Yield Curves and Interest Rate Spreads

There's been a lot of discussion about the yield curve lately. Some of you may be afraid to ask what a yield curve is and how it relates to interest rate spreads. For those who are, here's a simple illustration. Suppose there are three assets in the economy, a 3 month bond, a 5 year bond, and a 10 year bond. Let the interest rate be 3% on the 3 month asset, 5% on the 5 year asset, and 10% on the 10 year asset. To construct the yield curve, simply graph the time to maturity against the return [the points are (3 months, 3%), (60 months, 5%), and (120 months, 10%)]:

There is another way to present these data in terms of spreads. Here for example the spread between the 10 year (120 month) and 3 month rates is 10% - 3% = 7% indicating an upward sloping yield curve between these two points. Similarly, the spread between the 5 year (60 month) and 3 month rates is 5% - 3% = 2% again indicating an upward sloping yield curve between those two points. A third spread can also be calculated between the 10 year and 5 year rates and this is 5% (the line connecting the 3 and 120 month rates is not shown but is easy to visualize).

The following graph presents the spreads between the federal funds rate, an overnight borrowing rate between banks, and the 3 month, 6 month, 1 year, 3 year, 5 year, 7 year, and 10 year Treasury rates. Again, recall that if the particular spread is negative, the yield curve drawn through these two points would be negatively sloped:

Two popular spreads (see here) are the difference between the 10 year and 3 month rates, and between the 10 year and 2 year rates. Here's a graph showing each:

As the graphs show, the spreads move in concert for the most part with the largest movements, as expected, for the largest spreads. The particular choice of a spread determines the level of the difference, with positive spreads more likely when the time to maturity is further apart, but the particular choice is somewhat arbitrary. 

This brings up one more point. As many, including Jim Hamilton and Arturo Estrella have emphasized the yield curve should not be used in a binary fashion. That is, it should not be used to say all is fine until it has a negative slope, and once it has a negative slope, to say a recession is coming. One reason is that whether the spread is positive or negative in a given time period can depend upon the particular spread examined. Another is that the change in the chance of a recession is gradual, not binary. Historically, the narrower the spread between long and short rates, the slower is output growth on average, see Hamilton for more on this. There is not a sudden jump in the probability of a recession when one particular spread turns negative despite what recent news reports may have led you to believe. And as all who discuss this topic emphasize, the connection between the yield curve, interest rate spreads, and the probability of a recession is far from certain. A flatter yield curve does not gurantee slower growth.

Comments

[Navin]

Excellent description. Thanks.

Happy New Year !!

[calmo]

A flatter yield curve does not guarantee slower growth. And because few things in life are really guaranteed, Greenspan takes the ball from here and lets us know that we have nothing to worry about --that globalization and the disintermediation of risk coupled with sophisticated financial instruments have practically guaranteed us Nirvana.
I notice that the DOW's dip in the last week was blamed on this inverted curve by some writers. There appears to be genuine uncertainty about its relevance despite the historical evidence showing a significant correlation. It is important for Greenspan with his lengthy service and expertise to let us know that we, in our canoes paddling downstream, are in good hands. That roar ahead noted by Greenspan's juniors, is not the Niagra Falls, but some cheering committee --perhaps on the occasion of someone's successful retirement.
I prefer the last graph to note that the yield curve does not invert for long. Secondly, the weight of hedge funds depending on significant (not thin) spreads is unprecedented, yes? So I expect the duration of flatness to be short. This means either the long term rates move higher or the ff rates retreat and the latter seems doable and the former problematic, yes?

[Bruce Webb]

"Some of you may be afraid to ask what a yield curve is and how it relates to interest rate spreads. For those who are, here's a simple illustration."

Insert hollow laugh here, 'simple?'. Mark you're the greatest, and unlike Brownie you really, truly are doing a heck of a job bringing economic realism to a political discourse that needs it badly. And I owe you big thanks for tolerating me when I am cranky. But for a non-economist that was indeed an explanation, and I vaguely get it, but I suspect I would still have some trepidation taking the final exam in Prof. Thoma's finance course.

Happy New Year! (and brace yourself - I took the week off)

[slink]

nice exposition

[Perplexed]

Any comments to following from welling@weedon interview with Leon Copperman and Steve Einhorn (http://www.weedenco.com/welling/liframe.htm):

"Then I’ll ask Steve, aren’t you at all concerned about an inverted yield curve?

Steve: Not really. The worry that investors have about a flat or inverted yield curve causing a marked slowdown in the economy, or even a recession, is based upon a mechanical application of history. It is certainly the case, historically, that when the yield curve has flattened and/or inverted, there has been a material slowing in economic activity as measured by real GDP growth. However, in every one of those instances, the yield curve was inverting because both short and long-term interest rates were rising. It was just that short rates were rising more than long rates. In this current instance, however, long rates are essentially unchanged, and it’s short rates which are rising and threatening to invert the yield curve.

So?

