The nutshell evidencing IVs and risk reversals are for G10 currency space and they have the different nature of the maturity and currency risks make it possible to design a portfolio construction process in two steps:

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

Step 2: Allocating currencies to diversify that global risk across a basket of pairs (correlation)

Step 1: Tenor selection:

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

Gamma risk: Buying 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.

Step 2: Currency allocation

Once the tenor is selected, currencies must be allocated in the volatility portfolio to take advantage of the diversification effects. In the following examples, we stick to the eight currencies listed above and remove the EUR/GBP and EUR/JPY to keep the USD as the portfolio currency, leaving six currencies to allocate. We pick the 1y tenor. 

Notably the stability of the correlation matrix and setting expected returns. For equity or bond asset classes, dividend yield or carry are a relatively unbiased way to input returns. For the volatility asset class, there is no such natural metric. One solution would be to use the difference between the forward and the current volatility, but that would not be very helpful as it would only express the steepness of volatility curves, and it is well known that forward volatility is a poor predictor.

We adopt a scenario approach where we identify three periods of rising and falling volatility for the average of our six currencies since 2013. For each currency, the change in 1y implied volatility is annualised. The return input that we use is the average of the three annualised changes. Similarly, we compute the historical volatility of volatility and the correlation matrix in separating rising and falling volatility scenarios.