Framework for FX valuation – where is the USD heading?

Here is a metaphor to explain how to approach a situation when there are conflicting potential drivers of an asset.

You are sitting on a small yacht, drifting in the sea. You want to know in which direction you will drift: onto those scary rocks or safely away from them. There are two potential factors which could be very important – the wind and the tide. The wind is the one you will be most aware of; but the tide could perhaps be very important even though it is less clear what it is doing.

If you ask for help you may find advice split into 2 camps. Those who believe that the wind is always the critical factor and those who believe that the tide is always the critical factor. This ideological split is not very helpful because there is no consistent answer to this problem. Sometimes the wind will matter more, sometimes the tide will matter more. You have to use your knowledge and judgement to decide how to incorporate those factors.

As for asset markets, this is a useful metaphor for many macro markets from fixed income, to equities to foreign exchange. A clear and important example of this today is how to position ourselves in the USD.

FX Model

Tide – Value (proxy is the real effective exchange rate)

Wind – Relative monetary policy.

Monetary Policy (Wind)

Most FX strategy I have read over the past few months has been bullish the USD. The most common argument relates to divergence of monetary policy. The Fed is raising rates when few other countries are, and with Trump these expectations became even stronger.

The relationship between the movement of a currency and the relative interest rates in those countries is a good one. If we look at the last decade of the Euro vs the US dollar then we see what a great first approximation it is.

But in financial markets, it is often a mistake to assume that something you have found that works well for a period is always reliable. It is not possible to treat macroeconomics or investing as having “Laws” in this sense.

If we look at the prior decade for the Euro, then the monetary policy model is terrible.

Value (Tide)

The other first approximation model I want to look is value. For this post, I will take the real effective exchange rate (REER) as a simple proxy.

It is clear from this chart that assuming a mean-reverting tendency in the REER would not have been at all useful in the past 3 years. The USD has been above its average value and heading higher strongly.

Maybe value only matters at extremes? Taking a longer view, adding bands of +/- 10% gives us a sense of how far the USD can move before a value constraint starts to be meaningful.

If you take the model for the yacht as the same conditions last time you went sailing, when there was not much tide and the wind blew you safely away from the rocks, this is not sensible. It would be particularly dangerous if there is a rip tide and you are ignoring it by assuming that a light breeze will determine your path.

Why is everyone talking bullishly about the USD?

  • Recently value has been a terrible model.
    The US dollar is expensive and going higher
  • Rates differential has been a great model
  • Simple extrapolation means that people believe rates will continue to be the best model in the future

Signs this may be happening now

The recent strengthening of the euro is often “explained” with reference to a potential change in QE from the ECB. But rates have not moved. So perhaps we are seeing the influence of a force we have not had to pay attention to recently. Value.

Conclusion

Macro investing is hard. The world is complex and confusing.  Over the years I have noticed many people fall into one of two traps

  1. Become fixed in a single view of how the world works and happily ignore or rationalise away contrary information
  2. Form a fluid view of the world which adapts to a model which can make the most sense of their recent experience.

The time we can make the most money from markets is when they are the most wrong. This can happen people are using the wrong model.

How to reduce your Risk Part III

Trick question (click here for the question, and here for the answers)
There is no right answer because risk cannot be minimised.
It can only be transformed from one type into another.


What did people choose?

Option A was the most common answer. For those who trade in financial markets, this may be surprising.

If I reframed the question and asked:

  • Please calculate the DV01 of Options A and B
  • Please calculate the VAR of Options A and B
  • Please tell me which of A or B has greater risk

You would quickly work out that B has zero DV01 and zero VAR. Hence by the definition of risk used on trading floors, A has higher risk. Unsurprisingly asking this question to a room of traders at investment banks, I get the overwhelming answer B because that is the context in which they think about “risk”.

If I ask the question to people who work in property or private equity, then I am more likely to get the answer A as certainty of cashflow is critical, especially when thinking about assets and liabilities. In the accrual accounting world of regular banking, they think about Earnings at Risk (EAR) and Option A is the way to reduce the risk.

