Just as corporations have to deal with “forecasting error” in terms of the deviation of forecast exchange rates relative to the actual future rate, so investors have to deal with “tracking error” within their portfolios, which is the return of the portfolio relative to the investment benchmark index being used. Within this, there is “expected” and “realized” tracking error. Expected tracking error is as the name suggests determined before the fact — ex ante — whereas the realized tracking error is determined after the fact.
Determining the relevance of tracking error is also a function of comparing the portfolio’s hedging strategy with a random strategy, which creates hedge/don’t hedge signals with equal probability on a regular basis. Using polar benchmarks — i.e. 0% or 100% hedged — the equal probability of the outcome of the random strategy suggests that hedge deviations will be zero in half the cases and 100% in half the cases. However, with a partially hedged currency benchmark, the deviations will vary in direct proportion to the ratio of the benchmark. For instance, for a symmetrical or 50% hedged currency benchmark, the deviations will be 50% from each side of the benchmark.
From this, we can gather two things, firstly that the tracking error — or the deviation — is a function of the hedged ratio used for benchmarking and secondly that the tracking error for a partially hedged benchmark should be less than that for a polar benchmark. Indeed, generally, the tracking error for a symmetrical or 50% currency hedging benchmark should be around 70% of the tracking error using polar benchmarks. Expressed differently, the tracking error of a polar benchmark should be 1.41 (square root of 2) times higher than that of a 50% hedged benchmark. The advantage of a symmetrical or 50% currency hedged benchmark for a portfolio manager is that it reduces the tracking error of the portfolio and also enables them to participate in both bull and bear markets compared to the polar benchmark where the participation is limited to either/or.
Tracking error can be further reduced by a technique known as “matched hedging”, which increases or decreases the hedge ratio relative to the change in asset allocation. Historically, the act of asset allocation itself within fixed income portfolios has been a major and seemingly unavoidable factor in increasing a portfolio’s tracking error. Matched hedging can reduce though clearly not eliminate this.
Tracking error can also occur under passive currency management. This is because in order to implement a passive currency hedging programme a portfolio manager still has to adjust the amount of the currency hedge relative to the value of the underlying as it changes on a regular basis — i.e. once a month. In reality, many portfolio managers don’t bother to do this. As a result, the residual that is left over- or under-hedged contributes to the tracking error. In this, the portfolio manager has to balance the transaction costs of re-balancing the currency hedges against the negative effect on tracking error.
Tracking Error
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