This video presents 20 years of market data across the US Treasury Yield Curve, originally rendered at one trading day per frame for 24 fps, any correlation to Bach’s Air on a G string is purely coincidental.

Details over the video’s primary reference data and extrapolation factors are available at the end of this article. A higher resolution version is available for download here (requires X.264 video codec available as standard on the VLAN player).

WARNING: Backwards Extrapolation to the 1 Month YTM was erroneously set to extrapolate back to the 2 Month YTM – This affects all 1Month YTM figures from 2 Jan. 1990 to 30 Jul. 2001. The error range has a mean overstatement of (1.28 BP), st. dev (1.57 BP) and MIN:MAX range of (-3.92BP:6.08BP). BP = Basis Point = 1%/100. A correction and appropriate edit will be made as soon as possible.

But What Does The Yield Curve Represent?

Yield curves are a graphic representation of the cost of funding available for a particular set of securities such as US Treasury bills, notes and bonds. These curves represent the market price of an issuers debt profile: a high yield represents a high funding cost and, conversely, low yields represent a cheaper operating environment.

As my previous article on inflation and the Sharp End Of the Curve reviewed: these yield curves are critical in the analysis of financial conditions currently operating in the market. The common observation, at least for the US treasury yield curve, is that the price of government funding operates counter-cyclically to the broader market conditions.

In other words, when the economy is booming and going well, the government must pay a higher rate of return on its funds in order to compete with private sector capital requirements. This produces a high yield in good times and, logically, when times are rough and the private sector is offering low risk-adjusted returns, low yields for difficult economic environments.

The Inverted Loop of The Yield Curve

This inverse relationship with other broad economic metrics such as : GDP growth rates, unemployment data, stock market indices has as much to do with risk-aversion and a ‘flght-to-quality’ as it does with the inflation expectation horizon. When times are rough, investors seek protection and safety ahead of high potential returns. This leads capital to naturally seek out the safety inherent in the prime borrower of the market: the US Government. Also, combined with this decision, is the market’s own inflation expectation view.

Fixed income instruments, such as government bonds, pay a nominal coupon per year (a fixed amount set at the issue data of the security). The amount paid out is worth more for an investor during times of low inflation growth. As opposed to equities, which pay a floating amount based over a proportion (the dividend payout rate) of their earnings, a US treasury note will not shift the amount paid out from its inception until maturity.

Therefore, when an investor buys into sovereign bonds, he must price at least two aspects into his investment decision: one, on what the actual probability that the investment will pay out (its credit worthiness), and secondly over what that investment will be worth to him over the long term (its inflation adjusted value). The result is the risk-weighted value of the security should increase during periods of high volatility or when inflation expectations are low. In both of these cases, bond yields should go down and the sovereign note’s value should increase.

The Equity Inversion

For an equity investor, the inverse logic should occur, during times of strong economic growth two factors occur. First, private sector earnings usually go up and with this the opportunity for corporation to both increase their dividend payout rates and the amount of surplus earnings available for these dividend payments. Another way to look at this is via inflation measures.

Though we often say that inflation erodes the real value of goods in a society, inflation also actually just means that we increase the prices of our consumption goods. As these prices go up, so do the earnings of those selling these goods. The assumption underpinning this, of course, is that these private entities can still maintain low input costs. If this occurs, then the private sector can increase its net-profit during times of high inflation.

As inflation expectations pick-up, a usual concurrent factor is the concordant growth of equity valuations. This is due to the expectation that input costs, bought at today’s prices, can be sold at tomorrow’s higher prices and produce a natural profit. All other things being equal, a higher profit tomorrow can produce a higher dividend yield, which when discounted back today, can then produce a higher value for your current equity security.

Now, of course, these factors are all interrelated, one can also make the assessment that a higher pay-out tomorrow should also be discounted back further due to the increase in inflation: however, though inflation rates have sometimes reached up to the 5% mark over the past twenty years, they have rarely matched the year-on-year growth of private sector return on equity (ROE) ratios that are quite often in the double digit region, if not occasionally even higher.

These high 20 to 30% earnings growth available in the private sector are strongly linked to companies’ ability to leverage their operations. Additional debt on the books of a corporation, allow it to deploy higher capital into their daily operations and therefore multiply up (the leverage multiplier) the earnings available for their original equity base dividends.

And The Merry Go Round Goes Round and Round

To complete the loop: a private sector’s access to leverage is strongly related to its associated funding costs. As the funding cost of private debt increases, then so does the debt repayment requirements of the private sector institution. Therefore, logically, the higher funding costs should impinge again on the earnings of corporations. This funding cost is, in turn, strongly linked back to the risk-profile of the corporation and its ability to meet its payment obligation over both the short and long term. In order to gain a performance benchmark, this private sector riskiness is often compared, on a relative basis, to the riskiness associated with the safest of all debt borrowers, the US Government.