The answer given likely relates to your personal circumstances and the exact framing of the question. If I had the time running a series of experiments with slightly different wording, rates or quantities I think would give interesting results.

But for now, the practical lesson is important. People do not instinctively understand risk at all well. We are presented with questionnaires from investment advisors which ask us for our risk preferences with no definition of risk. From the results of typically recommended portfolios, it would suggest that bonds are low risk and equities high risk.

My approach

I think that the best way to think of this question is in terms of a balance sheet. Whether choice A or B “reduces” your risk depends on the extent to which it matches the tenor of your liabilities. If your liability is short term then Option B is the sensible answer. For investment banks, they have no corresponding long-term liability apart from capital. They typically hold wafer-thin amounts of capital against market-to-market assets so naturally recognise A as a risk. For someone who is keenly aware of what they see as fixed longer-term liabilities such as paying school fees or retirement expenses then the choice of a long-term asset i.e. Option A, is far more natural.

Risk matters

Whenever risk gets mentioned, I very rarely observe a discussion of this nature. Often only one side of the balance sheet is being examined and the vastly important implicit assumptions from the liability side are not considered. I am an advocate of multiple forms of risk measurement, including VAR, but only if it is used in the correct context. Many of the worst financial disasters have occurred by taking a risk and accounting concept that was appropriate in one context and transplanting it to another. AIG and Enron are the biggest ones that spring to mind.

Framework for valuing fixed income – Long end

I do a very different analysis of the long-end of the yield curve, compared to the front-end. (Framework for valuing fixed income – Front end) Mathematically, you could take the same approach and bootstrap the curve from a complete set of forecasts of short-term rates for the next 30 years. But this seems a bit silly and begs the question of how you would get these forecasts anyway.
To simplify the analysis, what we have to work out is what the long-term “equilibrium” rate will be and ignore for now how we get there or use the analysis from the front end to build a path.

Simple Hypothesis: Long-Term rates = Nominal GDP

An approach that appeals to me is to look for a link between long term interest rates and long term nominal GDP. I think of it as a “Wicksellian” natural rate which the market will tend to revert to i.e. If interest rates are consistently far away from the growth rate of nominal GDP then there would be a persistent drag or stimulus to growth which would not be sustainable. You can get to a similar idea from several different economic frameworks.

If we look at the data then, the hypothesis looks reasonable. Below is the 10-year average of nominal GDP growth alongside the 10y10y interest rate for the US. The 10y10y rate is the rate you can calculate as what the market implies the 10y interest rate to be in 10 years’ time.

Before the early 2000s, interest rates were consistently a little higher than GDP. Academics were happy with this and explained it in terms of some type of premium which bond owners would demand to own bonds. They were then confused in the early 2000s by the “conundrum” that long term yields dipped, explaining it either by Chinese ownership of Treasuries or a global “savings glut” which was forcing down yields.

Outlook for Nominal GDP

Current yields do not look very remarkable to me, but they are only correct if you think that nominal GDP will remain as low as for the past decade. The most prominent argument that we should expect this to continue comes from Larry Summers and his promotion of the idea of “Secular Stagnation” – http://larrysummers.com/2016/02/17/the-age-of-secular-stagnation/

I find these arguments a little hard to engage with as we must recognise how utterly useless long-term forecasts of anything generally are. I should admit that I am not a big fan of anything which looks like a restatement of the savings glut theory to me, but I do not want to engage here in an academic debate. As a more practical question, I think that the burden of proof is on ideas such as Secular Stagnation and the “New Normal” that the world will need permanently far lower rates than it has in the past. Arguing that nominal GDP will be lower, due to slower population growth, demographics and potentially lower productivity is easy. Explaining why it is 3% lower is not so easy.

