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It’s not fair! Sequence of returns risk

With the mindset of a long-term [1] investor, you avoid a lot of the worries that afflict the frightened hordes.

You’re not scared out by a stock market crash. Nor do you pile in at the top.

Instead you develop the tough-under-fire attitude of a Vietnam veteran on his third tour of duty. When share prices plummet you go surfing, Apocalypse Now-style, while others quiver before CNBC.

“Is that all you’ve got?” you laugh as the stock market falls 10%.

The average after-inflation annual return [2] from shares globally is 5% per year1 [3]. So as long as you sit tight and keep the faith, you’ll eventually be rewarded, right?

Well… yes, probably…2 [4]

The sequence of returns matters

You’d better know that there’s another kind of risk [5] you need to think about, and it’s potentially nasty.

It’s this: The return you get in your investing career might be different to the return I get – even if we both enjoy the same average 5% real return over three decades on our investments!


I know – it’s counter-intuitive.

It also has a clumsy name. It’s called the sequence of returns risk.

The sequence of returns risk is essentially the risk that fate will deal you a shocking hand – that the timing of bear markets [6] and bull markets will fall less favourably for you than it does for another investor.

It’s why we’re urged to reduce our exposure [7] to the riskiest assets as we approach retirement age.

It’s also why a decade of steep stock market falls could bode well for younger investors who have saved throughout the turmoil.

The best time to get bad hands when you’re regularly putting money into shares is when you’re starting out – because you learn your lessons early, and you’ve got less money to lose.

In contrast, the last thing you would want the day before you retire is to have all your lifetime savings in shares, only for the market to get sliced in half.

How to multiply your money

You might not think it matters what order the market tosses up its treats and its treacherous years.

Returns from investment are multiplicative – you multiply your money!

And every precocious child knows that it doesn’t matter what order you multiply numbers together. You still get the same result.

For example:

1 x 2 x 3 x 4 = 24

4 x 3 x 2 x 1 = 24

3 x 4 x 1 x 2 = 24

It’s exactly the same with investing.

When the market delivers a 20% return, it goes up 1.2 times.

When the market falls 10%, you multiply it by 0.9 times.

1.2 x 0.9 = 1.08

0.9 x 1.2 = 1.08

So why does it matter to us poor strivers exactly when the sturm und drang of a stock market crash hits us?

Well it wouldn’t if you were a member of the landed aristocracy [8] and you were just managing a big pile of loot before passing it onto the next generation (after six or seven decades of compounding and an unsavoury sex scandal or two).

But most of us are investing new money over our lifetimes to ensure our financial futures – and we also have to withdraw our savings in retirement.

And it’s because we add and subtract money from the market over time that the sequence of returns risk can have its wicked way with us.

Here’s one we did earlier

Let’s consider a real world example. Here are the total returns from the FTSE 100 for the five years from 2008 to 2012:

Year Return
2008 -28.3%
2009 27.3%
2010 12.6%
2011 -2.2%
2012 10.0%

Source: FTSE [9]

Do the sums and you’ll see that’s an average annual return of 3.9% per year.

Now let’s imagine you had invested £100 at the start of 2008. Here’s where your money would have stood at the end of each year:

 Year Return Investment
2008 -28.3% £71.70
2009 27.3% £91.27
2010 12.6% £102.77
2011 -2.2% £100.51
2012 10.0% £110.56

Note: £100 compounded for five years, as per the returns listed.

The first thing to note is that you’ve ended up with less than you might have expected from the 3.9% average annual return.

Plug 3.9% into a compound interest calculator [10] and you’ll see you might have anticipated £121. You got £10 less.

This is because investment returns are geometric, rather than arithmetic [11]. But that’s another article…

Investing in Bizarro World

Getting back to the sequence of returns, let’s imagine you fell through a wormhole and ended up in an alternative reality, and five years in the past.

(Stay with me here!)

Being a good saver, you shrug off your trip through space and time and make your way to the nearest stockbroker. People still need to save and invest for their retirement it turns out, even in this Bizarro World [12].

But things aren’t entirely the same.

In this alternative reality, the annual returns you get over the five years from 2008 to 2012 are reversed as follows:

Year Return
2008 10%
2009 -2.2%
2010 12.6%
2011 27.3%
2012 -28.3%

Source: Bizarro World Bank Headquarters broom closet.

This time the big crash comes at the end of the five-year sequence, rather than at the start as it did for us in our reality.

Do the maths and you’ll see you get the same average 3.9% return.

But what about your £100 investment?

Year Return Investment
2008 10.0% £110.00
2009 -2.2% £107.58
2010 12.6% £121.14
2011 27.3% £154.20
2012 -28.3% £110.56

Note: £100 compounded for five years on Bizarro World.

