# Meteorologists and Defenseless Receivers

The stock market really seemed to "want" to get to 2000 on the S&P. I
hope it was worth it. Now as real yields seem to be moving higher once again
(see chart below, source Bloomberg) - in direct contravention, it should be
noted, of the usual seasonal trend which anticipates bond *rallies* in
September and October - and the Fed is essentially fully 'tapered', market
valuations are again going to be a topic of conversation as we head into Q4
just a few weeks from now.

To use an American football analogy, the stock market right now is in an extended position like a wide receiver reaching for a high pass, but with no rules in place to prevent the hitting of a defenseless receiver. This kind of stretch is what can get a player laid up for a while.

Now, it has been this way for a long time. And, like many other value investors,
I have been wary of valuations for a long time. I want to make a distinction,
though, between certain value investors and others. There are some who believe
that the more a market gets overvalued, the more dramatic the ensuing fall
must be. These folks get more and more animated and exercised the longer that
the market crash doesn't happened. I think that they have a point - a market
which is 100% overvalued is in more perilous position than one which is a mere
50% overvalued. But we really must keep in mind the limits of our knowledge
about the market. That is, while we can say the market is x% overvalued with
respect to the Shiller PE or whatever our favorite metric is, and we can say
that it is becoming more overextended than it previously was, *we do not
know where true fair value lies*.

That is to say that it **may** be - I don't think it is, but it's **possible** -
that when stocks are at a 20 Shiller PE (versus a long-term average of 16)
they are not 25% overvalued but actually at fair value. Therefore, when they
go to a 24 PE, they are more overvalued but instead of 50% overvalued they
are only 25% overvalued because true fair value is, in this example, at 20. *What
this means* is that knowing the Shiller PE went from 20 to 24 has no particular
implications for the size of the eventual market break, because we don't actually
know that 16 really represents fair value. That's an assumption, and an untestable
assumption at that.

Now, we need assumptions. There is no way to keep from making assumptions
in financial markets, and we do it every day. I happen to think that the notion
that a 16 Shiller PE is roughly fair value is probably a good assumption. But
my point is that when you're talking about how much *more* overvalued
a market is than it was previously, with the implication that the ensuing break
ought to be larger, you need to remember that we are only guessing at fair
value. Always. This is why you won't catch me saying that I think the S&P
will drop eventually to some specific figure, unless I'm eyeballing a chart
or something. In my mind, my job is to talk about the probabilities of winning
or losing and the expected value of those wagers. That is, harking back to
the old Kelly
Criterion thinking- we try to assess our edge and odds but we always have
to remember we can't know either for certain.

Bringing this back to inflation (it is, after all, CPI week): even though we can't state with certainty what the odds of a particular outcome actually are, we can state what probability the market is placing on certain outcomes. In inflation space, we can look at the options market to infer the probability that market participants place on the odds of a certain inflation rate being realized over a certain time period (n.b. the market currently only offers options on headline inflation, which is somewhat less interesting than options on core inflation, but we can extract the latter information using other techniques. For this exercise, however, we are focusing on headline inflation.)

What the inflation options market tells us is that over the next year, market
participants see only about an 18% chance that headline inflation will be above
2.25% (that is, roughly the Fed's target, applied to CPI). This is *despite* the
fact that headline inflation is already at 2%, and median inflation is at 2.2%.
So the market is *overwhelmingly* of the opinion that inflation declines,
or at least rises no further, from here. You can buy a one-year, 2.5% inflation
cap for about 5-7bps, depending who you ask. That's really amazing to me.

Looking out a few years (see table below, source Enduring
Investments), we see that the market prices roughly a 50-50 chance of
inflation being above the Fed's target starting about three years from now
(September 2016-September 2017, approximately), and for each year thereafter.
But how long are the tails? The inflation caplet market says that there is
no better than a 24% chance that *any* of the next 10 years sees inflation
above 4%. We are not talking about core inflation, but headline inflation
- so we are implicitly saying that there will be no spikes in gasoline, as
well as no general rise in core inflation, in *any* year over the next
decade. That strikes me as ... optimistic, especially since our view is that
core inflation will be well above 3% for calendar 2015.

What is especially interesting about this table is that the historical record says that high inflation is both more probable than we think, and that inflation tails tend to be much longer than we think. Over the last 100 years (since the Fed was founded, essentially), headline inflation has been above 4% fully 31% of the time. And the conditional probability that inflation was over 10%, given that it was over 4%, was 32%. In other words, once inflation exceeds 4%, there is a 1 in 3 chance, historically, that it goes above 10%.

Cautions remain the same as above: we cannot know the *true* probability
of the event, either *a priori* or even in retrospect when the occurrence
will be either probability=1 (it happened) or probability=0 (it didn't). This
is why it is so hard to evaluate meteorologists, and economists, after the
fact! But in my view, the market is remarkably sanguine about the prospects
for an inflation accident. To be fair, it has been sanguine...and correct...for
a long time. But I think it is no longer a good bet for that streak to continue.

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