Finding and evaluating tracking error

bowlhead99

I think the charges have probably been consistent for class P since it has been running, given it hasn't been going long., at least for this class. It only launched earlier this year. However, their other retail one, the A shares, had been at 0.3%. So perhaps the returns for this one have been backfilled from that other class to give a slightly longer track record, from when the A class was branded moneybuilder and was the main one that a retail investor would have bought at launch at the end of 2012.

According to their prospectus they expect the tracking error (standard deviation) to now be kept within about 0.2% a year. And so perhaps after a couple of years, with a slightly bigger fee at the start, perhaps lagging the index by half a percent life to date is OK - there will, after all, be some costs other than those captured by AMC/TER and they are not claiming zero tracking error... However, the shortfall according to Morningstar chart is 0.7% and has sometimes been more.

One explanation for this is that the fund is priced at midday UK time each day, while the index data is from "when global markets close each day". End of day U.S. time is some 8 business hours later.

We have all seen the U.S. index and some others such as the UK have big inter-day swings in recent days. So it is entirely feasible that the Fidelity fund could take a value snapshot at noon, capturing Asia closing figures but only half of the UK / Europe daily movement and none of that day's U.S. movement and then UK recovers half a percent and U.S.goes up a whole percent, before MSCI say o.k., this is the closing price of all the constituent members of the index for October 22, 2014. US is the biggest component of the index and of the fund. If the numbers don't match, the index and the fund will show a different valuation, but it is merely a timing difference so overall you won't be off by 5% after five days or five years just because you're off 1% percent after one day or one year.

That effect also explains why you might think the Fidelity fund has "generally lagged" in a rising market. The fund is reporting all the daily or weekly growth data (depending on the scale of your graph) on a small lag with the index going up first and that last half of the day's global growth dripping into the next day for the fund.

It can also explain why a low fee UK ETF can appear to "hug" the valuation chart tightly. The market price of the ETF is captured at 4.30pm when the market closes, just like the index valuation is performed on the closing prices of constituent members at 4.30pm.

Feel free to correct me if I'm wrong.

guymo

Thanks for pointing me at the prospectus. That document raises the issue of the timing data and as you say it does go some way to explaining larger than expected apparent lag that nevertheless does not grow over time. It also makes sense of the patterns you can see in the chart.

i didn't realise that tracking error was defined as "standard deviation of excess return" and I am struggling to understand why that is a good definition. I am more interested in the mean gap between the fund and the benchmark than the standard deviation of that gap, surely? The standard deviation would measure the excess risk of the fund over the index; but in my tiny mind, "tracking error" means the size of the gap rather than its volatility.

The prospectus also says that the "ex-post tracking error is expected to be..." which is a bit of nonsense as far as I can tell. You can't expect ex-post, can you?

Thrugelmir

puk999 wrote: »

Would like help to find the tracking error in this fund and evaluate whether it's acceptable.

From the fund website.

Fund managers use derivatives to profit from the changes in the underlying price and can enhance those profits through the use of leverage or borrowing. In such situations performance may rise or fall more than it would have done otherwise, reflecting such additional exposure.

In addition the fund is not 100% invested in equities. But has both long and short cash positions.

bowlhead99

guymo wrote: »

i didn't realise that tracking error was defined as "standard deviation of excess return" and I am struggling to understand why that is a good definition.

I am more interested in the mean gap between the fund and the benchmark than the standard deviation of that gap, surely? The standard deviation would measure the excess risk of the fund over the index; but in my tiny mind, "tracking error" means the size of the gap rather than its volatility.

I see where you're coming from but actually it is a good definition if you think what is the purpose of a tracker.... to track movements in an index.

We all know that any real world fund will have a cost associated with it - funds in the real world pay brokerage fees, stamp duties etc etc when acquiring and disposing of assets, and legal fees, accounting fees, administration fees and a management fee on top. Whereas a hypothetical basket of shares does not. So a difference is inevitable. You are not trying to equal the index. You are trying to track the index.

