## Friday, March 25, 2016

### Macro: FOMC Dot Plots, The Secular Stagnation Illusion

One of the major surprises in the March FOMC meeting was the re-marking of the long term rates as expressed by the Fed dot plot.

While most speculators were cutting their short bets on the 10-year treasury (as per CFTC commitment of traders reports) and were actively going bullish on the long-end, the short end short positioning was mostly maintained. This was especially supported by the up-tick in the inflation data in core and headlines before the FOMC (as well as inflation now-casting from the Cleveland Fed).

There are conspiracy theories about the Fed's worry and motivation for a weaker dollars in response to the bold liquidity enhancement actions from other major central banks. However, if we really take a deeper look in to it, a different story emerges(1).

FOMC started publishing the dot plot in 2012, between the QE2 and the QE3 phase. Looking at the evolution of the dot plot implied fed fund term structure, there have been two major changes since. First one happened just before the start of the QE tapering. That was the beginning of a steady upward shift for the fed funds rate in the near horizon (~3 year), where they stabilized. The second set of changes came in later half of 2014, which resulted in another gradual move. This time it was a downward shift of the long term rate forecast. From the peak of 2014, the FOMC estimate of long term fed fund rate is down by 75 bps. (Note I have projected the long term rates from the dot plots to 5-year maturity bucket.) Some suggests the Fed is slowly embracing the secular stagnation theory.

There are certain amount of merit in that hypothesis. The current projection implies, assuming Fed's target inflation of 2 percent is realized, a long run real rate of 1.25 percent. And irrespective of your view on the r-g model, a lower r does signify a lower level of long run real GDP growth. For the balanced case of r=g, this implies a growth rate of 1.25 percent.

This seems pretty pessimistic from the recent trends in real GDP. Figure(2) below shows the trend in real GDP (normalized at 100 at the beginning).  The post crisis slope (since 2013) is definitely flatter than early 2000, but not by a huge margin (except Euro area). Add expected inflation to this numbers to get the long run nominal rates. Depending upon your preferred choice (10-year and 5-year swap market breakevens at 1.8 and 1.6 percent respectively, 5y5y TIPS breakeven at 1.66), this seems to imply a long-run rate in the range of 4.1 to 4.3 percent. Almost a full percentage point above FOMC dot plot.
The market seems to be even more pessimistic. The chart(3) shows the spread of 1 month USD Libor (implied from the euro-dollar futures and swap curves) vs the FOMC dot plot. The 2013 taper tantrum was the only time when the market got spooked with a rate hike and over-estimated the future path of rates. Since then, it has steadily become more and more pessimistic to the FOMC prediction. The largest disagreement is in 3 years and beyond.
This level of suppressed nominal rates means either the market is pricing a marked departure in the growth trend from what we have seen even post-crisis so far. Alternatively it means a near term recession and/ or more liquidity measures from the central bank. Or at least it is pricing in the Fed's inability to hike rates substantially given the situation in China and Europe and Japan. So far the Fed has been doing the catch-up to the markets pricing.

The first possibility is what secular stagnation is all about. So far most of the evidences have been important and potentially even supportive, but at the same time inconclusive. It is not certain the impact attributed to secular stagnation is really a not cyclical effect attributed to a long run structural change. In fact Larry Summers, who revived this idea of secular stagnation in 2013, is himself very much aware of this. See the disclaimer in the last paragraph here. There has been many different views on this, for example see here for the counter-view from former Fed Chairman Bernanke. Real-time economics is hard. It will be much easier to settle this debate after a decade or two. But right now, I think the biggest argument against secular stagnation is the prior probabilities. The long run world growth rate data (for example see here) shows a staggered improvement, with last great bottom around just before the Industrial Revolution.  All recent variation in world GDP since post war seems more or less cyclical phenomenon in this scale.

And the other possibilities to justify such depressed nominal rates are definitely cyclical. In fact the FOMC statement and general stance so far, downplaying secular stagnation and emphasizing inflation, clearly shows the Fed is eager to keep its options open. Secular stagnation is a rather long-term commitment to a particular view around equilibrium rates, GDP and inflation. It does not come handy to set appropriate monetary policy expectation and maintain credibility at the same time in real-time economics.