Therefore, as the US Government funding costs go up (the price point over the yield curve increases) in order to compete effectively with private sector capital returns, then so do the funding costs of the private sector also increase as though they are performing well, they still need to offer a risk-weighted value higher than that provided by a safe sovereign entity. This then affects the ongoing financial operations of the private sector, where earnings are reduced by increased debt funding rates, which in turn then reduce future dividend yields.

So What Does A Shift In The Yield Curve Represent?

Well, all other things being equal and as mentioned before, the yield curve then should move counter-cyclically to broader economic measures. But, as you can see across yield curves, the expectations of this relation change both over a maturity horizon and from a day to day basis.

This shift across the yield curve is natural to a certain extent. The further away from redemption (full repayment of a borrowed amount) then the more risky the investment can become for an investor. This market pricing of the ‘future risk’ of a repayment can shift from day to day.

However, as you might notice in the video above, there are also times when the far future (eg 10 or 20 years) is actually cheaper than the near future (1 or 3 months) or when the curve presents periodic kinks across its maturity horizon. Again, this relates back to both a shifting perception over future economic conditions and inflation growth expectations. The yield curve therefore therefore moves along and present a ‘surface’ for the market’s opinion of the future.

The Yield Curve Of A Kinky Future?

This changing market view of the future can present interesting facets to watch out for: lower yields in the far future can hint at potentially more risky environment beyond the near tomorrow, and, furthermore, lumpiness or un-smooth curves can represent increased market uncertainty over future events.

Therefore, reviewing the shifts, ripples, and shakes of the yield curve provides some ‘graphical’ cues into future market expectations. Quantitative models also try and build more accurate models from these variances by measuring, for example: shifts in stochastic measures (skewness, mean, standard deviation, etc.), shocks to the slope across the curve (“the Macaulay duration coincides with the opposite of the partial derivative of the price of the bond with respect to the yield”), and cross-correlation factors between different maturity horizons (see: Monte-Carlo modelling).

Can Ripples Turn Into Waves?

If we assume that these market opinions are based on substantial factors then these shifts should therefore price themselves back across the yield curve: by beginning in the far future, the 30 year point, and progressively rolling back to the near term, the 1 month price point, all the way over to the present day. As the video tries to display, this process can then ripple along the curve as the markets attempts to price in an ever-closer future on an ongoing basis.

But Why The US Treasury Yield Curve?

The US treasury yield curve, and its unique position as the price point for the de facto ‘risk free’ asset, is also then used as the core reference rate through-out global markets. Shifts and shocks across the US treasury yield curve therefore tend to reverberate and fan out across global capital markets.

For commodity and outright forwards, this factor is known as the basis risk, for cross-currency futures, this is more directly related to the relative yields occurring over multiple currencies, for equities, as noted above, this is often used in discounted earnings cash-flow valuation models and fundamental balance-sheet valuations.

Finally, the unique liquidity of the US Treasury market, due to both the number of investors involved (the higher number produces a higher granularity of opinions) and the sheer quantum of securities on issue, provides an as close-to-economic-theory example of efficient and clean price-discovery.

What About The Rest Of The World?

Now, of course, I would not want to discount the value of other sovereign yield curves, such as those, for example, of the British Exchequer (the English gilts yield curve), those of other European sovereigns (e.g. German Bunds, French ‘bons du TrĂ©sor’ et al.), Japanese Government Bonds (JGBs) and of any other sovereign state.

Each curve has its specific characteristics that are also critical factors in global capital markets and, especially, for their respective economic areas. However, from a global perspective, the US Treasury yield curve still retains a point of leadership and remains one of the principal reference rates used for cross-currency yield curve comparisons (so called spread-pricing) or, in other word, the leading benchmark rate. This referencing, in turn, therefore has the potential to both absorb and propagate price shifts across global markets.

AGB-ECB-US Treasury-Yield Curves-24-09-10

AU/EU/US yield curves - 24 Sep. 2010
Shocks across a national yield curve may propagate across to other sovereign curves with spread variances further revealing cross-market expectations for both current and future economic conditions.
Note: Australian yield curves were extrapolated backwards from the 2 yr data and interpolated for the 7 year data point; all other data as quoted by US Treasury or ECB.

So, when one looks at the US yield curve from a global perspective, one can analyse both the upcoming shocks/opportunities present across maturity horizons, and how these affect both local US denominated economic activity and potentially global activity through the relative shifts in global cross-currency yield curve spreads.

