The Unit Cost of Volatility

One of the challenges market participants face when analysing their FX transaction costs is how to compare results across different currency pairs and volatility regimes. A given spread for 1 million EURUSD might be considered very tight under certain conditions, but unjustifiably high in other circumstances. At present analysis of transaction costs is not dynamic across differing market conditions, so Broker A might be circumstantially better than Broker B, but when those circumstances are considered, the reverse might be true. This problem of comparative measurement is particularly acute when assessing algorithmic execution across different providers but is relevant to any form of execution.

NCFX are pleased to announce the introduction of a new approach that allows fair comparison of liquidity providers in all market conditions. Our solution is to normalise execution costs for volatility conditions and show execution costs in relation to volatility itself.

The rationale for this approach derives from the work of Grinold and Kahn on market impact models. Their work discusses the relationship between volume and volatility by demonstrating the link between inventory risk and time. This inventory risk approach to market impact proposes that it should cost approximately one day’s volatility to trade one day’s volume, plus a bid ask spread.

Where inventory risk is proportional to time

It follows that the volatility cost of a trade must be the amount of the order multiplied by the per period volatility such that an order that is completed in one second incurs a volatility cost equal to the inventory risk of holding that trade for one second.

By scaling volatility to the time needed to complete a trade we can then assign a dollar value to the cost of volatility. 1 million dollars’ worth of euros transacted over one second, where the second volatility in EURUSD is .00005 should cost USD50. Transaction costs above USD50 indicate that the ratio of transaction costs to volatility is greater than one.

Volatility is dynamic. This means the cost to trade changes throughout the day, and from month to month. It follows that the cost of volatility also changes. But if transaction costs are scaled to the implicit riskiness of a trade, the spread away from mid should also scale, and the ratio of transaction costs to the USD cost of volatility should provide insight into the relative costliness of a trade. In fact, because volatility is an external cost factor (market participants can only exercise discretion on the timing and size of orders, not volatility itself) it makes sense to normalise transactions cost by volatility because this is a cost that everybody pays.

Spread costs can be broken down into two components: an information cost and a liquidity cost. Information cost is permanent impact cost. It measures how much prices change over the transaction period. Liquidity costs are realised in the instantaneous skew away from mid at the moment of execution.

Consider the following comparison between two trades, A and B in the chart below. They were both made for the same amount, but on different days. We show the effective spread and the USD cost of liquidity that corresponds to each trade.

We express these transaction costs as units of volatility: we divide effective spread in USD by the USD value of volatility over the trade interval in which the trade was completed.

Trade B exhibits a particularly high unit cost of volatility. Not only was it more expensive in absolute terms (effective spread) but volatility was lower when Trade B was executed. The increased cost of execution cannot be explained by market conditions. We gain further insight by decomposing effective spread into permanent and temporary costs, to identify the information and the liquidity unit cost of trading.

In the above example, looking at the unit cost of liquidity, Trade B cost a relatively small spread, (.55 versus .7) but creates high market impact as shown when we examine the unit costs of information.

By measuring these costs as units of volatility market participants can better understand the cost implications of market movement and bid offer spread. Transaction costs can be scaled according to the riskiness of their trades. Given that riskiness scales with time, we can understand costs as units of time, assigning a dollar value to a discrete moment of time.

We arrive at unit costs by sampling the underlying NCFX benchmark rates. In the days when pretty much all wholesale FX activity was concentrated in one of two electronic platforms, EBS or Reuters, it made sense to estimate the clearing price from single source data. Liquidity is now fragmented over a number of different platforms, which means there will be instances when the transient sampling error of mid-rates across platforms is high. When it comes to measuring idiosyncratic costs, those transient sampling errors can all too often hide a significant portion of costs. By measuring costs against the NCFX Benchmark rates this sampling error problem disappears.

The implications for dealers are clear. Measuring unit costs of volatility enables dealers to grasp the actual cost of employing a specific liquidity provider. This is preferable to looking at circumstantial measures such as comparing costs to peers, which compare idiosyncratic costs. By their very nature, idiosyncratic costs do not lend themselves to meaningful measurement. Unit costs of volatility allow us to decompose transaction costs into relativistic terms- how expensive or cheap a trade is relative to the clearing cost of the trade.

For further information about New Change FX, please contact info@newchangefx.com