Yield Curve on 2012-11-20

The very short end of the yield curve continues to behave erratically. My best guess to its cause is still the concerns relating to the fiscal cliff. Nonetheless, the yield curve as a whole shifted up today. That shift might be attributed to the following action by the Federal Reserve chairman, as noted in a Bloomberg news article (link here):

“The yield on the 10-year Treasury note climbed to 1.67 percent from 1.61 percent as Bernanke’s comments suggested that a fiscal deal could remove impediments to growth. Stocks erased losses, with the Standard and Poor’s 500 Index advancing 0.1 percent to 1,387.82 at the close of trading in New York after losing as much as 0.7 percent.”

Newsmap (website link here) suggests that the “hottest” news at around 3 P.M. today are Twinkies, Chinese political news, and something positive relating to the fiscal cliff situation. I only included business news in the filter. For those of you that have never heard of Newsmap, here’s the description from the creator’s blog (link here):

“Newsmap is an application that visually reflects the constantly changing landscape of the Google News news aggregator.”

Thus, it appears the change in the yield curve today is due to two pieces of news – one affecting the very short end and the other affecting the longer end of the curve.

1-month Constant Maturity Yield Falling 6 Basis Points Today

The 1-month constant maturity yield fell 6 basis points relative to yesterday, while changes of other maturities are within what I would consider normal fluctuations. In terms of news, there are no 4-week bill auction today. There are some positive chatter about the fiscal cliff. For example, here:

“Optimism that President Barack Obama and Congressional leaders will reach a deal on the budget deficit and avoid the "fiscal cliff" helped stocks notch their first advance in four days.”

Looking back, the 1-month yield on Nov 1, Nov 2, and Nov 3 are 0.06, 0.08, and 0.09. It is 0.07 today and 0.13 yesterday. From what I can tell, the jump most likely is due to the news about fiscal cliff.

 

Yields Go Up, Yields Go Down, and Event Study Tradeoff

Yields (constant maturity estimated by the Treasury Department) went up yesterday…

… and it went down today.

Presumably, the increase yesterday has to do with supply issues, i.e.:

“Treasuries declined after the U.S. sale of $29 billion in seven-year notes drew of the least demand since May 2009.”

As for the fall today, a plausible explanation:

“Treasuries rose, pushing 10-year yields down from almost the highest in five weeks, as a report showing Spain’s unemployment rate at a record high raised concern the region’s debt crisis may worsen.” “There’s still a flight-to-quality bid being generated by concern for Europe,” said David Coard, head of fixed-income trading in New York at Williams Capital Group, a brokerage for institutional investors. “It’s a roller-coaster ride.”

These types of seesaw actions make event study hard. The problem can be alleviated by using intraday yield data, but that data is costly and you are still trading off measuring the effect of a particular news item versus trusting the market participant’s ability to evaluating the news and trade on it. For example, if you use a 5-minute event window to study the effect of the FOMC statement release – you hope the only relevant news within those 5 minutes is the FOMC release. That is likely. However, you are also trusting that the Treasury price will be able to reflect that news within the 5-minute window also. In some cases, the proper trade off isn’t clear.

Reference:  Treasuries Fall as Seven-Year Note Demand Is Least Since 2009 [Bloomberg],
  Treasuries Advance on Spain’s Jobless Rise After GDP [Bloomberg Businessweek].

Yield Curve on 2012-09-06

Presumably because of: ECB Details Bond Plan.

Yield Curve on 2012-08-31

Fell 5 to 7 basis points at the longer terms, presumably because of: Bernanke lifts Wall Street, keeps stimulus in play.

A Good Paper on Yield Curve Estimation

A very good paper by Kikuchi and Shintani titled "Comparative Analysis of Zero Coupon Yield Curve Estimation Methods Using JGB Price Data" (downloadable here; direct link here) on zero coupon yield curve fitting/estimating. They looked at various methods of curve fitting and concluded that the Steeley (1991) method is best suitable for estimating the Japanese zero coupon yield curve. These various methods include Svensson (1995), Nelson-Siegel (1987), as well as McCulloch (1975), and they judge the methods on the criteria of undesirable (negative) values, excessive unevenness, and fitness to market prices. They also make the estimated yield curve data from 1999 to 2011 available  (downloadable here).

One issue cause by the zero lower bound for many of the curve estimation methods is negative values at the short end of the curve. (The other common issue, particularly for yield curves estimated by Nelson Siegel or Svensson, being the up and down spike at the short end of the implied forward rate curve.)  You can see the negative value issue from the dataset used in Wright (2011) (data downloadable here). For example, the Japanese nominal 3-month zero coupon rate for 2002 October is -0.0132 in the dataset.

