Things my 2-year old has this morning successfully flushed down the toilet

1. A pair of socks.
2. A banana.

Spotted in Zagreb

Graffiti. In braille. In Croatian.

Pound cost averaging (Part II)

Pound cost averaging crops up a lot as an investment strategy.

Most proponents tout pound cost averaging as a way of "beating the market," but, to the extent that there's a meaningful comparison to be made, I claim it does not beat the market. That's not to say that it's a silly strategy; after all, "invest a little bit each month" is quite a sensible strategy if what you want to do is save money. Furthermore, there's a sense in which pound cost averaging does no worse than the market, either. In fact, there's a very sensible sense in which pound cost averaging is exactly the same as the market. I thought it would be interesting to work through John Kay's example to see what happens. To do so, we will need to fill in a number of details. It turns out that there are a lot of essential details to be filled in. 

In Kay's suggested strategy, we invest £100 each year in some particular stock (the single stock being a proxy for whatever equity investment opportunity is open to us). The stock is assumed to have a value in each year of 100p, 50p, 100p, 50p, 100p, ...

After 10 years the accumulated shares will either be worth £1,500 or £750, depending on the year in which they are sold. Therefore the return generated by this strategy is either 50% or −25%. (I am, throughout, ignoring the time value of money).

Now, if we are to decide whether or not that strategy "beats the market," presumably we will need a "market strategy" with which to compare it. What would such a strategy look like? Presumably it would roughly be "just invest everything you have and don't try anything clever." Suppose that every year we have only £100 to invest. In that case, investing everything you have would mean investing £100 per year; in other words, the "market strategy" just is pound cost averaging.

Obviously, in this sense, pound cost averaging is neither better nor worse than the market, but it's rather a trivial sense. 

Perhaps, however, we have choices to make. A simple model that captures at least some of those choices is to imagine that we have been given the £1,000 up front and have to decide how to invest it over the next ten years. In this model, we will need to assume, in addition, that we can also save money at zero risk; in other words, that whatever we don't invest this year can be carried forward to next year. 

In this version, it seems reasonable to define the "market strategy" as the strategy that is: invest the £1,000 straight away, and wait ten years.  Now we'll get back either £2,000 or £1,000 or £500 depending on the year in which the stock is bought, and the year in which it's sold. So the return generated by this strategy is either 200% or 0% or −50%. 

Which strategy is better? It's hard to tell, actually, because they're clearly not directly comparable. It's not like one guarantees a 100% return and the other guarantees only a 50% return. Instead, there's some uncertainty in both.

At this point, you're probably thinking, "why all this caveat venditor nonsense? It's obvious which year to sell your stock in: the year in which they're worth 100p a share. For that matter, it's obvious which year to buy in: the year in which it's worth 50p a share. So why wouldn't you just do that? 

This, I think, is a major problem with Kay's example. He chose a certain set of prices for the share to illustrate a point. But presumably he didn't mean to suggest that these prices would be known in advance. No-one knows what the share prices will be in advance. And presumably he didn't mean to suggest that pound-cost averaging is only a good idea for this specific set of share prices; he is claiming that it's a good idea in general. A more useful model would specify the probability that the share price would increase or decrease, each year, by a certain amount. 

But the end result would be similar to where we are: Both the "invest it all at once" strategy and the strategy of pound cost averaging produce a range of possible answers. The variation in that range is lower under pound cost averaging but the average return is also be lower. (There's a question of how to compute the average, of course.) A strategy of "save everything" would be the extreme of no variation, but no return either.

Here's the point: By varying the split between what you invest and what you save, you get to trade off risk and return: none of either for pure savings; lots of both for pure investing. Conceptually, any point along this trade-off line could be considered to be a "market strategy." Pound-cost averaging just puts you at one point on this trade-off, somewhere between the two extremes. But if that's what you want, you can get the same effect simply by saving some and investing some. There's nothing particularly clever about pound cost averaging; and it certainly doesn't beat the market.