Skip to main content
V-Lab
V-Lab

Fixed Income Analysis: User Guide

Understand yield curve forecasts using the ESR regime-switching model

Contents

  • Page Overview

  • Essential Concepts

  • Navigation Guide

  • Data Interpretation

  • Practical Applications

  • Understanding Data

  • Troubleshooting

  • Tips & Best Practices

Page Overview

Fixed Income Analysis uses the ESR regime-switching model (named for authors Engle, Siriwardane, and Roussellet) to forecast interest rates across the yield curve. The model identifies whether rates are in an upward, downward, or stable regime and projects how the term structure will evolve.

The page displays two main visualizations: a Term Structure chart showing rates across all maturities, and a Single Maturity chart showing how a specific rate evolves over time. Both include confidence bands reflecting forecast uncertainty.

Term Structure Chart

Forecasted yield curve showing the median forecast with confidence bands across all maturities. Diamond markers show actual realized rates, color-coded by whether they fell within the forecast bands.

Single Maturity Forecast

Time series showing how a specific maturity rate is expected to evolve. An orange line overlays actual realized rates for comparison with the forecast.

Interactive Controls

Horizon slider to set forecast period, maturity dropdown for detailed analysis, and Yields/Forwards toggle to switch curve views.

Forecast Accuracy

Compare forecasts to actual outcomes. An accuracy badge shows what percentage of realized rates fell within the confidence bands.

Was this section helpful?
Essential Concepts

These terms are essential for understanding V-Lab's fixed income forecasts:

Term Structure

The relationship between interest rates and bond maturities at a point in time. The term structure chart shows rates from short-term (3-month) to long-term (30-year) maturities.

Why it matters: The term structure reveals market expectations about future rates and economic conditions. Changes in its shape signal shifts in monetary policy outlook or recession risk.

ESR Model (Regime-Switching)

The ESR model (named for authors Engle, Siriwardane, and Roussellet) identifies three interest rate regimes: Upward (rates rising), Downward (rates falling), and Status-quo (rates stable). The model estimates which regime currently applies and forecasts accordingly.

Why it matters: Regime-switching captures how interest rate behavior changes fundamentally during Fed tightening vs easing cycles. This produces more realistic forecasts than models that assume constant dynamics.

Regime States

The ESR model classifies rate environments into three states: Upward regime (rates follow an upward trend with drift), Downward regime (rates follow a downward trend with drift), and Status-quo regime (rates mean-revert around a stable level). The model uses Fed policy rate data to identify regime transitions.

Why it matters: Regime behavior differs fundamentally: Upward and Downward regimes show trending behavior, while Status-quo shows mean-reversion. Check the current regime to contextualize forecasts. Regime transitions often coincide with major Fed policy shifts.

Nelson-Siegel Factors

The model decomposes the yield curve into three factors: Level (overall rate height), Slope (difference between long and short rates), and Curvature (the hump or bow shape in the middle).

Why it matters: These factors explain most yield curve movements. Level shifts affect all bonds equally. Slope changes impact duration strategies. Curvature affects barbell vs bullet positioning.

Yields vs Forward Rates

Yields (spot rates) are today's rates for bonds of various maturities. Forward rates are implied future rates derived from the current curve, representing what the market expects rates to be at future dates.

Why it matters: Use the Yields view for current positioning. Use Forwards to see market-implied expectations. If your forecast differs from forwards, you may see trading opportunities.

Confidence Bands

The upper and lower bound lines around the forecast showing the 5th to 95th percentile range of outcomes. The model runs 1000 Monte Carlo simulations of possible rate paths; the bands capture 90% of these simulated outcomes.

Why it matters: Narrow bands mean the simulated paths cluster tightly, indicating higher forecast confidence. Wide bands mean paths diverge significantly, indicating greater uncertainty. Band width is one factor some investors consider when sizing positions.

Curve Movements

The yield curve can change shape over time in three main ways. Steepening occurs when the gap between long-term and short-term rates widens, either because long rates rise more than short rates, or because short rates fall more than long rates. Flattening is the opposite: the gap narrows as long and short rates converge. Inversion happens when short-term rates actually exceed long-term rates, turning the normally upward-sloping curve upside down.

Why it matters: When the curve steepens, long-duration bonds tend to lose value relative to short-duration bonds. When it flattens, the opposite occurs. Curve inversion is closely watched because it has historically preceded economic recessions, though the timing varies.

Forecast Horizon

The time period over which the model projects future rates. Longer horizons show further into the future but with wider confidence bands due to increased uncertainty.

Why it matters: Match the horizon to your investment timeline. Short horizons for tactical trades, longer horizons for strategic positioning. Remember that uncertainty compounds over time.

Was this section helpful?
Page Layout

The page is organized into these main sections:

  • 1. Header with Controls

    Page title with the Yields/Forwards toggle to switch between spot rates and implied forward rates, a date selector to choose the forecast date, and a download button to export all data for the selected month.

