Good reads from around the Web.
The clever bods at The Value Perspective have been doing a sterling job recently in tackling the weird world of the average and what it means for returns.
From writing here on Monevator, I know a lot of people get confused when it comes to how average returns work in practice – or more specifically about the different kinds of average – and what it implies for our investment decisions, whether it’s asset allocation or investing a lump sum or confronting sequence of returns risk.
And when I say “a lot of people get confused”, I’ll admit that can include me!
So most people could do with a refresher on the maths.
Start with this Value Perspective article on the law of averages, which begins:
Let’s play a game we will call ‘Russian dice’, the rules of which were invented by a physicist/economist called Ole Peters. They are pretty simple – roll a dice and, if it comes up ‘one’, I will shoot you.
Do you fancy playing? It does not sound very appealing but, if you were a nihilistic mathematician, you might be tempted because – in the very strictest terms – on average you will be absolutely fine.
The word ‘average’, however, can be somewhat misleading if not defined very precisely. If 100 people roll the dice instantaneously, the average result is ‘three and a half’ – that is, (1 + 2 + 3 + 4 + 5 + 6) ÷ 6 – so, if you are judging the game on the average result, everyone survives.
However, if I asked you to roll the dice 100 times in a row, it is extremely unlikely you could do so without at some point seeing a ‘one’ come up. Bang. You do not get a chance to see the result of the 100-roll average over time.
Intuitively, we all know there is a difference between these scenarios without any complicated maths or concepts. Mathematically speaking, it is known as the difference between an ‘ensemble average’ (the average of an event happening many times concurrently) and a ‘time average’ (what happens when you do something a lot of times consecutively).
However, this concept and its implications are not well understood in investment.
After that first article provoked a fair bit of debate and confusion, their follow-up tried to explain it with a diagram:
[This time] you simply start off with a stake of, say, £100 in the pot and we toss a coin. Every time the coin comes up heads, you increase what is in the pot by 50%; every time it comes up tails, you lose 40% of whatever is in the pot.
The coin is a fair one – so it is always a straight 50/50 chance – and there is not a firearm in sight.
Would you like to play?
At first sight, there appears to be no reason not to play – after all, if on each coin toss the only two possibilities are going up 50% or falling 40%, then surely, on average, it is a winning game. And indeed it is. No matter how long you play it for, on average, the expected return is positive – but, as we argued in the previous article, the word ‘average’, if not defined very precisely, can be misleading.
In this particular example, the average obscures a pattern where the majority of people who play the game actually end up losing.
Here’s the pattern:
Would you play the Value Perspective’s counter-intuitive game?
It reveals:
In the above example, 11 of the 16 possible sequences of coin tosses are losing permutations and, the longer the game goes on, the more money is lost.
In a game where the only possible outcome each time is a 50% upside or a 40% downside, that would appear counter-intuitive so what is complicating matters?
It is that difference between time and ensemble averages.
Read the whole article for a deeper explanation.
the in-laws for Christmas.