And in that scenario, near to medium term growth and inflation outlooks are much more critical. This also means a higher volatility and data dependency as the markets as well as the Fed react to data. The recent inflation uptick has been feeble, but definite. The fear of Yuan devaluation has subsided significantly. Given Fed's stance, it is perilous to believe the only move for the long term rate for the dot plots are down.

(1) data from Federal Reserve
(2) data from BEA, Office for National Statistics, Eurostat
(3) data from Federal Reserve, Bloomberg

## Monday, March 14, 2016

### Brexit: Getting the Probabilities Right

Brexit is the next big known unknown macro event this year. And probably you have already heard enough about it from a multitude of different sources.

And if you have, one thing you must have noticed. While the opinion polls are neck to neck mostly, the betting market pricing is quite different. For example the latest from Telegraph poll tracker puts it at 51% for "stay" and 49% for "exit". The best current offer for "stay" from the bookies is at $4/11$ - which prices a 73% probability of stay.

This has (and continues to) caused quite a bit of confusions among economists and strategists - cursory glances at the estimates and research notes doing the rounds will give you the idea. It seems the opinion polls and the betting market are not consistent with each other. And it seems most sell-sides (and some buy sides too) are siding with the tight calls from opinion poll.

This confusion is utterly wrong and in all likelihood, both results are right and support each other.

No fault of the economists and the strategists of course. There are many cases where we humans have a good intrinsic sense of chance - like sensing the movement in our peripheral vision to determine the probabilities if it is friend or foe, and converting that to a swift "stay calm" or a "fight-or-flight" decision. Unfortunately, we are not naturally evolved to understand how the probability works in opinion polls!

The opinion polls and the betting market present two connected, yet different, measures. The poll figures shows how many will, if the referendum is held right now, choose "stay" - for example. The betting market odds indirectly gives a probability of "stay". The connection between these two measures is subtle. To understand that, assume an extreme case where we have no undecided voters in the opinion polls. Also the voters are absolutely certain and will not change their mind come what may. If we have 51 to 49 in favor of "stay", what is the probability of a "stay" outcome?

It is 100%! An absolute certainty. We will have 51% in favor votes and 49% against. Since this outcome is guaranteed and $51 > 49$, the resulting win for the "stay" choice is guaranteed as well. This hold true for a 50.5 to 49.5 split. We can go even further. This apparent 50-50 results are actually far from 50-50.

Of course, in real life, there are three deviations from this scenario. Firstly, we are not polling the entire population, hence that 51-49 split is just an estimate from a smaller sample. Secondly, opinions can change on the actual day of voting. Thirdly we do have undecided voters who will eventually vote one way or the other, and decided voters who will end up missing it.

We have statistics as our tool to do our best with the first observation. The entire thing called opinion poll is asking some $n$ number of people about a binary choice ("stay" or "exit"). This is much like a bi-nomial trial. Let's assume the true fraction in the entire population that supports "stay" is $\Pi$. What we are trying to estimate is $Pr(\Pi > 0.5| \pi )$. Here $\pi = X/n$ is our estimate of the fraction that support the "stay" outcome, $X$ being the number votes in favor.

The rest is straightforward, although a bit mathematically involved. We assume prior probability distribution of $\Pi$ as $f_\Pi(\pi')$, carry out the opinion polls, and from the results compute the posterior probability distribution $f_\Pi(\pi)$, using Bayes theorem. Doing just that, we plot the probability of a "stay" outcome against the percentage point difference in the opinion polls.

As you can see, the probability of "stay" quickly converges to $0$ or $1$ as the lead diverges from $0$ on either side. Around $0$, it is highly non-linear. In fact for our extreme case above, it would just jump from impossible (probability = $0$), just below lead $0$ to probability of $1$ (complete certainty) slightly above that - a step function.

The current spread between "stay" and "exit" vote (51 to 49) reflects a probability of "stay" at $0.80$. Inversely, the betting market probability of $0.73$ indicates a lead of $+1.55$ priced in. So obviously both the betting markets and the opinion poll results are not very different. Also another very good crowd-based event forecasting source with expert-beating results projects the odds at 75%.

