The Delusion Of Decimals

Keynes said "It's better to be roughly right than precisely wrong." So what precisely is wrong with analysts' forecasts?

I was sat behind a bench in the physics lab, ready to smash some more atoms (or perhaps my sandwiches) together, when the tutor announced he was going to take us through error estimation. It sounded like tediousness had formed the eighth Circle of Hell but I learnt a method of amazing power and one that ought to be applied to broker's estimates.

Let's say you buy a cube of 24 carat gold (cost about £5,000) and being a cynical type want to be sure it's 100% pure. You measure the side of the cube then weigh it. The cube is 2.45cm across and weighs 276g. The density is weight / (width cubed) = 18.77g/cm3. Pure gold is 19.30g/cm3. Have you been sold short?

Your scales are accurate to 5g (1.8%) and you can measure to within 0.5mm (2%) with your plastic ruler so the maximum error in the density of the cube is 2% x 3 + 1.8% = 7.8%. That's an error of +/-1.46g/cm3.

In other words you are confident the density of your cube is between 17.31 to 20.23g/cm3. Your glistening present is 24 carat within the error of measurement. Had you simply told someone the density was 18.77g/cm3 they might easily conclude that the gold was not pure since this is 2.75% less than it should be. A fair way to state the density would be to round it off to 19g/cm3.

Error estimation can be applied to any calculation no matter how complex. The Bank of England does so in its Inflation Report. The forecast of consumer prices index (CPI) have error bands that get wider as we look further ahead. Even as close as the end of 2009 the forecast is -0.5% to 3%.

So what's the point?

Let's take a small cap share, metal basher Severfield-Rowen, capitalisation £175m. The consensus EPS forecast is 29.42p. The consensus is usually the average of several recent broker's estimates. In this case it seems to be KBC Peel Hunt's forecast alone. KBC Peel Hunt also estimates a precise looking 19.79p for the year to December 2010.

How can they know the profit to within 0.05% a year and a half away? They can't. Even if they stated it as 19.8p that would still imply an accuracy of 0.5%. Yet in the last 12 months the consensus for 2009 has fallen from 41.08p to 29.42p, a 28% change.

Some companies have more reliable forecasts. The table shows the least to most change in the forecast for five randomish companies.

* (standard deviation of historic EPS's and forecast) / (average of historic EPS's and forecast)

In normal times we would not be seeing Tesco's profit at a virtual standstill year-on-year, never mind the massive drops elsewhere. Just for illustration, if we assumed the forecast error to be half of the 12m forecast change percentage, we'd see broker notes with figures like these:

That would much more helpful in making a risk-reward judgement. So why don't analysts help us out on this visibility of earnings issue? I guess the answers are those old bedfellows inertia and avoidance of risk. Which analyst wants to be the first to stick his neck out with a novelty like this, and probably upset the paymasters into the bargain?

Going back to the Circles of Hell, the punishment for fortune-tellers in Dante's Inferno is apposite:

They had their faces twisted toward their haunches
and found it necessary to walk backward,
because they could not see ahead of them.
…and since he wanted so to see ahead,
he looks behind and walks a backward path.

More from Alun Morris:

• What Not To Buy: Green Shoots
• Uranium Shares At Double The Discount
• Honestly, Don't Buy Our Shares