31 October 2014 - 2 minute read

Adding a new, uncorrelated strategy to a portfolio can improve the risk-adjusted performance of the original portfolio. 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.

## Sharpe ratio enhancement

In Figure 1, we show the resulting “combined portfolio” SR for various risk allocations to the added strategy. The light blue line shows how a new strategy with a modest SR of 0.2 can still add value if it is uncorrelated with the original portfolio.

## Figure 1: Combined portfolio SR for a given level of allocation to a new and uncorrelated strategy

Even if our expected long-term SRs are accurate, a portfolio does not always benefit from the inclusion of a new strategy in the shorter term. Figure 2 illustrates this by showing estimates of the probability that a 25% allocation to the new strategy improves performance.

## Figure 2: Probability of combined portfolio outperforming original portfolio over a number of years

The positive gradients indicate that the probability of outperformance increases over time and more quickly when adding strategies with higher SRs. This improvement is present even if the strategy has a modest SR; in the plot, we see that the chance of the combined portfolio outperforming the original portfolio is estimated to be always greater than 50%.

There is also a sizeable chance that the added sector underperforms over a number of years. For example, with a SR of 0.5, the outperformance probability over four years is nearly 77% – so about one quarter of the time, we can expect the combined portfolio to underperform, even if it will outperform the original portfolio over the longer term.

## Conclusion

We find that adding a new strategy to a portfolio can lead to underperformance versus the original portfolio at times. But this does not detract from the long-term investment case for seeking out and including new, uncorrelated strategies. This knowledge helps us make informed decisions, and hold firm to a sensible strategy, even during difficult times.

### References

[1] This is not a bad assumption; both are well explained by a T-distribution with approximately six degrees of freedom, which is close enough to normal for our purposes.

This article contains simulated or hypothetical performance results that have certain inherent limitations. Unlike the results shown in an actual performance record, these results do not represent actual trading. Also, because these trades have not actually been executed, these results may have under- or over-compensated for the impact, if any, of certain market factors, such as lack of liquidity and cannot completely account for the impact of financial risk in actual trading. There are numerous other factors related to the markets in general or to the implementation of any specific trading program which cannot be fully accounted for in the preparation of hypothetical performance results and all of which can adversely affect actual trading results. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any investment will or is likely to achieve profits or losses similar to those being shown.