All of these are quite comparable. And is nowhere near the 40% to 50% odds thrown in most research notes. Take a note before you put your position.

What still can change from here? Well we still have the observations two and three from above - a change in mind for the voters, and swing of the undecided. They add to the uncertainties. On the other hand, we have assumed an unbiased prior - but most likely the people of the United Kingdom has a certain bias to stay to start with. That will add support to a "stay" outcome.

Technical details: Here we have taken the YouGov January survey results - with a sample size of $n=1735$. Also we have assumed the prior distribution as conjugate beta (which leads to posterior beta distribution as well), with unbiased (non-informative) prior - beta distribution shape parameters as $\alpha=\beta=0.5$. The upper and lower bound is computed based on the standard error $\pm\frac{1}{\sqrt{n}}$. For more technical details, you can see here.

## Wednesday, March 9, 2016

### Markets: Sucker Punch - Trading Events Based on Standard Vol Parameters

The high expectation before the Thursday ECB has made the smile in both rates and equities very acute (I have not checked the FX, but that should be no different). For example DAX and Euro Stoxx 50 is priced for a crash with skewed and convex smile favoring the puts. However, you still hear many market participants talking about how the vol of vol or skew is still cheaper - probably under the impression that these skews and vol of vol is still not enough to capture the fat tails that can result from such an event.

Which is a bit surprising, given the expected outcome. It is generally agreed that whatever ECB does, we will have a significant move in either side and then the level will settle down. If this is the case, what we are talking about is a classical case of bimodal outcome. And compared to that, the vol of vols and skews - i.e. in general the tails are quite over-priced. To see why, read on.

It is not very clear to everyone when someone talks about cheap vol of vol or skew (or whatever parameters), what exactly is being expressed by that view. Technically this should mean different things to different styles of trading. For a speculator (no delta hedging), this means the underlying distribution with the implied parameters is different than what she expects to realized. In particular, if one thinks vol of vol is cheap, the expected realized distribution has wider tails than the implied one. For a market maker (delta hedger), the relevant distribution is the PnL distribution after delta-hedge, which is quite different (and a bit more complex - a gamma weighted function of above) than the case of a speculator.

Nevertheless, let's examine the case of the speculator in a situation like Thursday - a bimodal outcome. One simple way to capture a bimodal distribution is what is known as skew bimodal normal (opens PDF, a bit technical). This distribution can be described as below

$$\Psi(x) = \Phi(x) - a(x)\phi(x)$$

Here $\Psi(x)$ is the cumulative distribution function (CDF) for the bimodal distribution, $\Phi(x)$ is the CDF of a normal distribution, and $\phi(x)$ is the PDF of the same. Here $a(x)$ is a linear function of x. Using a normal distribution with mean $\mu$ and variance $\sigma^2=1/\psi$, it is useful to express $a(x)$ as

$$a(x)= \frac{(x+\mu-2\beta)}{1+2\psi [\delta+(\beta-\mu)^2]}$$

This allows us to parameterize the bimodal distribution in terms of $\beta$ and $\mu$ as the location parameters (mean), $\psi$ as the scale parameter (inverse of variance approximately) and $\delta$ as the bimodality parameter.

With this framework, we pick-up a 1 month option with ATM forward at 100 and ATM vol at 25% (annualized), and tweak the $\delta$ parameters to generate a range of bimodal distribution of the underlying (matching the forward and variance to above values, i.e. the first and second moments). Compare these with the normal distribution.

Next step is to use these distributions to price the entire smile for each case, inverting the price to get BS vol. We get the following results:
Yes! This is what a typical smile under bimodal distribution looks like. This is counter-intuitive. The fair tail vols are actually lower than ATM for a bimodal outcome - typical of what could happen in ECB (or in June during Brexit). This is of course extreme and idealized version. But the point is measuring the vol of vol (or skew) in the conventional ways through fitted parameters or through price of a fly is not a very useful way to trade options around such events. We are trying to fit a log-normal like distribution to a one that is completely different. It is not a case of wrong pricing parameters, it is wrong a bit more fundamentally! Bimodal has thinner tails.

