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# How large is the tracking error created by trend following?

###### Posted August 3, 2020
Jack Vogel, PhD
Alpha Architect

The post How large is the tracking error created by trend following? appeared first on Alpha Architect Blog https://alphaarchitect.com/blog/ By Jack Vogel, PhD.

A question Iâ€™ve received in the past is the following:

If you could go back in time five years ago and tell yourself something about investing, what would it be?

My response is the following:

Tracking error.

First, what is tracking error?(1)

Tracking error is a measure of how much a strategy deviates from a benchmark. If you are a U.S. equity investor, a standard benchmark is the SP500.(2) One can mathematically compute tracking error, which I will do below and is found here, but here is a simple exampleâ€“my portfolio is up 15% and the benchmark (SP500) is up 25%. Thus, I have lost by 10% to the index (or my simple â€śtracking errorâ€ť is 10%).

Second, why would I have gone back in time and told my younger self about such a simple concept? Also, why didnâ€™t I know about this 5 years ago?

Well, the answer is that I definitely knew about the concept (we had the calculations in our analysis files), but seeing it while running real-world portfolios is completely different than calculating it on paper portfolios!

Probably the main reason that I would have gone back and told myself about tracking error has to do with a portfolio strategy we like: trend following.

As many of our readers know, we are fans of trend-followed portfolios. For those unfamiliar with trend following, the idea is rather simpleâ€“invest in an asset class if the price/return to that asset class is trending up. If not, go to cash or hedge your exposure.(3)

The concept is simple, and for many investors who are unwilling to accept large losses in their portfolio, the idea sounds great.

To be clear, this portfolio will behave differently than B&H, which is the standard index.

And what happens when you are different than the index? You create tracking error!

In this post, I wanted to highlight how large and extremely painful tracking error can be â€” especially if you are benchmarked against a buy-and-hold (â€śB&Hâ€ť) portfolio.

First, letâ€™s examine simple trend-following performance.

Historical Trend-Following Performance

To give some broader context to trend-following, I am displaying the returns to trend-followed portfolios on the five major asset classes:

1. SP500 â€” SP500 total return
2. EAFE â€” EAFE total return
3. T-Bond â€” U.S. 10-Year Treasury Bond total return
4. REITs â€” NARIET index total return
5. Commodities â€” GCSI index total return

The portfolios and their returns are shown first without trend, and then with trend-following.

The returns below are from 1/1/1973-12/31/2017. All portfolios are gross of any transaction or management fees.

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index.

The returns below are from 1/1/1973-12/31/2017. All asset classes apply a 12-month moving average rule to the total return index, and either invest (1) in the index if a positive trend or (2) in cash (U.S. T-bills) is a negative trend. All portfolios are gross of any transaction or management fees.

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index.

As is shown above, the overall annualized returns to trend-followed portfolios, over long-time cycles, are definitely not that much different than B&H.

But what is the tracking error caused by trend following?

Trend-Following Tracking Error Statistics

So now that we have the baseline stats on B&H and trend-following, what is the tracking error of the trend-followed portfolios relative to the B&H portfolios?

The numbers are shown below the respective tracking errors for each of the asset class relative to its trend-followed component over the 1/1/1973-12/31/2017 time period.

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index.

So the numbers above give the annualized tracking error, which can be thought of as the standard deviation of the return differences between the trend-followed portfolio and the B&H portfolio. What we notice is that the tracking error is around 10% for the more volatile asset classes, whereas, for bonds (which are less volatile), the tracking error is around 5%.

But once again, as I highlighted above, it is easy to say, â€śYeah, the tracking error is 10%â€¦ I will accept this, no problem. After all, the returns to trend following are almost the same as B&Hâ€ť.

Notes:

1. â†‘ Note, I have given different perturbations of this answer, but this was the main answer

2. â†‘ This is generally true even if one is investing a portion of the equity portfolio in international stocks.

3. â†‘ We have articles here and here describing the pros and cons of trend-following.

Visit Alpha Architect Blog to review a list of Trend-Following Tracking Error Statistics: https://alphaarchitect.com/2018/10/25/how-large-is-the-tracking-error-created-by-trend-following/

The views and opinions expressed herein are those of the author and do not necessarily reflect the views of Alpha Architect, its affiliates or its employees. Our full disclosures are available here. Definitions of common statistics used in our analysis are available here (towards the bottom). Â· Join thousands of other readers and subscribe to our blog. Â· This site provides NO information on our value ETFs or our momentum ETFs. Please refer to this site.

###### Disclosure: Alpha Architect

The views and opinions expressed herein are those of the author and do not necessarily reflect the views of Alpha Architect, its affiliates or its employees. Our full disclosures are availableÂ here.Â Definitions of common statistics used in our analysis are availableÂ hereÂ (towards the bottom).

This site providesÂ NOÂ information on our value ETFs or our momentum ETFs. Please refer toÂ this site.

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