This paper proposes using an optimization mechanism in the currency overlay portfolio construction process, an area that has not been explored in the literature. Instead, existing research tends to focus on predetermined fixed weights, such as the trading volume of currencies from the Bank for International Settlements' survey, in order to construct overlay portfolios, which may not always be optimal. This paper optimizes the portfolio using the Cholesky decomposition-based multivariate time-varying correlation-generalized autoregressive conditional heteroscedasticity (TVC-GARCH) and constant correlation (CC) models as allocation schemes, with underlying currencies' returns originated from a moving average-based trend-following single foreign exchange (FX) strategy in a certain hedging criterion. This paper uses an FX strategy based on the equally weighted (EW) average of three different single moving average days to determine the hedging needs underlying the hedging criterion. We use the returns of the strategies of equally weighted-TFX (EW-TFX) and TFX to construct optimal currency overlay portfolios. Our findings reveal that EW-TFX portfolios with the TVC-GARCH scheme have the best risk-adjusted portfolio returns. There is some evidence of significant differences between the portfolio returns of the EW-TFX overlay portfolios and other currency portfolios, which supports the outperformance. Our findings also support existing evidence in the literature.