<![CDATA[Sigma-L - Market Cycles: Bonds & Rates]]>https://www.sigma-l.net/s/bonds-and-rates-cycleshttps://substackcdn.com/image/fetch/$s_!m_yU!,w_256,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fb3e8bd87-8d09-48d4-a753-99e097da6410_371x371.pngSigma-L - Market Cycles: Bonds & Rateshttps://www.sigma-l.net/s/bonds-and-rates-cyclesSubstackTue, 07 Apr 2026 06:39:28 GMT<![CDATA[TLT (iShares 20+ Year Treasury Bond ETF) | @ 526 Days]]>https://www.sigma-l.net/p/20-year-treasury-bond-cycles-20th-may-2025https://www.sigma-l.net/p/20-year-treasury-bond-cycles-20th-may-2025Tue, 20 May 2025 17:29:30 GMT

ΣL Cycle Summary

A wonderful cycle in this long term analysis of 20 year treasury bonds, via iShares popular ETF TLT. Running at around 526 days (or around 17 months - perhaps the 18 month nominal wave?) this component dominates the spectra at wavelengths below 1000 days over the last 15-20 years. Recently producing sideways price action, the next trough of this significant feature is imminent with a subsequent peak due toward the end of the first quarter 2026.

Time Frequency Analysis

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]]><![CDATA[US 10 Year Treasury Yield - 1st October 2024 | @ 517 Days | + 7.02%]]>https://www.sigma-l.net/p/us-10-year-treasury-yield-1st-october-2024https://www.sigma-l.net/p/us-10-year-treasury-yield-1st-october-2024Tue, 01 Oct 2024 09:46:03 GMT

ΣL Cycle Summary

Over the years many Hurst cycles practitioners have stuck to the mantra of the 18 month nominal wave existing in US stock markets. We, on the other hand, like to see good evidence of a cycle’s existence (via our robust time frequency analysis) and over the last few years, at least, there is little power in that region. However, if one makes the assumption that treasury yields largely move inversely to US stock markets then the following phasing in TNX becomes much more interesting and with wider implications. Indeed in the 10 year treasury yield there is an excellent signal around the bandwidth of the Hurst 18 month nominal wave, this has been the case for quite a few years. The high pass filtered price shows this signal most markedly below, the amplitude stationarity in the sample since 2009 is probably one of the better examples we see in financial markets.

Trade Update

Summary of the most recent trade enacted with this signal and according to the time prediction detailed in the previous report for this instrument, linked below.

Type: Late Sell - US 10 Year Treasury Yield 8th March 2024
Entry: 8th March 2024 @ 4.089
Exit: 30th September 2024 @ 3.802
Gain: 7.02%

Time Frequency Analysis

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]]><![CDATA[US 10 Year Treasury Yield (TNX) - 29th August 2024 | @ 491 Days | + 5.37%]]>https://www.sigma-l.net/p/10-year-yield-cycles-tnx-29th-august-2024https://www.sigma-l.net/p/10-year-yield-cycles-tnx-29th-august-2024Thu, 29 Aug 2024 08:49:09 GMT

ΣL Cycle Summary

This long term wave, which is particularly well phased to price lows in our sample of 8 iterations since 2013, took some time to breach the previous trough during the latest down swing. That low is now breached and leaves a neutral to bullish cycle shape (last cycle low ~ May 2023, see below) with the next trough of this component imminent. A test of the highs around 4.7 and 5 should be targets for the 10 year yield at this juncture with the next peak due mid 2025. Note the relatively wide margin of error (+- 65 days) in the signal details below which is inherently due to the longer wavelength of this cycle.

Trade Update

Summary of the most recent trade enacted with this signal and according to the time prediction detailed in the previous report for this instrument, linked below.