The main contribution of the Kikuchi and Shintani paper isnt't that Steeley (1991) is best for estimating the Japanese yield curve, but rather that the paper highlights additional considerations needed when estimating yield curves in addition to the standard tradeoff between fitting close to the market price and limiting excessive unevenness. If the purpose of the estimation is to find arbitrage opportunities, methods that fit close to the price would be preferred. If the purpose of the estimation is to understand the implications of the curve to the macroeconomics environment, a smoother curve is desired. If one were to use the curve to calculate implied forward rates, and find them to be the red line on the right (Figure 15 of Kikuchi and Shintani) – what implication should one draw about the macro economy?

Reference:
    Kikuchi and Shintani: Comparative Analysis of Zero Coupon Yield Curve Estimation Methods Using JGB Price Data (IMES) ,
    Steeley (1991): Estimating the Gilt-edged Term Structure: Basis Splines and Confidence Intervals (Journal of Business Finance and Accounting),
    Svensson 1995): Estimating Forward Interest Rates with the Extended Nelson and Siegel Method (Sveriges Riksbank Quarterly Review),
    Nelson and Siegel (1987): Parsimonious Modeling of Yield Curves (Journal of Business),
    McCulloch (1975): The Tax-adjusted Yield Curve (Journal of Finance),
    Wright (2011): Term Premia and Inflation Uncertainty: Empirical Evidence from an International Panel Dataset [http://pubs.aeaweb.org/doi/pdfplus/10.1257/aer.101.4.1514] (AER).

Comments on FOMC Actions (June 20, 2012)

From the FOMC statement last week (June 20, 2012):

“In particular, the Committee decided today to keep the target range for the federal funds rate at 0 to 1/4 percent and currently anticipates that economic conditions—including low rates of resource utilization and a subdued outlook for inflation over the medium run—are likely to warrant exceptionally low levels for the federal funds rate at least through late 2014.”

Late 2014 is about two and a half years from now, and this date is unchanged from the April FOMC statement. What has change is the end date of the maturity extension program:

“The Committee also decided to continue through the end of the year its program to extend the average maturity of its holdings of securities. Specifically, the Committee intends to purchase Treasury securities with remaining maturities of 6 years to 30 years at the current pace and to sell or redeem an equal amount of Treasury securities with remaining maturities of approximately 3 years or less.”

Contrast this with the original program announcement in the September 2011 FOMC statement from last year:

The Committee intends to purchase, by the end of June 2012, $400 billion of Treasury securities with remaining maturities of 6 years to 30 years and to sell an equal amount of Treasury securities with remaining maturities of 3 years or less.

The range of securities being purchased and sold has not change, though there are certainly fewer 3 years or less Treasury being own by the Federal Reserve than there were in September of last year given the $400 million sale of short Treasuries. From the Federal Reserve’s H.4.1 Release (data: here), there appears to be enough Treasury holding in the 1-5 years range for the program to go on. Table 1 below shows the Federal Reserve’s holding for end of September 2011 and middle of June 2012. However, I would need more data to break out the 1-5 years to see how many 3 years or less Treasuries are remaining as of now.

Table 1. Federal Reserve’s Treasury Holding by Maturity (in millions of dollars)

	Total	<15 days	16-90 days	91 days - 1 year	1-5 years	5-10 years	> 10 years
9/28/2011	1,664,655	15,909	22,877	129,112	714,534	583,690	198,533
6/20/2012	1,663,577	13,148	19,881	21,354	532,988	745,173	331,032
Difference	(1,078)	(2,761)	(2,996)	(107,758)	(181,546)	161,483	132,499

The table shows that from the end of September 2011 to now, the Federal Reserve’s Treasury holding has fallen in the short end. Note that the numbers for each row are holding of securities with remaining maturity as of that date. Those securities that are now 91 days to 1 years from maturity would have been 1 years to 1.75 years from maturity at September of last year. Also, the drop in the 91 days to 5 years is similar in magnitude in the rise in the 5-30 years – that is a goal of the maturity extension program to keep the reserve stable.

The stated goal of the FOMC actions is:

“This continuation of the maturity extension program should put downward pressure on longer-term interest rates and help to make broader financial conditions more accommodative.”

The constant maturity yield curve from the Treasury website between the day before the FOMC announcement to June 26 shows some moderate fall in yield for much of the yield curve.

 

10-year Constant Maturity Yield fell 27 basis point in the Past 3 Days

In the past 3 days, the 10-year constant maturity yield has fallen 27 basis points (i.e., 0.27%).

