over time.
• The price of the futures contract and the spot price will be roughly equal on the delivery date.
• If there are significant differences between the price of the futures contract and the underlying commodity price on the last day of delivery, the price difference creates a risk-free arbitrage opportunity.
• Risk-free arbitrage opportunities rarely exist because the price of the futures contract converges toward the cash price as the delivery date approaches.

Convergence trade is a trading strategy consisting of two positions: buying one asset forward i.e., for delivery in future (going long the asset) and selling a similar asset forward (going short the asset) for a higher price, in the expectation that by the time the assets must be delivered, the prices will have become closer to equal (will have converged), and thus one profits by the amount of convergence.

Convergence trades are often referred to as arbitrage, though in careful use arbitrage only refers to trading in the same or identical assets or cash flows, rather than in similar assets.

Formally, convergence trades refer to trading in similar assets in the expectation that they will converge in value. Arbitrage is a stricter notion, referring to trading in identical assets or cash flows, while relative value is a looser notion, referring to using valuation methods (value investing) to take long-short positions in similar assets without necessarily assuming convergence, and is more associated with equities. For example, in relative value investing one may believe that the stock of one mining company is undervalued relative to some valuation, while another stock is overvalued (relative to this or another valuation), and thus one will expect the undervalued stock to outperform the overvalued stock, even if these are quite different companies.

Risks

The risk of a convergence trade is that the expected convergence does not happen, or that it takes too long, possibly diverging before converging. Price divergence is particularly dangerous because convergence trades are necessarily synthetic, leveraged trades, as they involve a short position. Thus if prices diverge so that the trade temporarily loses money, and the trader is accordingly required to post margin (faces a margin call), the trader may run out of capital (if they run out of cash and cannot borrow more) and go bankrupt even though the trades may be expected to ultimately make money. In effect, convergence traders synthesize a put option on their ability to finance themselves.

Prices may diverge during a financial crisis, often termed a “flight to quality”; these are precisely the times when it is hardest for leveraged investors to raise capital (due to overall capital constraints), and thus they will lack capital precisely when they need it most.

Further, if other market participants are aware of the positions, they can engineer such price divergences, driving the convergence trader into bankruptcy compare short squeeze.

As with arbitrage, convergence trading has negative skew in return distributions it produces, resulting from the concave payoff characteristic of most such high-probability low-return strategies. Operators engaging in such trades will usually make consistent but relatively small profits, occasionally offset by significant losses, consuming previous profits earned over a long period of time. The low probability of encountering a loss in such strategies can lead inexperienced traders to underestimate the severity of such a loss, and assume excessive levels of leverage, potentially leading to bankruptcy.

On the run/off the run

On the run bonds (the most recently issued) generally trade at a premium over otherwise similar bonds, because they are more liquid there is a liquidity premium. Once a newer bond is issued, this liquidity premium will generally decrease or disappear.

Junk Bond/Treasury convergence

Typically junk bonds, given their speculative grade, are undervalued as people avoid them. Therefore the spread over treasuries is more than the risk of default, by buying junk bonds and selling treasuries, to hedge interest rate risk. Often profits can be achieved by buying junk bonds and selling treasuries, unless the junk bond defaults.

Reverse

A reverse version of this strategy also exists. This is when a trader believes that the futures contract is undervalued and the underlying asset overvalued. Instead of shorting the futures contract the trader would long this, and short the underlying asset.