Good reads from around the Web.

The clever bods at The Value Perspective have been doing a sterling job recently in tackling the weird world of the average and what it means for returns.

From writing here on Monevator, I know a lot of people get confused when it comes to how average returns work in practice – or more specifically about the different kinds of average – and what it implies for our investment decisions, whether it’s asset allocation or investing a lump sum or confronting sequence of returns risk.

And when I say “a lot of people get confused”, I’ll admit that can include me!

So most people could do with a refresher on the maths.

Start with this Value Perspective article on the law of averages, which begins:

Let’s play a game we will call ‘Russian dice’, the rules of which were invented by a physicist/economist called Ole Peters. They are pretty simple – roll a dice and, if it comes up ‘one’, I will shoot you.

Do you fancy playing? It does not sound very appealing but, if you were a nihilistic mathematician, you might be tempted because – in the very strictest terms – on average you will be absolutely fine.

The word ‘average’, however, can be somewhat misleading if not defined very precisely. If 100 people roll the dice instantaneously, the average result is ‘three and a half’ – that is, (1 + 2 + 3 + 4 + 5 + 6) ÷ 6 – so, if you are judging the game on the average result, everyone survives.

However, if I asked you to roll the dice 100 times in a row, it is extremely unlikely you could do so without at some point seeing a ‘one’ come up. Bang. You do not get a chance to see the result of the 100-roll average over time.

Intuitively, we all know there is a difference between these scenarios without any complicated maths or concepts. Mathematically speaking, it is known as the difference between an ‘ensemble average’ (the average of an event happening many times concurrently) and a ‘time average’ (what happens when you do something a lot of times consecutively).

However, this concept and its implications are not well understood in investment.

After that first article provoked a fair bit of debate and confusion, their follow-up tried to explain it with a diagram:

[This time] you simply start off with a stake of, say, £100 in the pot and we toss a coin. Every time the coin comes up heads, you increase what is in the pot by 50%; every time it comes up tails, you lose 40% of whatever is in the pot.

The coin is a fair one – so it is always a straight 50/50 chance – and there is not a firearm in sight.

Would you like to play?

At first sight, there appears to be no reason not to play – after all, if on each coin toss the only two possibilities are going up 50% or falling 40%, then surely, on average, it is a winning game. And indeed it is. No matter how long you play it for, on average, the expected return is positive – but, as we argued in the previous article, the word ‘average’, if not defined very precisely, can be misleading.

In this particular example, the average obscures a pattern where the majority of people who play the game actually end up losing.

Here’s the pattern:

It reveals:

In the above example, 11 of the 16 possible sequences of coin tosses are losing permutations and, the longer the game goes on, the more money is lost.

In a game where the only possible outcome each time is a 50% upside or a 40% downside, that would appear counter-intuitive so what is complicating matters?

It is that difference between time and ensemble averages.

Read the whole article for a deeper explanation.

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Some critics of passive investing say there’s “no such thing” as truly passive investing. They point out that even an investor who only uses index tracker funds has to decide:

• How to split their money across the various asset classes.

•  Which indices / trackers are the best in each class.

• How and when to rebalance their portfolios.

• Which platform to opt for, and whether to use ISAs, SIPPS, or both.

• What to buy the in-laws for Christmas.

That’s all true enough (especially the last one).

After all, Monevator is a site mostly about unwrapping the mysteries of passive investing. If such investing was utterly without nuance, we could have saved ourselves 1,000-odd articles over the past seven years!

But so what?

For every decision you need to make as a passive investor, someone else is making dozens if not hundreds as an active investor – almost by definition.

An active investor complaining that passive investing involves a lot of tricky decisions is like an air traffic controller being befuddled by a zebra crossing.

Moreover passive investing can be as complex or as simple as you want it to be.

My standard advice to new investors has long been to put half their monthly savings into a high interest savings account and to invest the other half into a broad index tracker fund. Do that in an ISA or SIPP, repeat for 30 years, evolve as you learn more, and I’m confident you’ll get a good result.