Given that the most recently auctioned 10-year security was issued on May 15, 2012, I would think most of the yield movements are due to demand – and particular flight to safety. The big news today is the bad employment numbers from the non-farm payroll release. The big news yesterday was Europe related (related post here). To sum it up, it is likely that the fall in yield reflect concerns about the global economy. Below are the daily yield change graphs for the past 3 days.

 

 

Yield Curve Movements for May 30, 2012

The US yield curve for the past weeks has been volatile. The daily change for today, using the constant maturity yields from the Treasury, is in the magnitude of over 10 basis points at the longer end of the curve.

Presumably, these movements have something to do with Europe, as the following article suggests: http://finance.yahoo.com/news/wall-st-falls-europe-worries-200935690.html.

The graph below plots the yield curves for the past 2 days, and shows the change in yield in a bar graph.

What I find interesting is that there tends to be these back and forth movement of the yield curve with these types of news. For example, below are 3 graphs for May 22 to May 24. The yield swings back and forth – up the first day, down the second, and up again on the third.

Because of these yield patterns, I am sometimes skeptical of research that uses event study (particularly 1 day change in yields) to measure effects of monetary policy - particularly on a new policy that market participants would not know well the effects. The 3 day cumulative change for the 10-year yield here is just two basis points. If one measures the effect of the news here, and use only one of the days, the estimated effected would be anywhere from 4 basis points to –6 basis points.

In a paper I hope to have time to work on again soon, I will dive into this issue more.

 

 

Inverted Yield Curve as Recession Predictor

Also Sprach Analyst has a post (here) about China’s slowdown showing through the lack of loan demand and inverted yield curves. The post’s comment about yield curve reminds me of this paper by Jonathan Wright, now professor at Johns Hopkins: The Yield Curve and Predicting Recessions. 

Of course, the idea is not new. Here is an older paper written 10 years before Professor Wright’s doing a very similar analysis: The Yield Curve as a Predictor of U.S. Recessions.

To calculate US recession probability is easy enough, because the needed data are publicly available. You can get almost all the data from FRED (here) alone. For China, it is a bit more difficult. In addition to the difficulty in obtaining the data for your regression model, you won’t have much recession observations. China has very few recessions, particular over the period where yield data are available. The graph below shows China’s real GDP growth rate (data source here).

Presumably Because of the FOMC Announcement….

From the FOMC statement today:

In particular, the Committee decided today to keep the target range for the federal funds rate at 0 to 1/4 percent and currently anticipates that economic conditions--including low rates of resource utilization and a subdued outlook for inflation over the medium run--are likely to warrant exceptionally low levels for the federal funds rate at least through late 2014.

And the resulting change in the yield curve today (data from US Treasury Department, see previous post for more information) below. The 5-year yield constant maturity yield derived from on-the-run securities dropped quite a bit – but there is also a $35 billion auction today (see auction results announcement).

Treasury Yields and Comments on Event Study

The graph below plots daily change in constant maturity yield (for five maturities from the 2-year yield to the 30-year yield) from October 20 to November 2. Given all the events in Europe these past weeks, the change swings from very negative to very positive to very negative again.

Now, if I were to study the actions of the European Government on US Treasury yields using an event study scheme, how would I analyze the events of the past month? Where would the events be, and how many days should my event windows covers?

These are important considerations when conducting an event study analysis, and underline the method’s potential issues. Outcome can be sensitive to event window size and event selection. Yet, this is a popular scheme in measuring monetary policy effects – from quantitative easing to FOMC announcement effects.

I am starting to think about a paper that I have been putting aside, tentatively titled “Policy Duration Effects under the Zero Interest Rate Environment.” The current version uses the standard event study scheme, and I find myself facing the issues I have described above. I think I have come up with a new way to analyze the data differently, and hope to have a new version of the paper soon.

As a side note, I also looked at the Federal Reserve’s Svensson Zero coupon yield (graph below). The Svensson yields are constructed using a different smoothing method than the constant maturity yields from the Treasury Department. The Svensson yields more importantly omit the on-the-run Treasury securities in its estimation, whereas the constant maturity yields use only the on-the-run securities. However, in the past month, the fluctuations between the two sets of yields are similar.

Reference: Daily Treasury Yield Curve Rates [US Department of the Treasury],
  FRB: Research Data [Board of Governors of the Federal Reserve System]

Constant Maturity Yield Changes for Today (The Day after the Day after Yesterday)

This should be the last in a series of 3 posts. The constant maturity yields estimated by the Treasury Department (data here) today gain another 23 points at the 20-year and 30-year maturity. I assume the yields are driven by the event depicted in this article: EU Crisis Deal Buys Time for Greece: Papandreou.

