Mind Games: Pound Cost Averaging

Published in Investing Strategy on 15 June 2009

Pound Cost Averaging sounds appealing but rarely works in practice.

Pound Cost Averaging (PCA) means investing a fixed amount at fixed intervals of time. That's eminently sensible, if it means committing yourself to investing a fixed amount of your salary every month toward your retirement.

However, some people also think you should pound cost (or drip feed) a lump sum over a period of months. For example, if you had £12,000 that you wanted to invest in equities, they would tell you to invest £1,000 per month over a year, rather than investing the whole amount immediately.

Assuming your objective is to maximise gains for a given level of risk PCA is not a particularly sensible investment strategy. Put simply, there are better ways to invest.

Discredited by academic research

For forty years academic research has consistently shown that PCA doesn't provide returns above other strategies. The most cogent argument was given by George Constantinides, 30 years ago, in a catchy little paper called "A Note on the Suboptimality of Dollar-Cost Averaging". All available evidence supported the assertion that, "Replacing one major gamble on a temporary shift of prices by a number of smaller gambles" doesn't necessarily work.

More recently, in February this year, advisor Michael Edesess ran an analysis on 83 years of stock market returns. His finding was that investing a lump sum, on average, beat PCA by over 3 percentage points per year for one-, three- and five-year rolling periods.

Although PCA achieves lower returns, on average, than other strategies the research does show that it achieves this with lower volatility or risk. But this demonstrates nothing more than the obvious: to achieve higher returns you must accept higher risk. If you want to achieve lower risk, you can better achieve this by holding more bonds, or cash. And, in any case, why invest monthly? Why not quarterly, annually, weekly -- or plain randomly?

But Pound Cost Averaging remains fashionable

PCA is often recommended to lower risk investors with a lump sum. The easiest way to see why is to look at a simple example.

Suppose you have £2,000 to invest over four months (£500 per month).

  • Month 1: Price £20, buy 25 shares
  • Month 2: Price £10, buy 50 shares
  • Month 3: Price £8, buy 62.5 shares
  • Month 4: Price £20, buy 25 shares.

You have acquired 162.5 shares for £2,000, an average price of £12.31 (2,000/162.5). 

However, the average share price over the four months was £14.50, being (20+10+8+20)/4. And your investment is worth £3,250 (162.5x20). 

This apparent mathematical marvel achieves at least four psychological benefits that make it an easy (and in my view lazy) sell:

1. It avoids "regret", that the price declines 50% in the second month. In fact we are now "delighted" because we are buying more shares.

2. It confirms we were very "clever" to phase our investment and not buy at the market "top"

3. It satisfies our deep seated need to avoid loss. And our fear of loss is twice as great as our hope for gain

4. In an instinctive way it seems more "prudent" to spread an investment over months than take a "gamble" on a large one-off investment.

But, and it's a big but, there are three important reservations we should have about the sales pitch.

1. The sequence of prices is usually presented as in my example. But that sequence is not necessarily a valid, or even representative, trend. In fact the trend I have used is highly unlikely.

2. It is not logical. The only point in adopting PCA is because there is an implicit expectation of a fall in prices. If this is the case why invest in month one at all. Why not wait for a price decline before the first investment?

3. It is simply not the best strategy, in investment jargon it is sub-optimal. If you believe (as a PCA investor must) that it is a "good thing" to buy more shares when prices are low, why not invest more than an equal amount in each month of lower prices?

That third point highlights the critical weakness of PCA as a strategy; it focuses on investment instalments and not portfolio value. Fortunately there is a technique called Value Averaging (VA) which can wean you off PCA and boost returns if you must insist on drip feeding a lump sum.

Use Value Averaging instead

A VA strategy would take as its start point the situation described above – the desire to invest £2,000 over several instalments. From there on it differs fundamentally. The PCA investor's objective is to simply invest £500 per month. For the VA investor the objective would be to buy shares such that the portfolio value increases by at least £500 per month. So, using the example above the schedule of purchases would be:

Pound Cost Averaging

MonthMarket priceInvestmentShares boughtPortfolio value
12050025500
21050050750
3850062.51,100
420500253,250
Total2,000162.53,250
Average price12.31  

 

Value Averaging

Total sharesPortfolio value b/fwdInvestmentShares boughtPortfolio value
0050025500
25250750751,000
10080070087.51,500
187.53,750502.53,800
Total 2,0001903,800
Average price10.53  

Because the VA investor is focused on increasing portfolio value, in the example above he is 'forced' to add 75 shares to his previous 25 to meet his valuation target of £1,000, when the price plummets. The PCA investor simply invests a further £500. The result is the value average investor buys more shares when they are cheap and less shares when they are expensive, and makes more money. That sounds a lot more sensible -- doesn't it.

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Comments

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johncolescarr 16 Jun 2009 , 12:50pm

Am I missing something here, or does this strategy not rely on predicting where the market is going over short term periods, the age old conundrum?

The statement "... buys more shares when they are cheap and less when they are expensive..." means they know (or rather have to guess) when the shares are at their lowest point and when they have reached their peak.

For the average investor, pound cost averaging is achieved more from circumstance rather than choice, it is simply because they get paid monthly and their budget allows a certain amount for investing.

I think the underlying message trying to be portrayed in this article is that timing of investments is just another permutation of the investment process. By investing in lump sums you have potential for greater growth and greater losses, whereas PCA has less potential for growth and less potential for loss.