We are better off to try to pick the strikes near ATM (or biased towards one of the peaks depending on your view - but before the intersections)  - this will be cheaper than what is priced in if this distribution is realized  And cheapen that with a spread by selling the tail strikes (which is costlier according to our assumptions, even go 2x if you want). That is the correct way to play an event with bimodal outcome.

Note, this is the fair smile only for speculators. For market makers, even for a clear bimodal outcome, the smile will never be like this - as she cannot control some one picking her off to some tail strikes and not trading the the entire smile.

## Sunday, March 6, 2016

### Macro: ECB - Rock and A Hard Place

ECB is widely expected to launch another round of monetary easing in the policy meeting this Thursday.

The chart below amply captures the apparent reason for an increased market expectation and willingness on the part of the central bank for further monetary stimulus. Both the general inflation (HICP here) and wage inflation (unit labor cost) levels are on a steady, relentless downward path.

However, notwithstanding the limitations of negative rates regime and QE, the moot question is how effective another round of monetary policy easing will be.

The contraction in Euro area credit growth since the financial crisis is still to see any sustained correction. And very lately it seems has turned another corner to unwind all the recovery made during last couple of years.

to dig deeper, we take a quick look at the ECB bank lending survey, that specifically probes the problems around demand and supply.

The survey shows a significant recovery in credit demand - both in terms of back-ward looking data and forward looking expectation. Similarly, the credit condition is comparable to the good days before the financial crisis

Going by these surveys, it appears neither credit tightening or potential demand is a problem right now. The relaxing of credit condition gradually started improving after the euro area sovereign crisis was averted, and now has settled down around the levels of best years during the pre-crisis era. The demand side started recovering a bit late, but nonetheless does not seems very off from the pre-crisis levels.

And this is no way a limited result. Even, the SAFE (Survey on the Access to Finance of Enterprises, latest April to September 2015) survey reports clearly notes:
"Euro area SMEs considered access to finance to be the least important problem that they faced (11% of respondents, unchanged from the previous round), although results differ across countries. Instead, finding customers remains their main concern (25% of respondents, down from 26% in the previous round)."
So what is the problem. Let's again look at the second chart again vis-à-vis US credit growth (technically it is not exactly apple to apple, as the US series is Bank Credit of All Commercial Banks from the FRED database, not just to resident non-government sectors). See the co-movement before the crisis and the decoupling after.

It seems a bit puzzling to say the least. The credit supply is definitely not under threat from credit standard tightening (i.e. no significant financial or liquidity stress). Nor the demand shows a particular hole in that area, at least according the surveys. Nonetheless the credit growth is dismal.

There can be many reasons. A recent note on the excellent IMF Blog hints at one - this probably can be a bank balance sheet and capital rules issue than a financial stress or liquidity story. And given the surveys, it seems the latent demand seems to be still around (note the contradiction of the SAFE survey and bank lending survey on the outlook on demand).

To me, it seems a further increase in liquidity or a reduction in rates will be just another round of insignificant attempt to correct the situation. The only effective monetary policy is perhaps an inflation expectation shock - and QE  (at least in its current avatar) is no shock anymore.

And on this front, what can really achieve a lot more bang for its buck is fiscal stimulus. Given the extraordinary economic situation, it is indeed surprising to see the tightness in fiscal situation is rivaling the pre-crisis period. But then again, unlike Canada, with average government debt of 90%+ of GDP, it is hard to push fiscal stimulus politically, even with the best of intention and economic clarity.

The most likely path for Euro area is to follow incremental monetary stimulus and hope for a global return of inflation, quick enough to avoid a general deflationary mind-set taking its root and a permanent damage to the potential output. Only a crisis can change things.