Type: Late Sell - US 10 Year Treasury Yield
Entry: 30th January 2024 @ 4.059
Exit: 28th August 2024 @ 3.841
Gain: 5.37%

Time Frequency Analysis

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]]><![CDATA[iShares Emerging Markets ETF (EMB) - 25th June 2024 | @ 183 Days]]>https://www.sigma-l.net/p/ishares-emb-cycles-25th-june-2024https://www.sigma-l.net/p/ishares-emb-cycles-25th-june-2024Tue, 25 Jun 2024 09:11:00 GMT
aerial view of city buildings during daytime

ΣL Cycle Summary

Within this ETF, which broadly represents emerging market bonds, an excellent periodic feature is present at a wavelength of around 180 days. Stationary in nature from our sample since May 2020, it has punctuated the underlying sideways price action with dominance over the last few years. The phase is currently hard up to peaking, with a larger wave evident around 800 days keeping a lid on price action it seems, being phased as hard down at the time of writing. The shorter wave may well peak early in this scenario (left translated) so we have designated this instrument, in the context of this particular cycle, an early sell.

Time Frequency Analysis

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]]><![CDATA[US 10 Year Treasury Yield - 8th March 2024 | @ 529 Days | + 16.42%]]>https://www.sigma-l.net/p/10-year-treasury-yield-cycles-8th-march-2024https://www.sigma-l.net/p/10-year-treasury-yield-cycles-8th-march-2024Fri, 08 Mar 2024 09:50:15 GMT

ΣL Cycle Summary

The excellent longer term cyclic component in the US 10 Year Treasury Yield moved up over the last year or so in a fairly sharp manner. This comes after the most recent trough of the wave, around April 2023, was established in line with expectations for the phase of this component. Price subsequently made new highs over the 2022 price peaks. The component is now in the process of peaking with a smaller wave forming a pullback to the initial price highs of the longer wave in the last few months. It seems likely that the price peak in January of this year will be the highest price within the cycle (a slightly ‘left translated’ price peak). Hurst aficionados will note the wavelength of this component as 17.38 months, or the 18 month nominal wave. We speculate the next trough of this wave should come around the start of the last quarter 2024, more detail below.

Trade Update

Summary of the most recent trade enacted with this signal and according to the time prediction detailed in the previous report for this instrument, linked below.

Type: Early Buy - US 10 Year Treasury Yield 24th April 2023
Entry: 24th April 2023 @ 3.515
Exit: 8th March 2024 @ 4.092
Gain: 16.42%

Before and After

Signal comparison between our last report and the current time, in chart format.

Time Frequency Analysis

Time frequency charts (learn more) below will typically show the cycle of interest against price, the bandpass output alone and the bandwidth of the component in the time frequency heatmap, framed in white. If a second chart is displayed it will usually show high-passed price with the extracted signal overlaid for visual clarity.

Read more

]]><![CDATA[US 10 Year Treasury Yield (TNX) - 30th January 2024 | @ 495 Days]]>https://www.sigma-l.net/p/treasury-yield-cycles-tnx-30th-january-2024https://www.sigma-l.net/p/treasury-yield-cycles-tnx-30th-january-2024Tue, 30 Jan 2024 10:27:13 GMT

ΣL Cycle Summary

In this new addition to Sigma-L we sample the CBOE US 10 Year Treasury yield (TNX) since 2012 for periodic components of interest. The main detected component with correlation to price, around 500 days average wavelength, has been stable since 2016, gaining correlation and exhibiting an excellent stationarity since 2020. Prior to 2016 there was some frequency modulation, clearly shown in the time frequency plot below. We come in slightly late to the price peak, likely having occurred in October 2023 but projecting the trough around August this year. Certainly the low in 2020 was a periodic driver of larger magnitude and likely the peak in October 2023 was also a peak of this larger wave. The 500 day component is ostensibly the Hurst 18 month nominal wave and is particularly useful because the power of this wave is difficult to discern in stock markets (indeed non-existent in some), so we can indirectly infer it from this instrument, to some degree.

Current Signal Status

Defining characteristics of the component detected over the sample period.

