Does mean-variance optimization enhance the performance of currency carry trades (long currencies with high interest rates and short currencies with low interest rates)? In their November 2012 paper entitled “On the Risk and Return of the Carry Trade”, Fabian Ackermann, Walt Pohl and Karl Schmedders compare a dynamic mean-variance optimal carry trade strategy to naive ones. Specifically, they consider a series of monthly investments that are long (short) those of the following currencies with the highest (lowest) associated interest rates: U.S. dollar (base currency), Swiss franc, Euro, Japanese yen, British pound, Australian dollar, Canadian dollar, Norwegian krone, Swedish krona, Singapore dollar and New Zealand dollar. For monthly mean-variance optimization, they estimate currency correlations based on the last 250 days (one year) of daily data and set an annual excess return target of 5% (relative to the risk-free rate), the approximate excess return on the S&P 500 Index over the same period. For naive portfolios, they consider 1 long/1 short currencies, 3 long/3 short equally weighted currencies and the S&P 500 Index total return. Using daily currency values and monthly S&P 500 Index data during January 1989 through June 2012 (using the first year for initial optimization),* they find that:*

- The dynamic mean-variance optimal strategy applied to the specified 11 currencies easily outperforms the naive carry trades:
- Over the entire sample period, the optimal strategy generates a gross Sharpe ratio of 1.01 (see the chart below), compared to 0.45 for the 1 long/1 short and 0.60 for the 3 long/3 short naive strategies and 0.36 for the S&P 500 Index.
- Over the subperiod since 2007, the dynamic mean-variance optimal strategy generates a gross Sharpe ratio of 0.58, compared to -0.05 for the 1 long/1 short and 0.17 for the 3 long/3 short naive strategies and 0.08 for the S&P 500 Index.
- Outperformance of the optimal versus naive strategies comes from return enhancement, not volatility suppression.
- Over the entire sample period, the optimal strategy is usually long the U.S. dollar, Euro, Australian dollar and New Zealand dollar. The Swiss franc and the Singapore dollar have the largest average short positions.

- Optimal portfolio turnover is substantial due to strong reactions to changes in interest rates and currency correlations. However, implemented via combinations of spot positions and rolling currency futures or swaps, trading frictions are low.

The following chart, taken from the paper, shows monthly excess returns (relative to the risk-free rate) for the dynamic mean-variance optimal carry trade strategy over the entire sample period. Analysis commences in January 1990 based on the first year of data. Volatility of monthly returns is very high during the financial crisis.

In summary, *evidence indicates that monthly mean-variance optimization of positions may substantially enhance currency carry trade returns.*

Cautions regarding findings include:

- Mean-variance optimization computations are fairly complex, or costly if delegated.
- Many investors may not have direct access to the low-cost strategy implementation described (and would have to pay a fund manager for indirect access).