So there has been no brake on the economy owing to a rise in long-term interest rates. Housing, while it is moderating, is certainly still at a very high level in terms of unit demand and price appreciation. Consumer spending, which would be affected by higher long-term interest rates, has held up quite well, remarkably well, when one considers the various hurricanes and energy shocks the economy has witnessed this year. So I think this notion of a flat yield curve becoming a material drag on the economy has not only been wrong, it will continue to be wrong. In that regard, the yield curve has been flattening now for two years—and we have had 10 straight quarters now in which real GDP growth has been 3% or more, which is unprecedented in the last 25 or 30 years.

That many quarters?

It’s not only a long stretch in terms of duration, but the real GDP growth we’ve been seeing has been very steady, very low-volatility. So the economy is fine. It will grow through 2006."

[anne]

Developed economies seem to be growing continually more resistant to shocks. So there may be a mild weakening of growth in the coming year as real estate slows, though I do not find convincing signs of a general weakening, but I am not at all worried about an interest rate or currency driven crisis. For now we need to ask ourselves why the apparent stability of developed economies, no matter recurring shocks. I am increasingly impressed by the flexibility represented and the growth stability.

[Winslow R.]

I also may appear 'grouchy' at times, but have found your perspective to be 'refreshing'.

"One reason is that whether the spread is positive or negative in a given time period can depend upon the particular spread examined. Another is that the change in the chance of a recession is gradual, not binary."

1) Please address money creation (this is what allows the economy to grow), banks borrow from the Fed's window at the Fed Funds rate not the 3 month t-bill etc. Why not look at this spread?

2) Please address the 'carry trade'. Why it's binary nature causes it to halt once there is no money to be made?

3) Please address the ability of 'savings surplus', wealth concentration, etc. to lower long-term interest rates. Why long-term interest rates will not increase until people (Asian CB's) no longer desire to 'save dollars'?

4) Please address how until wealth concentration is addressed (return on investment increased). Why we are likely to see low interest rates, slow economic growth, and little innovation as in Japan?

Thanks!

[anne]

Though I am not sure I understand the set of questions, the Federal Reserve found 15 years ago that watching money supply growth was giving little insight into the pattern of general economic growth. Short term changes in money supply may, however, be used to gauge changes in stock and bond markets. At least I thought so, and Robert Rubin thought so, as the Fed expanded and contracted the money supply in fall and winter and spring 2000, about the year 2000 worry.

Japan however has been and is certainly innovative, and has weathered the slow growth deflationary years remarkably well from a middle class vantage. I am impressed.

[Winslow R.]

Anne wrote:

"the Federal Reserve found 15 years ago that watching money supply growth was giving little insight into the pattern of general economic growth."

New forms of financial intermediation as well as shift from cash to checks to credit keep making M's obsolete. I find debt is tracked quite well and provides a much better indicator of economic growth Debt not only tells you an amount but also which sector holds the amount unlike the M's.

"Short term changes in money supply may, however, be used to gauge changes in stock and bond markets. At least I thought so, and Robert Rubin thought so, as the Fed expanded and contracted the money supply in fall and winter and spring 2000, about the year 2000 worry."

Call me a conspiratorist, but Bob Rubin as Treasury Secretary had too many connections to the financial industry and that is why he moved to Citigroup. Goldman Sachs etc. were/are an extended arm of the U.S. Treasury using cheap loans to buy stocks and bonds to support the 'market' and the pension funds that depend on it.

http://money.cnn.com/2000/03/06/companies/rubin/

http://www.ny.frb.org/newsevents/news/markets/2004/an040803.html

"Japan however has been and is certainly innovative, and has weathered the slow growth deflationary years remarkably well from a middle class vantage. I am impressed."

Japan 'innovative'? I guess it depends on your definition. If your definition is 'slow growth deflation'...

[Winslow R.]

Sorry, the link to the primary dealer list is:

http://www.ny.frb.org/newsevents/news/markets/2004/an040803.html

[anne]

Thanks Winslow, but if ever I appreciate anyone on economics or investing, I appreciate Robert Rubin.

Also, as I was taken with the competitiveness of the Nordic countries when they were pooh poohed, I am currently taken with Japan, though a little more cautiously. I have been arguing about slowness in Japan with Japanese friends for years, and none of us is quite sure of the nuanced history of these last 15 years, but we always noticed Japan changing and were impressed by the resilience and protection of the middle class. I wish we understood more of what I am becoming convinced is a renewal, but I am patient.

I always, at least try to, question stereotypes in investing :)

[Winslow R.]

"but if ever I appreciate anyone on economics or investing, I appreciate Robert Rubin."

Yes, he understands how the financial industry works. He knows how to make money and has the 'access' which makes it easy for him and his friends. The primary dealers have a 'sweet' deal which I consider a rigged monopoly that I wish did not exist.

"Also, as I was taken with the competitiveness of the Nordic countries when they were pooh poohed, I am currently taken with Japan, though a little more cautiously. I have been arguing about slowness in Japan with Japanese friends for years"

Japan is attempting structural reform of the postal 'saving' system. Speaking of Goldman Sachs...

"Since October 1, it has been possible for Japanese savers to buy shares in mutual funds directly at their post office windows. Three institutions--Goldman Sachs, Daiwa Securities, and Nomura Securities--were the winners in the first round of bidding to initiate mutual fund outlets in Japan’s post offices"

http://www.aei.org/publications/filter.all,pubID.23383/pub_detail.asp