So, once you acknowledge that you can't equal the index, and your returns are inevitably going to be lower, you can just accept that as a known issue. What you need to focus on, is how "well" you track the index as it moves up and down. We know and accept you will not get the results you would like to have, of equalling the index, because you're a real world fund. Your raison d'etre is to follow the index up and down, and if there is a fixed cost of doing business and you are not allowed to make active decisions, we do not expect you to be able to equal the index - you just need to follow it wherever it goes. If you don't follow it all the places it goes, you are not doing a good job of 'tracking'.

Say the fund has ongoing management fees of 0.08% and average annual trading costs (broker fees, stamp duties etc associated with churning the portfolio on quarterly index promotions and demotions and with deploying and redeeming additional capital) of 0.02%. In such a situation you would hope to track the index with a difference of 0.10% per year.

So if the index goes up by 10.0% in a year, that fund if it was able to track 'perfectly' would deliver 9.9%. If index goes up 49.5% the perfect tracker gets 49.4%. If it goes down by 20% the fund would lose 20.1% and so on. That is the behaviour of a fund with no tracking error. It does its job perfectly and captures every single upswing and down swing.

If it does this, it is a good tracker. At some point the index constituents change, and your perfect tracker changes at the same time with no lag. There's a great big spike in oil stocks and your tracker follows suit because it has the exact same percentage exposure to oil stocks. A tech firm crashes and loses half its value wiping a whole percent off your index in one day, and the tracker feels the same effect because it has the exact same percentage exposure to that tech firm. Obviously the tracker ALSO loses its average 0.0004% every single working day of the year, so that after 250 days it's lost about an extra 0.1% due to its own costs and charges. But basically if it does a good job it will track "perfectly". Zero tracking error. Not the same exact return as the index. A 0.1% p.a. worse return. But doing exactly what it set out to do.

Compare that to a fund that tracks badly. One year the index is up 10% and the fund is up 9.8%. Another year the index is up 15% and the tracker is only up 14%. Another year the index is up 12% and the fund is up 12.5%. Another year the index falls 5% and the fund is down 7%, but the next time the index falls 5%, the fund only falls 4.8%.

In that 'bad tracker' situation, sounds like the manager's computers aren't working very well...

-Maybe they cut corners and only track some of the most liquid stocks and several of the others they don't bother with in the hope that returns will not be affected too much.
-Maybe they take the hands off the steering wheel too long and redeem out of some holdings disproportionately when paying out their exiting investors, planning to buy back into those holdings before it makes a material difference, but then the expected new investors don't materialise.
-Maybe they don't reinvest the dividend income efficiently.
-Maybe they use some derivatives to replicate a portion of the index, but the derivative is expensive or a counterparty goes bust.

All of these things could lead to a big 'tracking error' where the expected 'index less 0.1%' is sometimes 'index less 0.5% and sometimes 'index less 1%' and sometimes 'index plus 0.5%'. The standard deviation of the differences between the index and the fund, is your 'tracking error'. But if there is NO deviation in the difference between the index and the fund, because the difference between the index and the fund is always 0.1% per annum at all times over all market directions, then there is NO tracking error.

So, when you are looking to select a tracker you need to consider two things.

Firstly, the tracking error. Does it slavishly follow the index (given the expected, broadly fixed, offset) or do its returns bobble around all over the place, sometimes ahead of the index, sometimes behind the index etc etc.? If there is a large tracking error perhaps it will not meet your needs and fit into your portfolio plan properly.

Secondly, what are its running costs like? Does it have a high management fee / OCF / TER? Is it growing rapidly meaning it has a lot of new money to deploy and lots of dealing costs and stamp duties on top of its normal operating costs? Or does the state of the market or its relative competitiveness mean investors are leaving, its NAV is shrinking, meaning that certain fixed costs of operations have to get split over a smaller fund size and increase the cost per unit and implicitly worsen its performance?

Bottom line, a fund's "tracking error" - the accuracy or inaccuracy of the fund's attempt to mirror an index return for good or bad in all market conditions - is a different concept to what that fund actually costs you to access.