You could even use a Vanguard LifeStrategy fund and skip the cash bit.

Is it the perfect passive strategy? Probably not, but it’s super easy-to-implement, logic is on its side, and it’s inordinately easier than implementing an active strategy over 30 years – never mind actually beating the market by doing so.

Market cap trackers are just fine

That’s all a long-winded way of saying that straying from a bog-standard basket of market cap weighted index tracker funds is decidedly optional.

Indeed, our current view around here is that there’s no magic in Smart Beta or equal-weighted indices. You’re simply taking on more risk for hopefully more reward, and in most cases you’ll also face a headwind of higher costs for doing so.

And while we’re all for considering tilting your portfolio towards value shares or small caps, we’ve stressed such factor bets are no slam dunk to outperformance.

As such, they can safely be left in the ‘too hard’ pile if you want without any danger or feelings of foolishness.

You see, even the experts don’t agree about these issues, as this latest video from Sensible Investing reveals:

As the Nobel Prize-winning economist Professor Eugene Fama says:

“The overall cap-weight market portfolio – including everything, not just stocks – model is always a legitimate portfolio.

In any asset-pricing model it’s always one of the so-called efficient portfolios.

But if you take, for example, our work seriously, what it says is there are multiple dimensions of risk and you can tilt towards these dimensions, so you can move away from the market portfolio towards these dimensions.”

In other words, start with the simplest, broadest vanilla trackers, and then research and invest where your passion takes you – and if that’s to the conclusion that simple is best after all, then that is absolutely a-okay.

Check out the rest of the videos in this series so far.

The Slow and Steady portfolio is back with another update! And this quarter’s progress has been both slow and steady.

We’ve inched forward another 2% over the last few months – Europe and UK equities holding us down like concrete boots, while the US stock market and Government bonds have been our buoyancy aids.

The Slow and Steady portfolio is Monevator’s model passive investing portfolio. It was set up at the start of 2011 with £3,000. An extra £850 ¹ is invested every quarter into a diversified set of index funds, heavily tilted towards equities.

You can read the origin story and catch up on all the previous passive portfolio posts here.

In terms of raw numbers, our portfolio has made just over £300 since our last Slow and Steady portfolio update. We’re now up over 20% overall, with an annualised return of 6.7%.

Here’s the portfolio lowdown in spreadsheet-o-vision:

The inevitable correction

The galloping bull market of the last five years is naturally causing a lot of jitters.

• Is our luck about to run out?

• Should we assume crash positions?

• If global markets are overvalued is it time to stop investing in equities?

Much of the nervousness stems from the seemingly universal law that what goes up must come down. The question is when?

For a scientific-sounding answer, many pundits reach for valuation measures like the P/E ratio and CAPE. If CAPE is any guide then the US is more than 50% overvalued right now.

But is CAPE any guide? A Vanguard study found that CAPE has previously only explained 40% of the variance in future returns over 10 years.

Now, 40% is pretty stellar in comparison to other metrics Vanguard looked at, but it still leaves us with more unknowns than Donald Rumsfeld.

Meanwhile, CAPE’s predictive power over the course of one year plunges to less than 10%.

According to financial researcher Michael Kitces, CAPE’s peak correlation with real returns occurs over an 18-year horizon.

That’s no basis at all for deciding to abandon your asset allocation.

Steady on

The desire to do something is driven by our human instinct to control the uncontrollable. But believing we can predict the future is an illusion. Any change we make could damage our prospects as much as help. It’s a crap shoot.

Remember, as ordinary Joes and Josephines, we have no information that is not available to every other investor in the world.

High valuation levels, the end of QE, geopolitical strife – it’s all on everybody’s TV screen.

What drives the market’s next move will be new information as yet unknown. We won’t be the first responders, so far better to stick to the plan and rely on long-term growth to lift us clear of short-term difficulties.

Consider too that the UK doesn’t look overvalued according to CAPE, and nor does most of the rest of the world.

The US accounts for 25% of the Slow and Steady portfolio. Even a nightmare 50% plummet in the US would only knock us back 12.5%.