As we expected, because returns are multiplicative, we end up with exactly the same £110.56 in Bizarro World as we got on Planet Earth – even though the sequence of returns is reversed.

So far so good!

Adding up the cost of bad luck

The complication comes if you are saving or taking money from your investment over the years.

Let’s say you add £20 at the end of each year to your ongoing investment.

In our reality on Planet Earth, this would have played out as follows:

Year Return Investment
2008 -28.3% £91.70
2009 27.3% £136.73
2010 12.6% £173.96
2011 -2.2% £190.14
2012 10.0% £229.15

Note: £100 initially invested, then £20 added at the end of each year.

What about in the alternate reality, where the sequence of returns was reversed?

Here you’d end up with a different result:

Year Return Investment
2008 10.0% £130.00
2009 -2.2% £147.14
2010 12.6% £185.68
2011 27.3% £256.37
2012 -28.3% £203.82

Note: Again, £100 in, then £20 added each year. Alternative return sequence.

As you can see, falling through the trouser leg of time3 [13] has reduced your final sum by around 10%.

Now I don’t know how much things cost in Bizarro World, but I’m sure you’d rather have that extra spending money.

More seriously, this is exactly what happens in real life to different investors with slightly different saving schedules. The sequence of returns varies over time, and so two regular savers with the same general strategy [14] but investing over different periods will see different sums accumulated by the end, even if they enjoy the same average annual return.

People who retired in the late 1990s as the stock market soared were laughing.

People who retired in 2003 after several steep market declines?

Not so much.

The science bit: As well as the multiplication, we now have addition in our sums. So the order now matters.

Withdrawal symptoms

More scarily, the same thing happens when you’re withdrawing money.

I say “more scarily” because there’s not much you can do about your savings once you’ve stopped earning.

At least if you’re dealt a rubbish hand while you’re still accumulating money, you can try to find more cash to invest before you retire. You might even enjoy a market rebound on the extra cash you put in.

Once you’re retired though, you’ve no choice but to spend less and cancel your subscription to Caravan Monthly.

Imagine you had £100,000 in 2008. For the sake of this example let’s say you kept it all in the stock market, and you withdrew £4,000 a year.

In the table that follows the third column shows how £100,000 would fare if you kept all your money invested. The fourth column shows the impact of withdrawing £4,000 at the end of each year:

Year Return Hands off With withdrawal
2008 -28.3% £71,700 £67,700
2009 27.3% £91,274 £82,182
2010 12.6% £102,775 £88,537
2011 -2.2% £100,514 £82,589
2012 10.0% £110,564 £86,848

Note: £100,000 in with no withdrawals, versus £4,000 taken out each year.

It’s no great surprise to see that taking £4,000 out a year reduces how much money you’re left with at the end.

But let’s now shift our telescope to Bizarro World, to see how its alternative sequence of returns plays out with the same £4,000 withdrawal rate:

Year Return Hands off With withdrawal
2008 10.0% £110,000 £106,000
2009 -2.2% £107,580 £99,668
2010 12.6% £121,135 £108,226
2011 27.3% £154,205 £133,771
2012 -28.3% £110,564 £91,914

Note: Alternate sequence for retirement assets on Bizarro World.

As we saw a few months ago when I began this article with the £100 example, with no withdrawals, the ‘hands off’ pot of £100,000 compounds [15] to the same £110,564 in both sequences of returns.

However in Bizarro World with £4,000 per year withdrawals, the sequence of returns turns out to be more favourable for the retiree. She has £5,000 or so extra in her pot in 2012 than the same investor on Planet Earth.

Interestingly, this is the opposite of what we saw with regular savers on Bizarro World earlier on in this article. They did did worse over the five-year period than we did.

But let’s not get too hung up on these specific numbers.

The point is that the sequence of returns can make a difference to how your retirement plays out. Neither you nor I know exactly what those returns will be.

Don’t risk doing badly

Can you do anything to sidestep the sequence of returns risk?

Not a lot. Its impact is mainly down to luck.

You might try to guess if various markets are cheap [16] and to shift your investments accordingly, but many – probably most – people will do worse using such active strategies than if they had just saved and rebalanced automatically.

I think the main response to sequence of returns risk should be:

All investing involves risk [19]. By diversifying your portfolio and playing a bit safer, you can try to reduce the role of luck, and to increase the odds of your plan working out.

Next week I’ll explain why elaborate strategies probably won’t help you much when it comes to sequence of returns risk. Subscribe to ensure you get it!

  1. Source: Credit Suisse Global Yearbook 2013 [ [22]]
  2. As always it’s worth remembering a handful of markets, such as pre-communist Russia, have been completely wiped out. Never put all your eggs in one basket! [ [23]]
  3. With apologies to author Terry Pratchett. [ [24]]