My view is that this economic cycle does not require new theories to explain it. A financial crisis results in a very deep recession and leaves scars which mean the recovery is slower than many expect. These hangovers from the financial crisis are what Yellen refers to as “headwinds” which are slowing down the economy. Risk aversion among consumers and businesses after such a bad recession is only to be expected and the impairment of the credit channel after such a disruption is also understandable. But there is no reason to think that these headwinds are permanent. They can abate and we can return to a world similar to the one before, both in terms of the level of nominal GDP and also the relationship between interest rates and growth. The financial crisis has been traumatic, especially for countries like the US and the UK, that have not seen one like this recently. However, the history of financial crises is that they are worse than people think, but they are not permanent.

Are we renormalizing?

Unemployment fell slowly but is now down to 4.5%. wages have been sluggish but are now picking up.

If I draw the first chart again but this time use a 5yr rather than 10yr moving average then perhaps I can argue the market is reacting too slowly. Nominal GDP has been rising recently and with rising wages and inflation can easily be seen to be likely to continue to do so. If that is true then market rates are too low.

Why are long term rates still so low?

The idea that long term rates are too low is hardly new. After all this was the whole point of QE!! The central banks buy huge amounts of long term debt to drive up bond prices and yields down. This helps to stimulate the economy and boost other asset classes which look relatively cheaper to bond markets, and so drives reallocation flows.

As I mentioned in this post (https://appliedmacro.com/2017/05/01/government-debt-framework-uk-follow-up/), we are living in a new era of financial repression. Therefore, I really do not need any grand theory from the supply side of the economy to explain low rates. I just look at the huge boost in demand for bonds from the central banks.

Is there a catalyst for change?

  1. One potential catalyst would be from the front end. If the Fed hikes rates faster than the market expects, then this can cause a shock to ripple down the whole curve. We saw an extreme version of this in 1994.
  2. If wages start to accelerate then the Fed, economists and market participants would have to radically reassess their assumptions about the inflation outlook and the appropriate level of rates. If you are very confident this cannot happen, you have more faith in our understanding of this type of macro variable than I have.
  3. Even without any fundamental driver we may see a repricing simply from a change in the supply and demand dynamics of the bond market.

QE buying has been high for the past few years but it is finally slowing down. This may be the catalyst for a repricing of bonds.

Conclusion

A simple and yet historically useful framework for considering long term rates is to use nominal GDP. In recent years, we have seen the combination of a major downshift in long term expectations for both nominal GDP and the level of rates relative to nominal GDP. While many arguments justifying this change as permanent have some merit, I think that they are more temporary then current market pricing implies. Which means that I do not think that bond markets are cheap. In fact, I think they are wildly expensive.

 

Framework for valuing fixed income – Front end

In a previous post, we looked at a model of relative value of equities versus bonds (https://appliedmacro.com/2017/05/09/are-equities-expensive-part-i/).
But it does beg the question of whether bonds are good value themselves.

I am not aiming for a full review of global bond value, I will focus purely on the US market. In this post, I shall look at the front end of the curve and in a later post the long end.

Expectations

The simplest and best model for the short end of the yield curve is the expectations hypothesis.
The yield is an average of short-term interest rates that are expected to prevail through the life of the security


Such expectations may not match the market yield, so there may be a residual. This residual r is sometimes called the premium (choose any: risk premium, term premium, liquidity premium, it does not matter which). At times such as during the financial crisis, I spent a long time modelling precisely the premia, but in normal market conditions it’s not very productive. Merely knowing if the premium is large or small, positive or negative is sufficient.

The other term often used for premium is expected return. If you think in terms of academic “efficient market” models or asset allocation in a real money environment, then you may prefer to use excess return but the language does not matter here.

US Front End

short term interest rates, the Fed Funds rate, and these days they helpfully publish quarterly forecasts of where the committee thinks it will be. A sensible starting point is to compare these forecasts to the tradable yield and calculate the residual.

