This is from Psy-Fi Blog, good stuff
“All I want to know is where I’m going to die, so I’ll never go there” - Charlie Munger
Carl Gustav Jacob Jacobi was a nineteenth century mathematician famous
for his work on elliptic functions, amongst other accomplishments.
Oddly he ends up being frequently quoted by Charlie Munger and Warren
Buffett, despite having no known connection with the investment world.
Jacobi's great contribution to investor thinking was his maxim “man muss
immer umkehren”: invert, always invert. Of course, Jacobi was actually
making a statement about mathematics, not investment thinking, but we
shouldn’t much care where we get our models from, as long as they have
the distinct advantage of being useful.
Charlie Munger uses the Pythagorian proof that the square root of 2 is
irrational as an example of inversion – because they started by trying
to prove it wasn’t irrational and wound up with a contradiction that
could only be resolved by assuming it was. This idea – that we should
try to prove the opposite of what we really want – is the key concept
behind inversion.
It hopefully goes without saying by now (c.f. The Big List of Behavioral Biases)
that we’re all biased in various ways, many of which are beyond our
conscious control, which leaves us with the tricky conundrum of knowing
that we’re making mistakes but being unable to control them. Dealing
with this is obviously difficult, but one of the recommended techniques
is to try and take multiple viewpoints on the same problem – which is
easy enough to state but fiendishly hard to put into practice, since it
tends to be quite hard to build Chinese walls in our minds, short of
having some rather brutal and irreversible brain surgery.
Backwards Thinking
Technically there is a way of finding the optimal path to achieving the best solution, and we’ve discussed it in Dividends Keep You Anchored and (more subtly) in Games People Play:
it’s called backwards induction. At its simplest this involves
identifying where you want to end up and then working out the best route
to getting there by reversing the sequence of events. Think of it as
playing chess in reverse; at each move you work out the best next move
and then go back in time to consider the previous step.
Of course, life and investing isn’t really like chess, which is one
reason why it’s quite hard to apply game theory in the real world –
although you can create artificial situations where it does apply, as in
the wildly successful auction for cellphone bandwidth carried by the UK
government, which was expected to raise £5 billion ($8 billion) but
ended up bringing in £22.5 billion ($36 billion) – see The Biggest Auction Ever. Nonetheless taking an inverted view of the investing world can often provide illuminating results.
1999 and All That
Consider Warren Buffett’s analysis of the growth prospects for the markets back in 1999.
Instead of rosily projecting forwards the astonishing growth rates seen
in the previous two decades, as most investors were happily doing, he
looked at how investment returns were fundamentally dependent on GDP
growth and interest rate fluctuations and argued that:
“I think it's very hard to come up with a persuasive case that equities will over the next 17 years perform anything like--anything like--they've performed in the past 17. If I had to pick the most probable return, from appreciation and dividends combined, that investors in aggregate--repeat, aggregate--would earn in a world of constant interest rates, 2% inflation, and those ever hurtful frictional costs, it would be 6%. If you strip out the inflation component from this nominal return (which you would need to do however inflation fluctuates), that's 4% in real terms. And if 4% is wrong, I believe that the percentage is just as likely to be less as more.”
Which, of course, has turned out to be more or less correct. Buffett
was inverting the then current focus on the wonderful dotcom growth
story to look at the end game: stock prices ultimately depend on
earnings to grow and earnings depend on GDP growth.
Inverting the Future
Inversion is a favourite technique of Buffett and Munger and was set out in detail in the Berkshire Hathaway Shareholder letter of 2009 (where the starting quote from Munger is taken from):
“Just because Charlie and I can clearly see dramatic growth ahead for an industry does not mean we can judge what its profit margins and returns on capital will be as a host of competitors battle for supremacy. At Berkshire we will stick with businesses whose profit picture for decades to come seems reasonably predictable. Even then, we will make plenty of mistakes.”
So if we apply inversion, when we come to a conclusion we should then
work backwards from that conclusion and try and figure out what it
should mean in the real world. So, let’s say you’ve decided to purchase
some stock or other – Facebook, say. You believe strongly that
Facebook is destined for many years of great growth because the power of
social networking is frighteningly strong. Of course, we don’t know
exactly how social networks will monetize but let’s put that to one side
for the time being.
Inverting Facebook
So at IPO Facebook launched with a market capitalization of about $100
billion and a price earnings ratio of over 100. These are staggering
numbers but let’s not worry about that – we’ve decided that this a a
go-go-growth stock and the temporary post-IPO setback is nothing to
worry about. But let’s invert a little and compare Facebook to the
world’s biggest company, Apple which has a market cap of about $500
billion and a price earnings ratio of around 12 – it earned around $40
billion last year.
Now let’s assume that Facebook will become the world's largest company -
on that growth rating it probably needs to, to justify it. To do this
let's assume it grows its earnings to half the level of Apple, but has a
price earnings ratio of double – so it has to grow its earnings by
around 20 times to $20 billion. If it achieves that and becomes the
world’s biggest company it will have grown its share price, from IPO, by
a factor of 5.
Assuming Apple doesn't grow then Facebook would need to compound
earnings at 17% to catch up by 2032. To catch up by 2022 then earnings
need to grow by 35% a year. Now given the caveats outlined above by
Buffett in terms of new business sectors does that seem like a
reasonable risk-reward balance? Do we think the barriers to entry in
social networking and the likely sources of monetization will make this
sort of growth achievable? Even if we think it's possible do we think
it's probable?
Beauty Contests
Of course, many people will have bought Facebook with the calculation
that others would buy it out of excitement, and we saw a lot of evidence
of what Keynes called “beauty contest” investing – where everyone tried
to outthink everyone else (see: A Keynesian Theory of Mind).
And in this particular case failed dramatically as Facebook’s post-IPO
price tanked – possibly because of the well-publicised technical
problems, but more likely because the price was simply too damn high.
In an investing sense inversion can be a great way of testing your
analysis – it can force you to think through the problem in a different
way. All too often investors start their analysis with a purchase in
mind – the issue becomes justifying the decision. If you invert and
start by thinking about why you shouldn’t buy the stock you often get
interesting, and different, answers. If a company is growing fast look
at the competition and see if they are also. If they’re not then why
not? Remember that the invisible hand will drag back the flyaway winner
unless they have something that can’t be copied.
Jacobi's Rule
Investing inversion is a powerful tool, if used honestly: it’s all too
easy to ignore confounding factors, but at least it pushes investors in
the right direction. Always look for reasons to do the opposite of what
you’re considering, because then you’re pushing against your biases,
even if you don’t realize it.
Remember: always invert before you invest.
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