Tuesday, June 16, 2015

Looking some more at an at-risk based interest rate model.

In the previous post, I discussed the possibility of using the at-risk rate as the starting point for discount rate models instead of the risk-free rate.  This rate seems to be fairly stable over time, allowing it to be a useful benchmark.  From this we would first deduct a "fixed income" discount.  This would get us to a simple version of the Capital Asset Pricing Model, where required returns on equity are equal to the risk free rate on long term bonds plus an Equity Risk Premium (ERP).  I would treat the ERP as a discount from the at-risk rate for avoiding cash flow uncertainty, rather than a premium added to the risk-free rate for taking on uncertainty.  This is semantic, but I think it is a first step toward a more coherent framework for thinking about market values over time.

Then, there is a further discount within fixed income for maturity, which is the discount one accepts for avoiding duration risk.

Cyclical Movements in Long Term Interest Rates

Imagining discount rates in this way gives a different flavor to monetary policy, I think.  The Fed tends to focus on short term rates.  But, if we look at, say, the iShares Core Aggregate Bond Fund, a benchmark for the high quality bond market, it has a long-running average duration of around 5 years, which is between the duration of 5 year and 7 year treasuries.  This is the duration of the typical fixed income security in the US economy.  So, the movement of rates among these durations is a more accurate measure of credit markets than movement of overnight rates.

One signal of cyclical disequilibrium is the discount accepted for avoiding duration risk.  It seems like, if we are using interest rates as a measure of monetary policy, a better signal of optimal policy would be a quickly recovering short term yield, which would be reflected in compression of rates among the higher durations.

Here is a graph of several durations of treasuries.  Note that 5 and 7 year treasuries move more closely in line with long term bonds than with short term bills.  Deviations in short term rates tend to reflect steep short-term yield curves, where rates are expected to fairly quickly recover (excepting the recent zero lower bound problem).

Before 1990, 5 and 7 year rates remained very close to long term rates throughout the cycle.  And when short term rates rose, long term rates tended to rise also.  In the 1991 contraction, we began to see periods where 5-7 year rates pulled down below long term rates, reflecting an expectation of slow recovery.  A lack of any inflation recovery during this time suggests that short term interest rates were not below the natural rate.  (It is worth noting that throughout the 1980s, the yield curve was fairly steep at the very short end, and flat at the mid and longer ranges, even while inflation was plummeting and remaining low.  Rates at the very short term range don't have that much of an effect on at-risk investment.)  But, when short term rates did rise in the 1990s, long term rates compressed and the full range of durations rose with them.

In the 2000s, we continued to see these extended periods where 5 to 7 year rates fall below long term rates.  And, in the 2004 recovery period as well as today, the Fed is raising short term rates while that separation remains.  And, long term rates did not rise with short term rates.  So, compression happened, not as a function of recovered long term risk perceptions, but because of Fed tightening.  By the end of 2005, after the recovery of inflation from the very low levels of the recession, much of the excess inflation was coming from this premature tightening, which cut the bottom out of new housing starts, and sent rent inflation soaring.  Core inflation (less shelter) never crossed above 2% except for a couple brief periods in 2008 and 2010.

There is an assumption that the low short term rate was funneling cheap credit into risky investments, but a steep yield curve at short durations had been the norm for 20 years in a declining inflation environment, and, if we look at this from the long-term at-risk point of view, with discounts for risk aversion, the unusual spread between 5-7 year treasuries and long term rates was signaling risk aversion among savers.

Today is even worse than in 2004, because then the brief housing recovery did reduce shelter inflation before the tightening undermined new building.  Today we are already dealing with rent inflation and a lack of building.  A bold loosening in mortgage markets could counteract monetary policy now, but while there have been some signs of that, a full recovery of mortgage growth might require several fundamental shifts in the banking sector that would give borrowers with less than perfect credit access to the market, and this portion of the market seems totally blocked out right now.

So, looking at this from a bottom-up perspective, the Fed could raise short term rates to 2%, compressing long term rates from the bottom.  And, they could be looking at 2.5% inflation that is really 1.5% after factoring in the lack of housing supply, and they would think that low long term rates are stimulative, and high inflation is a sign of overheating.  If we are using interest rates as our monetary communication device, wouldn't it be nice if the Fed announced that they wouldn't begin to tighten until 7 year rates converged toward 30 year rates?

Secular Movements in Long Term Interest Rates

I had speculated that there could also be a secular benefit to seeing rates from this perspective, and that high long term rates and a low ERP (reflecting a low fixed income discount) would change the shape of investments, pushing investments into longer-focused, more risky projects.  Qualitatively, this seems to have been the case in the late 1990s, where a very low ERP was coincident with the internet boom.

Of course, the 15 years since then have not exactly been heralded as an era of high growth.   But, if we look at real GDP / Labor Force growth, there is actually a seemingly tight relationship between stock returns and GDP/LFP growth.

