Risk preferences, global market conditions and foreign debt: Is there any role for the currency composition of FX reserves?

I use a transition probability matrix associated with different global market conditions and I assume that it captures switches in central bank preferences between approximated constant relative risk aversion (CRRA) expected utility and approximated increasing relative risk aversion (IRRA) expected utility. I approximate CRRA and IRRA expected utility, to construct and propose constrained portfolio selection frameworks with skewness, for the currency composition of FX reserves over different global market conditions that influence central bank preferences. These portfolio selection frameworks account for portfolio rebalancing, they satisfy Pratt-Arrow measures of risk aversion and are constrained by the country's currency composition of foreign debt. Thus, for these portfolios, the currency composition of FX reserves is motivated by its country's currency composition of foreign debt. I propose these frameworks for 6 emerging market economies (EMEs) and this is only for a small portion of the total portfolio of FX reserves. These EMEs are Brazil, India, Indonesia, Mexico, South Africa and Turkey and five of these EMEs have been denoted as the "Fragile Five". Using different methods of computing expected FX reserves returns and different maturity structures on FX reserves, I validate my proposal using data over the 2010-2018 period on these EMEs by simulating optimal FX reserve weights for each EME; where each country's actual currency composition of foreign debt is a constraint.