Interestingly, the chart below shows that the yields on the Japanese Government Bonds head toward the opposite direction. (Data is here)  Sometimes, the discrepancy is due to the difference between the market close times for the US and Japan markets. But the change in yield has been negative for the past two days. Also, the change in yield is relatively small.

Reference: Bloomberg [Bloomberg]

Constant Maturity Yield Changes for Today (The Day after Yesterday)

Constant maturity yields estimated by the Treasury Department (data here) today recover 9 basis points at the 20-year and 30-year maturity.

The volatility in asset prices is why one should always take event studies with a grain of salt, and especially the choice in window size. A lot of papers on Quantitative Easing effects (my area of research) use event studies. A couple of examples include Gagnon, Raskin, Remache, and Sack (2011) and Swanson (2011).

Here are the headlines on Bloomberg’s main webpage at the moment (3:12pm October 26, 2011).

Banks: No EU Deal Yet on Greece
Supercommittee Dems Said to Pitch $3T Plan
U.S. Stocks Advance as EU Bank Agreement
UAW Members at Chrysler Ratify Labor Contract
Apple May Gain as VA Seeks Device Security
Bove: Goldman May Get ‘Windfall’ If It Buys MF
Stanford Proposes NYC Engineering Campus
Aflac’s Third-Quarter Profit Advances 7.8%
Trader Kupersmith Indicted for $60M Fraud

Reference: Bloomberg [Bloomberg];
  Joseph Gagnon & Matthew Raskin & Julie Remache & Brian Sack, 2011. "Large-scale asset purchases by the Federal Reserve: did they work?," Economic Policy Review, Federal Reserve Bank of New York, issue May, pages 41-59; 
  Eric T. Swanson, 2011. "Let’s twist again: a high-frequency event-study analysis of operation twist and its implications for QE2,"Working Paper Series 2011-08, Federal Reserve Bank of San Francisco.

Constant Maturity Yield Changes for Today

Constant maturity yields estimated by the Treasury Department (data here) felt 14 basis points at the 20-year and 30-year maturity.

Despite the description in the “About Me” box on the right side of the blog, I rarely talk about automation. The graph above is an example of the type of automation I do to help me keep tabs on the economy. My Linux computer runs a bash script everyday to get the constant maturity yield data from the Treasury Department website, and then the script uses Matlab to generate the graph. Finally, it emails me the graph by email. If the change in yield is large, the email adds the words “(LARGE MOVEMENT)” in the email subject.

Today, the yield changes are quite large. The numbers in the title of the graph are the day to day yield change. The top graph plots the yield curve for the past two days. The bottom graph plots the change in a bar graph. The email helps me keep tab on the economy – since large movement in the Treasury yields are usually meaningful. Of course, it is often difficult to pinpoint why.

However, for today at least, I am guessing the drop in yields is related to the Europe situation. Here are the headlines on Bloomberg’s main webpage at the moment (6:00pm October 25, 2011).

Asia Stocks Fall as Europe Uncertainty Grows
Japan Signals Coming Action as Yen Hits Record
Chinese Banks’ Profits May Not Lift Valuations
Amazon Profit Plunges; Shares Tumble
Australia Inflation Slows, Currency Declines
BlackRock Expects “Massive” Mining M&A
IBM Names Ginni Rometty as First Female CEO
Merkel Puts Rescue Fund to German Vote
S. Korea Growth May Slow, Pressuring BOK

Reference: Bloomberg [Bloomberg]

Svensson Yield Curve for Euro Bonds

I can’t seem to download multiple time series (say 1yr to 30yr) easily from the web interface, but Euro area bonds’ implied Svensson yield curve data are available via the European Central Bank (ECB) here. The series are available in par, instantaneous forward, and spot rate.

The 2yr instantaneous forward rate starts at September 6, 2004. The rate for October 10, 2011 is 2.818129%. Under a lot of assumptions, this is the expected rate of a very short rate - like an overnight rate that a central bank controls - 2 years from now.  In (I hope) simpler terms, the bond market on October 10, 2011, is expecting that the very short interest rate on October 10, 2013, to be 2.81%.

The time series:

The spiffy flash version that shows the whole yield curve for various dates is here:

http://www.ecb.int/stats/money/yc/html/index.en.html

Reference: The estimation of the Term Structure of Interest Rates under the Compressive Sampling approach: Some initial considerations [Calzón, Martínez, and Rodríguez-Piñero]