However, some investors try to lump it all into one concept, and compare the gross return of the index with the net return of the fund, and say any underperformance must be down to an error in tracking the index and the whole lot should be termed 'tracking error'. That is NOT the classic meaning of the term. You have good and bad attempts to track the index and you have high and low fees. You should aim to find one that makes a good attempt (does not miss out on any components of the index's annual return), and does not have a high fee, but they are two separate concepts that contribute to the overall success of your portfolio.

A brief wiki page also summarises the classic definition of tracking error: http://en.wikipedia.org/wiki/Tracking_error
It makes the point, as you did, that if you have the same 'active' difference from the index at all times, you have a tracking error of zero because the standard deviation is zero, but of course your fund is getting further away from the index over time.

So, you don't want the offset to the actual index return to be a large offset - a percent a year will compound up to a large percentage over time. But you *do* want to aim for a standard deviation of zero if you can, because that would be an accurate tracker and you could reliably know that performance factors driving the index were also driving your fund performance in the same proportions.

The prospectus also says that the "ex-post tracking error is expected to be..." which is a bit of nonsense as far as I can tell. You can't expect ex-post, can you?

By ex-post they mean viewed /calculated after the fact, based on knowledge of the past. A measure of past performance that they are using as a yardstick to manage your expectations.

As opposed to ex-ante, a looking-forward view of what could happen, used by fund managers in building risk and performance models etc (also mentioned briefly on the wiki page above)

bowlhead99

puk999 wrote: »

Just want to make sure I understand. Are you saying that the reported fund performances figures are after fees have been paid to the manager, etc? I understand the bit about platform fees being completely separate.

Is it always the case that performance figures are shown net (i.e. part of regulation)?

Just to clarify... YES, reported fund performance figures are always after management fees.

The NAV per share or per unit declared at a point in time has already taken into account the management fees and other expenses up to that point in time - whether those fees were physically paid in cash already or are simply owed to the manager and planned to be paid over at the end of the week or month or quarter.

guymo

bowlhead99 wrote: »

By ex-post they mean viewed /calculated after the fact, based on knowledge of the past. A measure of past performance that they are using as a yardstick to manage your expectations.

As opposed to ex-ante, a looking-forward view of what could happen, used by fund managers in building risk and performance models etc (also mentioned briefly on the wiki page above)

I know. That's why it doesn't make sense to say "the ex-post error is expected to be…" From where does that expectation come? It must come from modelling and/or guesswork. So it's actually the ex-ante error.

bowlhead99

Maybe I mis-explained myself /them.

When you observe the results and derive the tracking error standard deviation, from the actual historical data received over the fund's lifetime, and you write down that figure, what you have calculated and written down is an ex-post measure of tracking error. That is necessarily the case because how you got to the number was by reviewing actual events after the fact, correct?

So you will derive the measure by observation of historic data and you will be referring to it as your ex post tracking error.

The company is saying that when you calculate that TESD (your ex post calculation and derivation coming from the review of actual data) and write it down, they expect that (based on their experience and an assumption that market conditions are not extraordinary) the number you wrote down will likely be less than about 0.2%.

So, the ex post measure is likely to be measuring 0.2% or less, when you measure it. Their expectation of an ex-post measure is that it will stay within 0.2% over the time period you're reviewing it. It is not a logical fallacy

Quite separately, fund managers can create a whole variety of ex ante methods and models of predicting tracking error. Usually these are based on choosing a set of suitable explanatory variables or risk factors used to form predictions. The ex ante projections of tracking error are what they use to decide when and how to trade to maintain the portfolio to best effect. They would hope that the internal models of ex ante tracking error will be a good actual predictor of ex post tracking error, but it could actually look quite different depending on the selection of the risk factors, measurement time interval and model specification.

Amusingly, creating an extremely good model of ex ante (predictive) tracking error and using it to adjust and manage the portfolio at all times, means that you might never observe same tracking error on an ex post basis. I digress.