My proxy here for bond returns is based on the interest rate of Moody's AAA corporate bond yields.  There is not a systematic relationship here because long-term persistent trends in inflation have had a large effect on the real returns on fixed rate nominal bonds.  Although, the return on real bonds doesn't necessarily look like it would have any more systematic relationship to GDP growth.

The lack of a bond relationship suggests that my speculation doesn't hold.  Even if the theory can be defended, it looks like future growth is overwhelmed by real and nominal shocks.  So, it is the real GDP growth that is the causal factor in the relationship between equity returns and GDP/LF growth.

GDP growth is on the right scale and stock returns are on the left scale.  Long term stock returns follow pretty closely alongside GDP/LF growth rates, but with a scale about 10 times larger.  Over time, equities gain (lose) from the proportional rise (fall) of GDP, but much of the gain in returns should be coming from related higher (lower) growth expectations, since required total returns are fairly stable.  Here is a graph of total required returns to equity, based on Damodaran's measured ERP.  There is a bit of a dip in the early 70s and a bump in the early 80s, but this is partly due to the difficulty of estimating real bond rates during volatile inflationary periods.  Inflation expectations would be somewhat backward looking, and would depend on expectations of Fed behavior.  I have simply deducted GDP inflation from bond rates, here.  Inflation expectations were probably a little lower than actual inflation in the early 70s and slightly higher than actual inflation in the early 80s.  So, there was probably a brief period of higher required returns in the early 1980s, but not as pronounced as it looks in this graph.

To the extent that there was movement in the required total return, a low discount rate in the 1970s would have called for a higher relative valuation and the high rate in the 1980s would have called for a lower relative valuation, so this was working in the opposite direction of equity price trends and growth expectations trends, at any rate.  The idea of a low ERP being a policy target that would raise future growth levels appears to be weak.  ERP levels appear to be a lagging indicator.  So, they tend to decline when business cycles have been long and shallow.  Low ERPs are less a guarantee that we will do well than a sign that we have been doing well.

Equity Risk Premiums and Capital Income

But, even though low risk aversion either doesn't improve our capital allocation decisions or doesn't overcome the uncertain noise of real shocks, in the here and now, where the future has not yet been manifest, it still has an effect.

"dlr" left some great comments on the previous post, and put some firm doubts on the idea that corporate income wasn't down as sharply in the late 1990s as the BEA suggests.  But, I believe that there is still evidence that stability and high real growth expectations are related to current high compensation levels.

I don't ascribe to the notion that transfers from capital to labor are something good, in and of themselves.  Labor income is measured in terms of time, but capital income is measured in terms of time and risk.  So, this is a sort of free lunch.  In times of low perceived risk, capital owners gain the same level of utility from less income.  Naional income has risen, even if we don't have a simple way of describing or measuring it, because the rise is coming from a change in capital's denominator (risk).  Some of that unmeasured extra income accrues to labor.

These are a couple of graphs that I have shown before, along these lines.

And, real wage growth moves pretty strongly with the unemployment rate.  Here are a couple of graphs comparing real wage growth and the unemployment rate, first in a scatterplot, then in a line graph.  Nominal stability leads to higher growth expectations, lower ERP, lower unemployment, and higher wages.  And, these are hourly wages of production workers, so confusion caused by stock options and returns to entrepreneurs in the 1990s should not have an effect on this measure.  In fact, I would argue that real wage growth has been understated since 1995, since some of the inflation is coming from the supply problem in housing.

Source: http://www.frbsf.org/economic-research/files/JEP-slides.pdf
The Beveridge Curve moved to the right in the 1970s and early 1980s and appears to have shifted back to the right again recently, due to persistent unemployment.  Job openings during these high ERP periods appear to remain at normal levels, but unemployment rises.  That suggests that job openings per unemployed worker is not as large of a factor in real wage growth as the unemployment rate is.

One common bit of wisdom that I think is mistaken is that low unemployment will lead to inflation from rising wages.  But, I think employers are too forward looking for this.  They don't tend to raise wage rates in an inflationary response to temporary labor supply factors.  There are too many frictions related to their many cost considerations for this to happen.  The lack of a wage response to job openings corroborates this idea.

Instead, real wage growth is related to unemployment levels because the growth in wages is coming from labor supply.  In a low risk environment, employees are more free to move to higher productivity positions and better matches for their skills and characters.  Real wage growth comes from better job matching and more fluid labor markets.  In a way, the unemployment rate is a proxy for labor's "ERP" - the Employee Risk Premium.  And, this ties into the idea that lower ERPs lead to higher wages.

Another way to look at this is to think of an employment contract as having an embedded interest rate swap, where the employer naturally takes on the residual cyclical risks.  When ERPs (both kinds) are low, the discount that employees must accept in their employment contracts is lower, and wages are higher.  But, again, this comes from a complex foundation of risks, so the higher wage it leads to is higher in real terms.  The employer does not need to compensate with higher revenues because they are being compensated through lower perceived risk.

1 comment:

  1. Thanks for sharing and it was very informative..I need more tips from your side..I am working in Erp In India