Adding an uncorrelated strategy to a portfolio can improve its risk-adjusted performance. But even when the long-term performance is expected to be superior, the new portfolio can still underperform the original portfolio over shorter time horizons. Here we show why.

## Model assumptions

To model the combined returns of our original portfolio and added strategy, we assume:

1) The original portfolio has a Sharpe ratio (SR) of around 0.7 – which is close to the long-term Sharpe ratio of Winton’s longest running investment program;

3) The added strategy is uncorrelated with the original portfolio;

3) Returns are normally distributed [1];

4) The original portfolio and added strategy are targeting the same level of risk.

Clearly, the expected SR for the new strategy is the biggest unknown. At Winton, we spend a great deal of time trying to establish reliable estimates, but ultimately we still have uncertainty about what the future holds. We therefore assume a range of expected Sharpe ratios: 0.2, 0.5 and 0.8.