## Tuesday, March 1, 2016

### Macro: Revisting The Dog That Did Not Bark

Very recently we have seen some rising voices on the upside inflation possibilities from various corners.  Soberlook covered it the other day. Deutsche has recently had a rather strong publication. Even the St Louis Fed has something to say on this. I am not so sure that inflation is just around the corner, but I have also covered it before (See here,here, here and here). The point is not to say we should worry about rising inflation now. The forecasting accuracy of economists are, well, not certain. And hence as market participants, investors should care about other possibilities than just their beliefs. Even when (and perhaps especially when) they tend to diverge. And these points are valid concerns to juxtapose against a general deflation concern, driven by Chinese and European economies.

The major points raised in favor of a more positive outlook on inflation are broadly
• the recent rising inflation in the US
• the subdued wage inflation may be just a lagging indicator, and when corrected for productivity gain, unit labor cost inflation may be higher
• inflation markets are too pessimistic about oil and finally
• fighting deflation may be unproven, but fighting inflation is not easy either.

Let's look at some charts to see where we stand on this. To start with, what is driving the recent pick up in inflation  in the US (click to enlarge)

Yes, it has been mostly driven by a recovery in the transport (read energy) component, and steady housing and healthcare components. The massive fall in oil price in late 2014 skewed the transport component and if oil steadies at these levels, this major effect will cancel out (as the Fed expects).

However, that is no cause of merriment, looking at a broader picture. As alleged, the wage rise has indeed been subdued, to historical standard. And as pointed out by numerous analysts, the traditional Philips curve has been much weaker (the chart on the right shows correlation to wage growth and inflation, with shaded area as US recession). Oil, and in general commodities have, in recent times, much stronger correlation to inflation that wage growth. Now this can be read as you like. One hand this means even an increase in wage may not reflect in a substantial increase in inflation (argued from the supply side, with so much excess capacity in the commodity sectors, which most analysts generally agree upon). On the other hand, notice the case of the early 90s recession and how the wage and inflation correlation picked up during the late stage of the recovery. As I have mentioned before, the current recovery is not entirely unlike that of this one.

The take-away here is wage growth or not, the supply side excesses will have to run its course before it can put pressure on commodity prices (perhaps not much downside from here, at the same time). What we really should try to figure out is what is the health of the demand side.

And here we see the mixed signals, especially if we consider the global point of view. Below charts shows GDP-weighted headline and core (ex-energy) inflation. While we have a strong recovery in the US, the rest of the world does not look that impressive at all. It is true we are not very much near a deflation scenario given the current levels, but not a fat lot of improvement in sight.

The point here is more nuanced than worrying about either deflation or inflation. On one hand we should remind ourselves not to write of return of inflation. On the other, we may not be near deflation, but that situation may change drastically if we face a sudden crisis. Given the current monetary and fiscal policy stance, it is very hard to see the wriggle room. And that is precisely the reason to worry for risk assets. Given status quo we should do fine. But in either case it is hard to see a fitting policy response that is credible and effective in either way. It is more like a short convexity trade. If you are in it, you better make sure you are getting paid for it.

Finally, yes, the oil market is indeed pricing the scenarios too pessimistically. But it is hardly fair to blame the traders. You may as well know the breakeven levels are likely wrong, but if you have stop losses it is hard to fight all in. Similar in rates markets. Understandably,  the Sterling markets, with all Brexit talks warming up, are not very optimistic compared to Euro. But given the inflation difference and fundamentals, this is likely a mis-pricing too. At the same time, how long the USD 10y can maintain a 100bps+ differential to Euro rates without attracting yield chasers. The table shows three month forward curves across markets and the policy action priced in.

 Today EUR GBP USD JPY Current -0.34% 0.51% 0.49% -0.03% Max 1.49% 1.88% 2.42% 1.42% Long-run average 0.98% 1.27% 2.22% 1.26% Next Hike Mar-19 Mar-19 Jun-16 Dec-21 Initial Hiking Pace 8.3 7.4 6.9 4.5 Peak Time Mar-29 Mar-27 Mar-33 Mar-34

Eventually all these will correct, may be sooner than later. But rather than being directional, it is time to see how to position for the volatility when we edge towards either extreme and the market overreacts. I would rather like to sit on gun powder now than trying to cover later.

I think this entire arguments and counter arguments are nicely captured in this Galilean dialogues from Gavyn Davis on FT.

For title reference see this and this.