Framework for valuing fixed income – Front end

In a previous post, we looked at a model of relative value of equities versus bonds (
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.


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

In the US, the Federal Reserve effectively sets 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.


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.

Framework for valuing equities Part I- 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.


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.

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.


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.


Government Debt Framework – UK Follow-up

Relevance to the present

Previously, we looked at the UK government debt in the post WW2 period.

Two clear questions arise –

“How did the UK manage to keep its rates so far below nominal GDP?”
“Should we expect to be able to do the same in the future? “

The key to inflating away national debt is the ability to force domestic investors to hold government debt at well below the yield they would get in a free price-setting environment.
Sometimes this is reported as financial repression.

Again, this paper does a really good job of giving the details of the post WW2 period.

Comparison post WW2 period to Current

I am interested in the extent to which the situation could be the same for other countries today.
My bias is that it would be significantly more difficult and we should not assume that because it worked in the 1950s it will work today.

  1. Ability to force domestics to hold govt debt
    This is probably the easiest and we are seeing plenty of this at the moment.
    e.g. pension funds and banks being required to hold government debt for “liquidity” or “prudence”

But the danger of the current system is leakages

  1. Capital controls
    Post war Bretton Woods we had globally imposed coordinated capital controls that reinforced home bias. In effect, countries agreed not to compete for capital through the price mechanism. I see this as a form of cartel which managed to hold together until the 1970s. We are a long way from that kind of cooperation today.
  1. Ownership of debt
    It is much easier to coerce domestic investors than foreign ones. In many heavily indebted countries, the issue is that debt markets are owned by foreign investors. This was a big factor in the Asian crisis of 1997/8 and the Mexico crisis of 1994. Currently, the Gilt market is 25% owned by overseas investors which makes it perhaps a little vulnerable. In contrast Japan has a higher debt level but virtually all the debt is owned by domestics.
  1. Trade surplus/deficit
    Post WW2, the UK was close to balance and now has a large deficit (over 4%). This deficit needs external funding which currently comes from FDI. All this adds extra pressure and vulnerability to the situation.
  1. Sensitivity of average rate on the of debt
    In ideal world, the debt market would be structured as conventional Gilts with as long tenor as possible whilst running a primary surplus to offset the interest payments. Even if short rates and inflation rose, the rate paid on the debt would stay the same thus somewhat mitigating rollover risk or the risk of paying much higher rates overall. Unfortunately, this is not the case in most developed countries as QE has been making situation worse.

QE shortens duration of the debt market

One way to think of QE is as a shortening of the duration of debt issuance (another post I think) then the impact on the debt profile is to significantly shorten it. In this light, QE on the Bank of England’s balance sheet simply means that rather than having a £435bn liability of long duration it is paying overnight rates on bank reserves. When (/if?) the Bank raise rates then they are immediately paying higher rates on the debt. (note debt and liability mean the same thing here).

Below is a chart of the average duration of the Gilt Market since 2000


Final Thoughts

I have frequently read the argument that we can inflate our way out of our current debt problems by having faster growth and inflation. The obvious flaw in this argument is it requires independence of nominal GDP growth and interest (i.e. Central Banks would not raise rates in the face of higher nominal growth which is clearly not the case). In the modern market economy, nominal growth and interest rates are highly related and so just assuming they are not is both bizarre and surprisingly common. Alternatively, you can concede that there is a link between growth and interest rates but remain very confident in the ability of modern nation states to impose financial repression with no leakages.

From my understanding of the modern financial system, I do not share that confidence that current debt levels can be easily reduced and therefore, I do not think they can be raised with impunity. It does not however follow that I become an austerity-hungry debt and deficit hawk.

This debate that I read between economists and political commentators appears depressingly partisan with far more noise and anger than analysis. What really matters is whether the current situation is risky enough to merit policy action or, as investors, some active asset re-allocation. This is highly complex but in my view, economic analysis is falling short in its ability to help. If your answer to the question of whether government deficits should be higher or lower is the same at all times, across all countries, then I would suspect that your economic model is not going to be very helpful in making policy or investment choices.

Government Debt Framework – UK


For anyone interested in the long-term investment outlook for fixed income, or more simply the future of our current sovereign nation states, an understanding of government debt must be a key element. Much is written on this subject but I find a lot of it confusing with partisan politics dominating analytical perspectives and terminology which is often inconsistent and emotive.

In this note, I want to focus on episodes where large debt level has been managed.
The large debts of WW1 and the Great Depression were reduced, on the whole, by various types of default. These always come with large economic costs and are to be avoided.
The period after WW2 is more interesting, commonly used as evidence as grounds for optimism and as grounds for opposing “austerity”. (in quotes as this term is generally emotively used by the opponents of current fiscal policy and has a pretty loose definition and usage)

(This paper by Reinhart and Sbrancia does a nice job of laying out the economic history.

Government Debt Model

So, I thought I would start by making a simple framework within which I can look at debt dynamics. Breaking down the change in government debt into 2 parts:

  1. Primary surplus
  2. Interest payments

(put simply Overall Deficit = Primary deficit + interest paid)

Note, this is not intended to be a complete model as there are clearly other factors which can change the debt level. For example

  • Change in currency level for foreign-denominated debt
  • Change in yields leading to change in market value of the debt
  • Due to Extraordinary items e.g. the government takes on additional debt which for accounting reasons they do not show up in the primary deficit

But it is pretty decent and captures the vast majority of the debt dynamics, certainly all of the ones which drive long-term trends.

Model UK Gilt History

Here is the model vs actual data since WW2 for the UK.

There are two clear episodes (~1974 and ~2008) when the actual increase in government debt were far larger than the model would suggest. It would be nice to understand what drove it (for example, in the financial crisis, did the government balance sheet absorb private sector banking debt without having it showing up in the deficit?)

Below is the chart of UK debt since WW2


It is commonly described that the UK ran deficits thought this period and the debt level was brought down by high growth. This is not incorrect but I find it a bit narrow and misleading.

Budget Deficit v Primary Deficit

First, the idea that the UK ran deficits. Well it is true but if you split the deficit into primary surplus/deficit and interest payments then the picture looks quite different.


During the 1950s and 60s, the UK run a deficit virtually every year. But we can also see that the UK ran a primary surplus for the entire period. So the reason the UK ran a deficit was simply that the debt levels were very large and so the interest payments were very large.

Whilst it is true that the main way the UK brought down its debts level was running nominal GDP at a higher rate than the interest rate paid on its debt, compounding effects are huge (running this for a long time) particularly when the debt level is large.

Between 1947 and 1951, debt levels fell from 246% to 165% of GDP. The cumulative primary surplus over that period was 29%, so the balance, about 2/3, of fall in level came from the impact of nominal GDP vs the rate on the debt. compared with only 1/3 from running large primary surpluses.


Relevance to the present

How did the UK manage to keep its rates so far below nominal GDP?
Should we expect to be able to do the same in the future?