One should choose an investment strategy that best suits their appetite for risk and how much control they wish to have over their investment decisions that ultimately relies on their knowledge of the stock market.

(Written by an investment newbie!)

87crashdummy 16 Jun 2009 , 12:58pm

Interesting article, of course assumming you have xxx to invest, and if you have the lump sum, you p would probably invest in some other medium.
Most average joe punters only have a few pounds to
drip feed into a portfolio, so for them this remains
a good option, besides i like the fun of trying to
put my money on a "share pick" every month!!
At least Tudor didnt bang on about the Champion Shares .....yawn ....
I use TMF sharebuilder which for poor punters is ideal!!!

Iniq 16 Jun 2009 , 2:14pm

The "value averaging" startegy is a delusion, because you cannot predict before you start how much money it will cost you overall. If the price fell every month, you would end up investing far more than your planned £20,000.

Pound cost averaging certainly works - do some simple arithmetic and you will find that if the price varies randomly but spends as much time below the starting price as it does above it, and ends up where it started, you will end up with more shares overall than if you had bought at the "average" price, which is the only fair comparison. And the more widely it fluctuates, the greater you will profit.

The only catch is that to realise your gain, the smart thing is to sell in stages also, but to sell a fixed number of shares (NOT a fixed monetary value) every month.

supersol42 16 Jun 2009 , 2:53pm

Pound cost averaging is for the long term. A year is far too short.

The example the article opens with, pension saving, is indeed a good use of pca. But so, for example, is saving to repay a mortgage.

Most people do not have lumps sums to invest; the vast majority drip feed over decades, out of hard earned income, even if it's "just for a rainy day".

gordonbanks42 16 Jun 2009 , 9:51pm

I have a problem with the headline "rarely works in practice" - as against the situation examined by the article itself, which is about how best to invest a lump sum.

Surely the vast majority of situations where PCA is used are where there is no option to invest a lump sum - the money is put in as it is earned. So how come these situations, where PCA must be admitted to work, are considered "rare"?

I would have thought that the scenario where PCA doesn't work that well - the investment of a lump sum - was the relatively rare case.

The "value averaging" approach illustrated as superior is really rather hard to execute for a lot of people. You'd have to be dealing in individual shares, ITs or ETFs to have enough certainty of price to be able to do it reliably.

Can you imagine the chaos that would ensue if people tried to do that kind of thing with a forward-priced AUT or OEIC?

Added to which, and probably the real crunch point, the monthly standing instruction "buy another £500" is just too convenient. I can't place a standing instruction to buy "enough to increase the value of my holding by £500" and I don't suppose anyone else can either.

So the only people who can do this in effect are those who deal in real time or near real-time.

And by the way, the article isn't really clear what is meant by "works". Does it mean "improves returns" or does it mean "reduces risk"? Reducing risk is a perfectly valid thing to want to do, and PCA certainly does that without too much opportunity cost to returns.

Iniq 17 Jun 2009 , 8:22am

Gordonbanks42 puts it very well. How on Earth can you give automatic investment instructions in the way advocated?

Even for lump sums, PCA "works" in the sense that, over any defined period, you are likely to end up better off if you "drip feed" the money in than if you invest it all at once.

Example, for those who still don't get it:
Month 1 price £10 invest £100 buy 100 shares total 100 shares
Month 2 price £5 invest £100 buy 200 shares total 300 shares
Month 3 price £15 invest £100 buy 66 shares total 366 shares
Month 4 price £10 invest £100 buy 100 shares total 466 shares

Starting, ending and average price of shares = £10, but you end up with 466 shares worth £466 for an investment of £400. Result!

Of course, you could have waited until the price was £5 and made all your investment then. That works really well if you can predict the future and believe in time travel. For normal people in the real world, even more lump sums, PCA works and the more widely the price fluctuates the more profitable it is.

PCA is NOT just a "risk reduction" strategy.

tigerroach 17 Jun 2009 , 9:02pm

If you've been value averaging for a while then the market crashes down you're going to have to commit a lot of cash to keep the strategy going - possibly not a bad strategy when in for the long-term but gotta have deep pockets. Of course if that's the case you've got a lot of cash in an easy access account which is perhaps not ideal.

spinquark 03 Sep 2011 , 1:34pm

As any Maths or Science student will point out, the missing thing here is any proper definition of the problem parameters and assumptions.

We presumably want to assume something like:

1. A rising share price trend over time at some average rate (7% per annum perhaps).

2. A random fluctuation about trend with some defined level of volatility or standard deviation.

3. Some investment horizon at which we plan to liquidate the investment (10 years perhaps).

4. The time over which the investment will be drip fed - (perhaps 12 months).

5. The initial conditions - i.e. whether we have any information as to whether the investment is above or below trend on day 0.

6. Some kind of risk/loss tolerance limit. i.e. What level of decline in value would cause the investor to panic sell (60% perhaps)

The maths could then be worked out perhaps statistically or more likely using Monte Carlo simulation.

Anyway the point is - different assumptions - different optimal strategy will apply. It is no way as trivial as the above makes it seem.

In the end you have to choose how to view the markets - as entirely random number streams with a rising trend - or as capable of being judged/timed in some way.

Imagine buying bank shares in the collapse this way - at what point would you have stopped buying more shares every month - after losing 50% of your existing investment - after losing 90% of it - never unless or until the bank was liquidated and you had lost everything ?

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