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The Flaw in Fed's Model of Long-Term Interest Rates.

I have been very surprised to read an analysis from the Federal Reserveof Cleveland by Joseph G. Haubrich and Kent Cherny: The Yield Curve, June 2010.

It shows that the Fed who let publish this article doesn't have a clue about the nature of long-term yields:


In order to predict the recessions it compares the slope of the yield curve to a lagged rate of growth of the GDP:



They conclude some expected growth rate from that slope through a model called Probit.



Apart from the fact that the predicted GDP growth is much lower than the prevalent forecast of economist it shows a flaw in the interpretation of the yield curve which overstate the expected future rate of growth.

First the flaw is evident as with a 0% short-term yield it is impossible to have a "inverted" yield curve, which had happened several time for during the sample serie. That should be evident to anyone after after their first year BA in economics and raise the eyebrows of any statistician.

In a more involved way I have demonstrated that in the "normal" yield curve long-term yield are the compounded rates of options on shorter yields.

A simple example of that formula is:

A 10 years yield is the composition of a 5 years yield and a forward yield in 5 years of a 5 years period. (Starting date in 5 years andending date in 10 years.) The forward yield is a call option with a term in 5 years of a 5 years yield with a strike at 0% (forwards yields can never be negative) and a current value of the today 5 years yield.

Anyone with some basic knowledge of option pricing theory understands that for the same volatility of interest rates the lower the yield ofthe underlying asset (a five year interest rate) the higher the yield of the option. The slope being the time value of the option.

The long term yield (10 years) is a composition of the spot yield for a five years yield and an option of that 5 years yield, The difference between the the option and the spot rate being the time value of an option.

By using shorter and shorter forward yields we get a more precise yield curve and we can obtain a continuously compounded model of the normal yield curve.

Consequence:

The slope of the yield curve is the time value of an option.

The closer the short term yield the steeper the normal yield curve. The higher the implied volatility of interest rates the steeper the yield curve.

That explain why since the Fed target for fed funds has been close to 0% the yield curve has been exceptionally steep by historical standard. It has no economic meaning but the result of the option valuation.

A long-term yield is a composition of options. We hence define a steep yield curve as an overvalued option and a inverted yield curve as an undervalued option. This goes counter the classic al definition of steep, normal and inverted yield curve.

In general an overvalued yield curve is quickly arbitraged which result in the efficiency of an accommodative monetary policy in increasing the growth of GDP. On the other side it is very difficult to arbitrage the undervalued option which means that a restrictive monetary policy is very inefficient.

As it compares the slopes of interest rates over periods with very different short term yields the Probit model is a GIGO model: Garbage In Garbage Out. More worrying is that it shows no understanding by the Fed of the nature of long-term yields and its predictive models.

Another worrying point is that the Leading Indicator defined by The Conference Board uses the same crude and flawed data and most of the positive part of its components has been, since the Great Recession, that overvalued steepness of the yield curve.

If we were trying to forecast recession and growth using the yield curve we should be using the difference between our normal yield curve and the actual slope which would actually measure the accomodative or restrictive character of monetary policy.

It is because the short-term rates shoot up from 1% to 5.25% in a short period when long-term yields grew by around 1% only that the long-term yields became too undervalued and caused the Sub Prime Mess.

Today:

My estimation of the normal Yield of the 30 years US Treasury Bonds given that short-term yield of 0% and the value of the implied volatility of interest rates is around 4.60%. The long term yield have been over that normal rate for very short times since the Great Recession as it can be easily arbitraged.

We conclude that at the present yield of 3.90% that yield is grossly under priced. We know that this underpricing can stay that way for quite a long time however when that underpricing becomes too large a sudden retreat from that low level of yield toward its fair value will cause a large displacement of liquidities from long-term assets to cash equivalents. It will be as brutal as have been the result of any restrictive monetary policy in the past. This time however the Fed won't be able to lower short-term yields and any non conventional monetary tools will be ineffective. Off course given the present defiance for any further government deficit it will be impossible to use fiscal policy.

That switch from long-term assets toward cash equivalents can be already seen in the evolution of M3, the amount of liquidities that are effectively used for long-term investments.



The Future:

My estimate is that any level of the yield 30 US Treasury Bonds below 3.80% would be extremely unstable. Although I expect that this yield will stay in the 3.825% - 3.890% range for the first part of summer I expect it to go down steeply on the August 12th auction and result in asharp return to its fair value causing a crash shortly after September 9th most probably during the Quadruple Witching Hour from 3:00 PM EST till 4:00 PM EST on September 17th.
The lowest yield would be from a technical standpoint between 3.60% and 3.80%.





Foreign Yields:

The long-term yield on European Bonds sit at 3.27% much lower than the extreme case for US TBonds. This is possible only thanks to the fast decrease of the Euro against US Dollar.

The low yields are the consequences of the high revenue gap between rich and poor. That would make the Chinese market even more fragile.

Related Resources:

The European 30 Years Yield is now at 
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