Detected Signal Class: B - learn more
Average Wavelength: 495.23 Days (16.27 Months)
Completed Iterations: 9
Component Yield Over Sample: 460.45% - learn more

Time Frequency Analysis

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]]><![CDATA[US 10 Year Treasury Yield - 14th August 2023 | @ 64 Days]]>https://www.sigma-l.net/p/us-10-year-yield-tnx-14th-august-2023-cycleshttps://www.sigma-l.net/p/us-10-year-yield-tnx-14th-august-2023-cyclesMon, 14 Aug 2023 15:48:53 GMTTrade Update

See also: Live ΣL Portfolio & History

Summary of the most recent trade enacted with this signal and according to the time prediction detailed in the previous post for this instrument, linked below.

Type: Sell - US 10 Year Treasury Yield 10th July 2023
Entry: 10th July 2023 @ 4.006
Exit: 14th August 2023 @ 4.1660
Gain: - 3.99%

Read more

]]><![CDATA[US 10 Year Treasury Yield - 10th July 2023 | @ 64 Days]]>https://www.sigma-l.net/p/us-10-year-treasury-yield-10th-july-cycleshttps://www.sigma-l.net/p/us-10-year-treasury-yield-10th-july-cyclesMon, 10 Jul 2023 08:46:39 GMTTrade Update

Summary of the most recent trade enacted with this signal and according to the time prediction detailed in the previous post for this instrument. For a composite analysis, each constituent’s respective gain over the period is displayed, in descending order. The average of the constituent gain is also shown.

Type: Buy - US 10 Year Treasury Yield 6th June 2023
Entry: 6th June 2023 @ 3.70
Exit: 7th July 2023 @ 4.05
Gain: 9.46%

Current Signal Status

Defining characteristics of the component detected over the sample period.

Detected Signal Class: C - learn more
Average Wavelength: 64.2 Days
Completed Iterations: 11

Time Frequency Analysis

Time frequency charts (learn more) below will typically show the cycle of interest against price, the bandpass output alone and the bandwidth of the component in the time frequency heatmap, framed in white. If a second chart is displayed it will usually show highpassed price with the extracted signal overlaid for visual clarity.

Read more

]]><![CDATA[US 10 Year Treasury Yield - 6th June 2023 | @ 65 Days]]>https://www.sigma-l.net/p/us-10-year-treasury-yield-6th-june-65-day-cyclehttps://www.sigma-l.net/p/us-10-year-treasury-yield-6th-june-65-day-cycleTue, 06 Jun 2023 08:50:46 GMTTrade Update

Summary of the most recent trade enacted with this signal and according to the exact time prediction detailed in the previous post for this instrument. For a composite analysis, each constituent’s respective gain over the period is displayed, in descending order. The average of the constituent gain is also shown.

Type: Sell - US 10 Year Treas…

Read more

]]><![CDATA[US 10 Year Treasury Yield - 5th May 2023 | @ 63 Days | Snippet]]>https://www.sigma-l.net/p/us-10-year-treasury-yield-5th-mayhttps://www.sigma-l.net/p/us-10-year-treasury-yield-5th-mayFri, 05 May 2023 09:04:32 GMTTrade Update

Summary of the most recent trade enacted with this signal and according to the time & price prediction detailed in the previous snippet.

Type: Late Buy - US 10 Year Treasury Yield 20th April 2023
Entry: 20th April 2023 @ 3.54
Exit: 5th May 2023 @ 3.35

Gain: -5.37%

Read more

]]><![CDATA[US 10 Year Treasury Yield - 24th April 2023 | @ 536 Days | Snippet]]>https://www.sigma-l.net/p/us-10-year-treasury-yield-24th-aprilhttps://www.sigma-l.net/p/us-10-year-treasury-yield-24th-aprilMon, 24 Apr 2023 14:53:19 GMTSignal Class & Attributes

Defining characteristics of the component detected over the sample period.

Detected Signal Class: B - learn more
Average Wavelength: 536 Days
Completed Iterations: 8

Time Frequency Analysis

Time frequency charts (learn more) below will typically show the cycle of interest against price, the bandpass output alone and the bandwidth of the component in the time frequency heatmap, framed in white. If a second chart is displayed it will usually show highpassed price with the extracted signal overlaid for visual clarity.