Obviously nothing happens in isolation, but the point is this is a diversified portfolio that doesn’t stand or fall purely on the fortunes of one market.

Furthermore we already have an inbuilt mechanism to take the edge off overheating markets.

It’s called rebalancing.

Incoming

Enough of the mental anguish, let’s get on with counting the spoils.

The British Government paid £21.93 interest into our bond fund last quarter. More loose change than life-changing.

Rather than blow it on pies, we’re automatically reinvesting our windfall using an accumulation fund.

New transactions

Every quarter we propel another £850 ² into the financial cosmos – hoping that one day our little pound probes will take us to a new world where the rat race does not exist.

We use Larry Swedroe’s 5/25 rule to trigger rebalancing moves. We haven’t breached any of our thresholds this quarter, so there’s no need to trim any funds.

All that remains then is to split our cash in line with our asset allocation strategy:

UK equity

Vanguard FTSE U.K. Equity Index Fund – OCF 0.08%
Fund identifier: GB00B59G4893

New purchase: £127.50
Buy 0.66 units @ £192.64

Target allocation: 15%

Developed World ex UK equities

Split between four funds covering North America, Europe, the developed Pacific and Japan ³.

Target allocation (across the following four funds): 49%

North American equities

BlackRock US Equity Tracker Fund D – OCF 0.17%
Fund identifier: GB00B5VRGY09

New purchase: £212.50
Buy 146.45 units @ £1.45

Target allocation: 25%

European equities excluding UK

BlackRock Continental European Equity Tracker Fund D – OCF 0.18%
Fund identifier: GB00B83MH186

New purchase: £102
Buy 62.73 units @ £1.63

Target allocation: 12%

Japanese equities

BlackRock Japan Equity Tracker Fund D – OCF 0.17%
Fund identifier: GB00B6QQ9X96

New purchase: £51
Buy 38.84 units @ £1.31

Target allocation: 6%

Pacific equities excluding Japan

BlackRock Pacific ex Japan Equity Tracker Fund D – OCF 0.19%
Fund identifier: GB00B849FB47

New purchase: £51
Buy 23.63 units @ £2.15

Target allocation: 6%

Emerging market equities

BlackRock Emerging Markets Equity Tracker Fund D – OCF 0.26%
Fund identifier: GB00B84DY642

New purchase: £85
Buy 75.62 units @ £1.12

Target allocation: 10%

UK Gilts

Vanguard UK Government Bond Index – OCF 0.15%
Fund identifier: IE00B1S75374

New purchase: £221
Buy 1.63 units @ £135.67

Target allocation: 26%

New investment = £850

Trading cost = £0

Platform fee = 0.25% per annum

This model portfolio is notionally held with Charles Stanley Direct. You can use its monthly investment option to invest from £50 per fund. Just cancel the option after you’ve traded if you don’t want to make the same investment next month.

Take a look at our online broker table for other good platform options. Look at flat fee brokers if your portfolio is worth substantially more than £20,000.

Average portfolio OCF = 0.16%

If all this seems too much like hard work then you can instead buy a diversified portfolio using an all-in-one fund such as Vanguard’s LifeStrategy series.

Also note, there are currently cheaper, similar index trackers that can be used to build this portfolio. The existing Slow & Steady funds are competitive enough that it’s not worthwhile switching immediately. We can afford to wait for the competition to settle down.

If you’re a new investor, though, then do compare the Vanguard and Fidelity index fund range against the BlackRock components.

Take it steady,

The Accumulator

1. The Slow & Steady portfolio is virtual. It’s a model portfolio designed for discussion and to show how a passive portfolio might operate and perform on a small scale.[↩]
2. The Slow & Steady portfolio is virtual. It’s a model portfolio designed for discussion and to show how a passive portfolio might operate and perform on a small scale.[↩]
3. You can simplify the portfolio by choosing the do-it-all Vanguard FTSE Developed World Ex-UK Equity index fund instead of the four separates.[↩]