In our recent posts, we’ve already mentioned, the eight most liquid currencies pairs (in decreasing order) are EURUSD, USDJPY, EURJPY, GBPUSD, EURGBP, AUDUSD, USDCAD, and USDCHF.

The further illustrations are limited to this pool, according to market spreads.

The different nature of the expiration and currency risks make it possible to design a portfolio construction process in two steps:

Step 1: Choosing a single tenor corresponding to a macro level of risk (volatility of volatility)

Step 2: Allocating FX baskets by diversifying that macro risks across a basket of pairs (correlation)

Being choosy in the best maturity mainly depends on these considerations: portfolio risk, gamma risk, liquidity. Volatility assets with different tenors do not bring significant diversification, so a single maturity should be sufficient to build a volatility portfolio.

The relationship between the ATM implied volatility and its own volatility exhibits again a clear segmentation of the curve (equi-weighted average of the eight pairs for each tenor).

The first observation is that the average volatility increases with the tenor, which reflects the average steepness of the ATM volatility term structures. There are about one volatility points between the 1m and the 1y average implied volatilities.

The second observation is the decreasing and convex relationship between the implied volatility and its own volatility. The most decreasing part corresponds to the 1m-3m segment.

Then the volatility becomes more stable in the ‘vega’ segment (3m-2y) and it turns out that volatility risk significantly dampens in the long-dated segment (2y and beyond).

Gamma risk: Initiating longs in options to trade volatility (vega) while getting rid of the directional risk requires dynamic delta-hedging. That risk diminishes with duration of the option, and the gamma risk diminishes faster than the notional reduction which maintains the vega exposure constant. This suggests that it is not necessary to select very long-dated options to reduce the gamma risk significantly.

The issue still exists in a slightly different form in trading volatility derivatives instead of options. With a short-dated volatility swap, the realised volatility is sampled on a limited number of observations. This is an important source of gap risk, introducing uncertainty in the level of the final realised volatility.

The volatility of volatility of our eight pairs is represented on Graph for tenors from 1m to 2y. For each pair, we observe the suspected decreasing relationship between the tenor and the instability of the implied volatility. Since 2009, GBP volatilities have been more stable, while the most volatile have been JPY and AUD/USD volatilities.