This component is at the last stages of the current wave iteration, pushing hard down currently and troughing in the next couple of months.

Signal Detail & Targets

Here we give more detail on the signal and our expectations for price, given the detected attributes of the component. In most cases the time target to hold a trade for is more important, given we focus on cycles in financial markets. Forthcoming trough and peak ranges are based upon the frequency modulation in the sample.

Phase: Hard Down / Troughing1
FM: +- 54 Days2
AM: 0.0633
Next Trough Range: May 1st - August 17th 2023
Next Peak Range: January 16th - May 3rd 2024

Sigma-L Recommendation: Early Buy
Time Target: ~ 10th March 2024

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DISCLAIMER: This website/newsletter and the charts/projections contained within it are intended for educational purposes only. Results and projections are hypothetical. We accept no liability for any losses incurred as a result of assertions made due to the information contained within Sigma-L. This report is not intended to instruct investment or purchase of any financial instrument, derivative or asset connected to the information conveyed in the report. Trade and invest at your own risk.
1

Signal Phase: This is ‘how far along’ the cycle is in it’s period at nowtime and is related to the predicted price action direction.

2

Signal Frequency Modulation: This is how much, on average, the signal detected varies in frequency (or wavelength) over the whole sample. A lower variance is better and implies better profitability for the component. Frequency modulates relatively slowly over several iterations usually.

3

Signal Amplitude Modulation: This is how much the component gains or loses power (price influence) across the sample, on average. Amplitude modulation can happen quite quickly and certainly is more evident than frequency modulation in financial markets. The more stable the modulation the better.

]]><![CDATA[US 10 Year Treasury Yield - 20th April 2023 | @ 65 Days | Snippet]]>https://www.sigma-l.net/p/us-10-year-treasury-yield-snippethttps://www.sigma-l.net/p/us-10-year-treasury-yield-snippetThu, 20 Apr 2023 13:23:01 GMTSignal Class & Attributes

Defining characteristics of the component detected over the sample period.

Detected Signal Class: C - learn more
Average Wavelength: 65.19 Days
Completed Iterations: 8

Time Frequency Analysis

Time frequency charts (learn more) below will typically show the cycle of interest against price, the bandpass output alone and the bandwidth of the component in the time frequency heatmap, framed in white. If a second chart is displayed it will usually show highpassed price with the extracted signal overlaid for visual clarity.

Signal Detail & Targets

Here we give more detail on the signal and our expectations for price, given the detected attributes of the component. In most cases the time target to hold a trade for is more important, given we focus on cycles in financial markets. Forthcoming trough and peak ranges are based upon the frequency modulation in the sample.

Phase: Trending Up1
FM: +- 10 Days2
AM: 0.063
Next Trough Range: 26th May - 15th June 2023
Next Peak Range: 26th April - 15th May 2023

Sigma-L Recommendation: Late Buy
Time Target: ~ May 5th 2023
Price Target: ~ 3.8

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DISCLAIMER: This website/newsletter and the charts/projections contained within it are intended for educational purposes only. Results and projections are hypothetical. We accept no liability for any losses incurred as a result of assertions made due to the information contained within Sigma-L. This report is not intended to instruct investment or purchase of any financial instrument, derivative or asset connected to the information conveyed in the report. Trade and invest at your own risk.
1

Signal Phase: This is ‘how far along’ the cycle is in it’s period at nowtime and is related to the predicted price action direction.

2

Signal Frequency Modulation: This is how much, on average, the signal detected varies in frequency (or wavelength) over the whole sample. A lower variance is better and implies better profitability for the component. Frequency modulates relatively slowly over several iterations usually.

3

Signal Amplitude Modulation: This is how much the component gains or loses power (price influence) across the sample, on average. Amplitude modulation can happen quite quickly and certainly is more evident than frequency modulation in financial markets. The more stable the modulation the better.

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