If you have not been following fixed income markets for the last few years or have learnt how markets work from finance textbooks, you may find this chart surprising.
We, as market participants, are well used to the fact that the market is pricing that rates will be significantly lower than the people who set them expect them to be. This has been the case for a long time but so far, the market has been better at predicting how the Fed will behave than the Fed itself.

If we look at a chart over the past 2 years where rates have been expected to be at the end of 2018, we see some fluctuations but very little net movement. In contrast, the Fed has been consistently revising lower its forecasts of where it thinks rates will be.

If we cannot just assume the Fed know what they will do, we must form our own opinion on where rates might go and determine whether the market is under or over pricing the path. The way to do this is to break down the elements of the forecast and analyse each of them.

The Fed’s reaction function & the Taylor rule

To start with the obvious, the Fed decision can be thought of as a function of things they care about. It is often called their “reaction function” and the things they care about are employment and inflation, their explicit objectives as given to them by Congress.

A common and useful form of this is the Taylor rule, which models Fed behaviour on just two variables.


Using this to make investments

The Taylor Rule is not that useful as a predictor of rates, but it forms a useful framework to think of what drives them.

There are 3 obvious places where you can disagree with the market and so make an investment call.

  1. A different view on growth

One of the largest and most obvious trades in my career was short term rates in 2002. The economy had been very poor in 2001, but the memory of the bubble was perhaps still so vivid that the market priced a rapid rebound in growth and thus interest rates. 2002 did not turn out to be the year of recovery and rate expectations fell accordingly all year.

  1. A different model of the economy

A good example of this would be 2008. Even after Lehman went under in October 2008, it took a long time for people to understand how serious it was and the devastating impact on the broader economy. The market was still pricing that rates would be nearly 3% at the end of 2009. They ended up close to zero. Rates eventually plummet in 2008 because the economy is falling apart.

A counter-example where a commonly believed idea turns out to be wrong is the idea that Quantitative Easing (QE) is going to lead to high inflation and so bonds will collapse. This comes from the idea that inflation is caused by “money” and the Fed is “printing money”. A simple and appealing argument that comes from a misunderstanding of what “money” is and how the monetary and banking system works. (a good topic and controversial later post I am sure).

  1. A different view on reaction function.

An example here would be that after the crisis many people were very premature in thinking that the economy would get back to normal.

In the summer of 2013, rates were still zero and the Taylor Rule suggested that was appropriate. But taking the economic forecasts at the time and projecting what that meant, suggested that rates would be much higher. So back in 2013 the market was pricing that rates would currently be about 3 %. In fact they are around 1%.

This difference is not because the economic growth forecasts were wrong. But the reaction function was. If you listened to Fed Chair Yellen’s speeches she was clear that the Fed would be very “patient” in raising rates. They desperately wanted to avoid hiking prematurely and actually wanted inflation to be higher. So a new reaction function should have been understood – that the Fed were waiting longer to hike to get the economy to be running hotter.

What about now?

My experience of financial markets is that is that expectations are more commonly adaptive than rational. By this I mean that humans (including market participants) tend to overweight recent experience. Given that the Fed has been consistently too high in their forecasts for the last few years, people expect that will continue to be the case. I am not so sure.

I am inclined to use an even simpler new reaction function for the Fed based upon wages. In previous cycles, they would hike before wages rose because

  1. They were confident in the economy
  2. Inflation and wages were high enough already to take a risk if they go lower again
  3. Wages are a lagging indicator, so by the time wages rise the economy will have been running too hot for too long

This time they want wages and inflation to be higher before they even start. The data suggests to me that wage growth is finally recovering.

It is reasonable to think that the economic cycle works the same now as in previous periods, and so wages are a lagging indicator. That means that the labour market has been tight for a while now and is continuing to get getting tighter adding more upward pressure on wages.

Conclusion

This cycle has been very different from prior periods because

  1. The recession was very deep
  2. The recovery was slow
  3. The Fed wanted to wait until they were sure they needed to raise rates.