Now, it is important to note, that I am not stating unequivocally that this yield curve always predicts everything that will or must occur, indeed, a large part of successful financial analysis, consists of acting when prices mismatch to core fundamentals and, in common parlance, to take a position over the curve, or in other words, to make a financial decision.

However, from an Efficient Market Theory perspective, as all investors should only be price-takers, they should therefore only be able to represent their particular opinions at an aggregate level. This should then ensure that the future yield price point is a ‘clean’ point representing a rational market opinion on economic conditions prevailing for the specific maturity date. This opinion should then sharpen itself as the relevant maturity date approaches the present and the more granular side of the curve.

But Are Today’s Volatile Prices Really A Stable And Reliable Measure?

The current economic environment, however, is not quite as clean-cut as Efficient Market Theories would suggest. The past decade in particular has seen a substantial rise of increased institutional sovereign entities in the market and especially in the US Treasuries market.

Notably, to take but one example, the growth in China’s foreign-exchange reserves has caused their opinion to become dramatically closer to that of a ‘price-setter’ rather than that of a ‘price-taker’. This issue of ‘capacity’ in the market is one that is met across many other securities and that contributes to market inefficiencies and, therefore, potential market mispricing (for other examples of ‘capacity: see past article on institutional ownership and agency issues).

Fighting Fire With Fire

This being said, the recent economic crisis also included dramatic involvement by several sovereign central banks in what is now called Quantitative Easing programs. These operations deliberately seek to engage in price-setting positions within capital markets. In part, this is in order to absorb the cost of past market mispricing and to reduce their concurrent forward effects over future yield curve price points.

As noted above, these operations designed to ‘smooth the yield curve’ should therefore reverberate out from their initial investments in a particular security, e.g. the US treasury issues or European Government bond issues, and over through global markets due to the referencing and benchmarking process detailed above.

Ironically enough, the process of referencing a security’s funding rate or valuation mechanism back to a benchmark yield curve is what is know in finance as ‘fixing’ of the rate.

Yield Curve Source Data: Data Scrubbing Methods

All the yield curves produced for the video, The Value Of Time at 24 fps, were created based on the historical constant maturity yield curve data service provided by the US Treasury Department (assumptions underpinning the data set are available through the US Treasury website). Graphs are accurate to 1 basis point for relevant data points (1mo, 3mo, 6mo, 1yr, 2yrs, 3yrs, 5yrs, 7yrs, 10yrs, 20yrs and 30yrs), curve smoothing interpolation was employed for intermediate periods.

However, due to some limitations in the data available and the lack of other data feeds, secondary extrapolation was still applied for the 1 month and 30 year data points over specific perios. Traditionally, bootstrapping of market data is preferable with, if still required, associated interpolation across the required periods.

WARNING: Backwards Extrapolation to the 1 Month YTM was erroneously set to extrapolate back to the 2 Month YTM – This affects all 1Month YTM figures from 2 Jan. 1990 to 30 Jul. 2001. The error range has a mean overstatement of (1.28 BP), st. dev (1.57 BP) and MIN:MAX range of (-3.92BP:6.08BP). BP = Basis Point = 1%/100. A correction and appropriate edit will be made as soon as possible.

The erroneous backward extrapolation measures for the 1 month data between 2 Jan. 1990 and 30 Jul. 2001 used the following weighted method:

The correct and intended extrapolation measure should have been for the 1 month data between 2 Jan. 1990 and 30 Jul. 2001 using the following weighted method:

The forward extrapolation measures for the 30 year data between 15 Feb. 2002 and 8 Feb. 2006 used the following weighted method:

7 Responses to “The Foresight of the Curve and its Maturing Future”

  1. [...] This post was mentioned on Twitter by Tariq Scherer, TwentyFour Something. TwentyFour Something said: New Article: The Foresight of the Curve and its Maturing Future #uncategorized [...]

  2. Super nice stuff, loved this read!

  3. [...] is in place, this does add on yet another factor that needs to be managed across (see Basis Risk in Foresight of the Curve and Inflation and the Curve). The rise of electronic trading venues and so-called dark pools or [...]

  4. [...] of 2010. I tried to render a similar 3D plane back when I was doing all those yield curves (see Foresight of the Curve and its Maturing Future), unfortunately my little excel charter didn’t handle too well beyond 500 days worth of data, [...]

  5. [...] As previous posts have already noted, China’s FX currency controls are, by their very nature, both an unstable and unsustainable long-term policy setting (See Arbitraging the FX Windmills and the ending section of the Foresight of the Curve and its Maturing Future). [...]

  6. [...] In planning this post, I was worried of once more facing off with Excel’s interpolation smoother function. Thankfully, the nice guys over at the CBOE have saved me some time by doing the work for me (for my past efforts on roughly 5000+ days worth of treasury curves see: Foresight of the Curve). [...]

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