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A regular savings puzzle

When you save regularly your returns are often very different to the average return on your fund over time
October 2, 2014

How can 7 per cent a year fund growth deliver more than 12 per cent a year to savers?

And how can 7 per cent a year fund growth deliver less than 2 per cent a year at other times?

This fascinating puzzle - which applies only to regular savings - confuses most investors, and it's not well understood by all the experts, either.

Indeed, some financial advisers only promote the upside to this puzzle (the first example above), so it's an important concept to understand.

Let's start by thinking about the return we receive when we invest a lump sum of money into a fund.

In this case, our return will simply be the same as the total fund return - after charges and tax.

However, when we save regularly (monthly or annually, for example) our returns could be very different to the average return on our fund over time.

 

Let's take a simple example.

■ Say we make just three regular investments of £1,000 into a fund.

■ The first is made now, and let's say that the fund's unit price stands at £1. So we buy 1,000 units in the fund (£1,000 divided by £1 per unit).

■ The second investment is made one year later when, let's say, the unit price has fallen by 50 per cent to 50p. So now our £1,000 second payment buys 2,000 units.

■ Then our final payment is made one year later when, let's say, the unit price has recovered back to £1. So we buy another 1,000 units in the fund.

■ We now have 4,000 units (1,000 + 2,000 + 1,000), each valued at £1, giving a total of £4,000.

■ But remember that we only invested £3,000 in total (three lots of £1,000), so we've made a profit of £1,000 despite the fact that the fund has not grown over the period. The unit cost started and finished at £1.

 

That's incredible, eh?

Yes, we have a greatly enhanced return because the price drop in the second year meant we bought a lot more units at that time.

Now, this magical property of regular investments is commonly called 'pound cost averaging' (or 'dollar cost averaging', as they say in the US).

But before we get too excited about it, or get taken in by advisers who do so, we need to understand what would happen if the price of our fund had gone in the other direction.

What if, instead of falling, the fund price grew in the first year - from £1 to £2, before falling back to £1?

In this case we'd be less pleased with the returns. Let's see why.

 

Our regular investments of £1,000 would have bought:

■ 1,000 units @ £1 per unit, and then

■ 500 units @ £2 per unit, and then

■ 1,000 units at £1 per unit

So this time we end up with 2,500 units, which, at £1 per unit, is just £2,500.

And that's less than the £3,000 we've paid in.... Oh dear!

 

To summarise, the final value of a regular savings plan is fund price path dependent.

Or, if you prefer plain English, the final value of a regular savings plan will depend on how the fund price travels up and down over time.

The result is that returns will be:

■ fantastic, if prices fall heavily (or stay flat) at the beginning of our savings period before rising steeply in the later years, or

■ disappointing, if prices shoot up initially and then level off or fall later on.

Of course, if fund prices follow a path between these two extremes, then the outcome will also be something in between.

 

When 7 per cent a year becomes 12 per cent a year

Having grasped the concept with this three-year savings example, we can extend the term of the investment and explore other shapes of price movement to see the impact on our returns.

The charts below explore the very different returns that might arise from a regular savings plan over a 10-year period, depending on the fund price path.

Notice that in all cases, the fund price doubles, from £1 to £2, over the term.

This is equivalent to an average compound rate of return of just over 7 per cent a year.

■ The solid lines show the path that the fund price would have taken if it had progressed smoothly from £1 to £2 over the period.

■ The heavy dashed lines show the very different paths that the fund price could take to reach that £2 final price. In figure 1, the price is flat for nine years and then jumps up to £2. In figure 2, the price jumps up to £2 in the first year and then remains flat.

■ The dotted lines represent the equivalent (smoothed) rate of return that we'd need to earn (in, say, a bank account) in order to build the same final fund as we'd achieve if the fund price followed the heavy dashed line.

Now, I've crunched the numbers on these different scenarios, and what we find is that, if our fund price followed the path:

■ In Figure 1, we'd achieve the equivalent of more than 12 per cent a year on our regular savings. This is because all 10 of our investments (from time (t) = 0 to t = 9) are made at a fund price of £1, and then the whole amount doubles in value in the 10th and final year.

 

■ In Figure 2, we'd achieve the equivalent of less than 2 per cent a year on our regular savings. This is because only our first regular investment enjoys a doubling in value while our next nine investments achieve no growth at all - they're all made when the fund price is at £2.

Of course, we wouldn't expect a real fund price to follow either of these paths. I've just used these as extreme examples to demonstrate the point.

I'd suggest that fund price movements something like those below are much more likely in the real world.

You can see that the fund price path in Figure 3 is initially below the trend line and then catches up later on. This enhances our returns.

The fund price path in Figure 4 runs up ahead of the trend initially and then cools down - and this drags down our returns.

There is, however, no certainty of getting 7 per cent a year fund growth - or any other number over any period by whatever path.

Investment is about accepting some uncertainty in our fund values, in exchange for potentially higher returns.

The thing to remember about a regular (stock market-based) savings plan, is that the annual average return we experience on our funds will not be the same as the average return on the funds in which we invest.

It could be a lot higher or lower depending on the price path of the fund.

Paul Claireaux is the author of Who Can You Trust About Money?, a book that cuts through the usual financial jargon to explain the big issues of money management.