Long story short and direct latin semantics aside: ex ante tracking error, in the industry jargon, refers to a model of predicting tracking error that fund managers use to help them look after the portfolio. While ex post tracking error is what investors experience when they look at the returns of the fund and the index that were achieved and wonder how they correlate. So once you've seen a few references to the topic written by fund managers, you'll "get" why it's completely normal for them to say that the ex post tracking error standard deviation should hopefully be 0.2% or less.

guymo

Bowlhead,

I feel a bit bad for having caused all that typing. I do understand the concepts and the overoperationalisation of them in the finance industry. As you succinctly say in your last paragraph, what's going on is that the finance industry has said "values coming from these kinds of models we call ex-ante, and these other kinds of forecasts we call expectations of ex-post." From a philosophical point of view that is nonsense.

I am pretty sure that you appreciate what I mean and I hope you can believe that I appreciate your exposition of the industry version of terminology too.

Isn't ex-ante just another word for your father's sister who sadly died?

puk999

Thanks to all who responded on this. I went a little quiet towards the end as it got a bit technical for me. I am learning more and more so will understand it one day.

bowlhead99 wrote: »

According to their prospectus they expect the tracking error (standard deviation) to now be kept within about 0.2% a year. And so perhaps after a couple of years, with a slightly bigger fee at the start, perhaps lagging the index by half a percent life to date is OK - there will, after all, be some costs other than those captured by AMC/TER and they are not claiming zero tracking error... However, the shortfall according to Morningstar chart is 0.7% and has sometimes been more.

One explanation for this is that the fund is priced at midday UK time each day, while the index data is from "when global markets close each day". End of day U.S. time is some 8 business hours later.

I received a very glossy Interim Short Report from Fidelity in the post today the PDF of which is here. On Page 50 (PDF page 52) it says:

The fund aims to achieve long term capital growth by closely matching the
performance of the MSCI World Index (Net). Therefore, the return of the fund
and the index should be similar over time, before costs. However, the fund is
priced at midday, whereas the index is priced based on global stock market
closing prices. This timing difference can cause positive or negative variations
in apparent relative returns and increase the reported tracking error of the
fund. By revaluing the P accumulation shares of the fund at global market close
and comparing this return of 7.98% to the return of the index over the period,
the difference in performance amounts to 0.40%. Ordinarily, this difference is
expected to be negative and mainly explained by this class’ ongoing charges
and transaction costs. Taxation may be a positive source of tracking difference
where the fund’s withholding tax treatment is more favourable versus the net
index. Gains or losses may also be made from currency exchange rates. The
fund belongs to a group known as “passive” or “index tracker” funds, whereby
the portfolio holds securities that are representative of the index. This fund is
constructed to efficiently replicate the characteristics of the index, but may not
hold all the company shares in the index or hold those shares in exactly the
same weightings. The costs and expenses that the fund incurs means returns
may not exactly match the index performance. Please note, the fund’s cash
position does not mean that it is under exposed to the index, as any cash
balance is typically equitised with equity index futures contracts. This helps to
efficiently manage cashflows in the fund at reduced costs. When taking into
account exposure achieved by these futures contracts the fund’s sector and top
holdings weights more closely match the index.

Confirmation that the midday pricing vs global market close is the main issue in the performance numbers not simply being -TER.

EDIT: Rereading your messages I see you already found them mentioning the valuation timing in the prospectus which I didn't even think of looking at. Sorry for being a bit sloppy in all of this.

bowlhead99

puk999 wrote: »

Confirmation that the midday pricing vs global market close is the main issue in the performance numbers not simply being -TER.

EDIT: Rereading your messages I see you already found them mentioning the valuation timing in the prospectus which I didn't even think of looking at. Sorry for being a bit sloppy in all of this.

Yeah, mentioned that back up in post #22...

No shame in not seeing it though. Usually my actual answers are preceded and followed by a load of waffle which is only tangentially relevant to the question at hand... And would you believe it's mostly written on a smartphone, which explains most the typos and bizarrely ordered paragraph that could have been better planned out... Thanks Android developers for inventing Swype rather than "tap one letter at a time", otherwise I'd have to be a lot more concise