This has meant that being long the front end has been a reasonable trade for a long time i.e. the front end was cheap against my expectation of where the Fed would set rates. But with the signal that wages are finally rising, we may be approaching the end of this phase. Furthermore, with so little still priced for rate hikes from the Fed the front end does not look good value to me.

If the US recovery has been slow, but the economy not long-term impaired then this means that the rate cycle has been delayed, not that it is not coming or that where rates end up will be so much lower than in previous cycles. But that is the topic for the next post.

How to reduce your risk?

Let’s do an experiment.

I am going to present with you with an investment decision with two options.
Please choose the one which will reduce your risk.

You have £100k.

A. You can invest your money by buying a 10-year bond with a 10% yield

This means you will receive £10k per year and your £100k back at the end.

B. You can put your money in a bank checking account which currently pays 10% APR

This means that if interest rates stayed at 10% then you again receive a total of £10k every year with your £100k initial capital still yours.

These investment options look identical if interest rates never change.  But the rate of interest is not going to stay at 10%.  To make it very clear I will let you know that interest rate are going to change tomorrow and will either be 5% or 15% but you do not know which.

Remember I’m asking for the option which reduces your risk.

Answer in a later post.

Framework for valuing equities Part 1- Compared to bonds

A useful framework for considering one investment is to compare it with another, you can then do analysis to decide if you prefer one to the other. This is of course relative value and if the benchmark asset is government debt, this is a solid place to start.

The “Fed Model”

The “Fed Model” is that the stock market yield is related to the yield on long-term government bonds. Like so many models, it has fallen into disrepute seems to come more from its misuse over the years as opposed to its intrinsic failings.

Expected Returns for Equities and Bonds

A way to start thinking about this model is to start with the expected returns on the two investments, equities and bonds. Consideration of the spread of returns and the distribution around the expected return can come later.


Bonds

Expected return for US government bonds in nominal terms is as easy as it gets – yield to maturity.
I will ignore the remote possibility of a default on the debt.

Equities
Expected returns for equities is harder; there is a choice of possible yields, with none necessarily equating to the eventual return.

  • Dividend yield
    Problematic given that dividend policy is a management decision. Microsoft’s decision not to issue dividends was not a good indicator of its total return.
  • Earnings yield
    More sensible i.e. E/P (or just PE ratio inverted).
  • Earnings yield + Inflation

Considering we are using historical earnings, to get a future value we could add an inflation component given that earnings would be expected to rise along with inflation, in the long run.

Testing the expected returns model for Equities

Back-testing expected returns to 10 year actual returns, the US equity market shows surprisingly good results, especially post WW2. This makes intuitive sense as one would expect that buying equities with a lower PE or when inflation is higher would produce better returns. But the strength of the relationship is eye-catching, implying that current earnings do on average provide a good guide to expected equity total returns.

If you come from a purely “efficient markets” view of the world, this may seem blindingly obvious with equity value as simply the present value of the earnings stream. But bear in mind that earnings yield (E/P) is not a yield in the same way that bonds have a yield, unless you make an argument where the word “assume” occurs very frequently.


Expected Returns for Equities versus Bonds

Given that we are happy with our model of expected returns for both equities and bonds, we can move on to comparing one versus the other.

The model for expected return of equities over bonds would look like

We can use data from end 2016 to get actual numbers

This difference/expected return is often called an equity risk premium (ERP).

We can now back-test its use in predicting if the equity market will actually outperform the bond market. Chart below again shows pretty decent relationship – but can we say how good?

expected vs actual

Given the nature of the data we should not perform a regression, and instead here is a truth table for the data back to 1950.

With ex ante premium (i.e. model) above 2%, then equities outperform bonds 93% of the time.
With it below 2%, then equities only outperform 37% of the time. That is a pretty solid result.

Summary

This investigation that equities look cheaper than bonds. If this is the only model you use then the clear imperative is to buy equities now. Before I make my mind up, I want to think about fixed income valuation next.