  • 2. Term Structure Chart

    Main yield curve showing forecasted rates across maturities (3M to 30Y). Includes a horizon slider to set the forecast period (1 week to 5 years). Diamond markers show actual realized rates at each maturity, with an accuracy badge indicating how many fell within the confidence bands.

  • 3. Single Maturity Forecast

    Time series showing how a specific maturity rate evolves over the forecast horizon. Use the maturity dropdown (3M, 6M, 1Y, 2Y, 3Y, 5Y, 7Y, 10Y, 20Y, 30Y) to select which rate to analyze. An orange line shows actual realized rates alongside the forecast.

Using the Interactive Controls

Master these controls to customize your analysis:

  • Horizon Slider

    Drag to set how far ahead to forecast (1 week to 5 years). Longer horizons show more of the expected rate path but with wider uncertainty bands.

  • Yields/Forwards Toggle

    Switch between Yields (today's spot rates at each maturity) and Forwards (implied future rates derived from the current curve).

  • Maturity Dropdown

    Select a specific maturity to see its detailed forecast in the Single Maturity chart below. Available maturities range from 3-month to 30-year.

Reading the Term Structure Chart

The term structure chart displays forecast lines and actualization markers:

  • Median Forecast (Center Line)

    The middle line shows the median (50th percentile) forecast for rates at each maturity. This represents the model's central expectation for where rates will be at the selected horizon.

  • Upper Confidence Band

    The upper line shows the 95th percentile of simulated outcomes. Rates could be this high, but there is only a 5% probability of exceeding this level.

  • Lower Confidence Band

    The lower line shows the 5th percentile of simulated outcomes. Rates could be this low, but there is only a 5% probability of falling below this level.

  • Actualization Markers (Diamonds)

    Diamond-shaped markers show actual realized rates at each maturity. Green solid diamonds indicate the actual rate fell within the confidence band. Red hollow diamonds indicate the actual rate fell outside the band. These markers only appear for dates that have already passed. If viewing a recent forecast date, you may not see diamonds until enough time has elapsed for actual rates to be observed.

  • Accuracy Badge

    Displayed in the chart header, this badge shows how many actualizations fell within the confidence bands (e.g., '7/9 within band'). A higher percentage suggests the model's uncertainty estimates are well-calibrated.

Using the Single Maturity Forecast

Focus on a specific maturity for time-series analysis:

  • Select Your Maturity

    Choose the maturity most relevant to your portfolio. The 10-year is often a benchmark; shorter maturities respond more to Fed policy.

  • Time Series View

    Chart shows the rate path from today through the forecast horizon. Watch for trend direction and any inflection points.

  • Actualization Line (Orange)

    An orange line overlays actual realized rates alongside the forecast. Compare this line to the median forecast to see how well the model predicted rates. Where the orange line falls within the confidence band, the forecast captured the actual outcome. This line only extends through dates that have already passed. For recent forecast dates, the line may be short or absent until actual rates become available.

  • Hover for Exact Values

    Hover over the chart to see precise rate values and confidence intervals at any date along the forecast path. The legend also displays the actual realized rate at that point, allowing direct comparison with the forecast.

Was this section helpful?

Use the ESR model outputs to understand expected rate movements and inform your positioning decisions:

Key Patterns to Watch

Important yield curve patterns and their implications:

  • Curve Steepening

    Long rates rising faster than short rates. Often occurs early in economic expansions. Long-duration bonds may underperform; consider barbell strategies.

  • Curve Flattening

    Long-short rate gap narrowing. May indicate Fed tightening or slowing growth expectations. Long-duration bonds may outperform on a relative basis.

  • Curve Inversion

    Short rates above long rates. Historically precedes recessions with a 12-18 month lead. If the forecast shows inversion, consider defensive positioning.

Was this section helpful?

The ESR model forecasts support a range of fixed income investment and risk management activities:

Duration & Curve Positioning

Adjust portfolio duration based on rate direction forecasts. If the ESR model predicts rising rates in an Upward regime, consider shortening duration. Use curve shape forecasts to implement steepener or flattener trades. The confidence bands help size positions. Wider bands suggest smaller, hedged positions.

Interest Rate Risk Management

Use the forecast distribution to stress test portfolio performance across the confidence band range. Design interest rate hedges sized appropriately for the forecast uncertainty. The regime identification helps assess whether current hedges are appropriate for the rate environment.

Research & Model Validation

Track forecast accuracy using the actualization markers and accuracy badge, which show what percentage of realized rates fell within the confidence bands. Study how regime transitions affect forecast errors by comparing the orange actualization line to the median forecast across different time periods. The ESR model's explicit regime structure provides testable hypotheses about rate dynamics during different monetary policy phases.

Was this section helpful?

The forecasts are generated using the ESR-NS-AQD model (Engle-Siriwardane-Roussellet with Nelson-Siegel factors and Auto-Quasi-Difference), a regime-switching framework specifically designed for interest rate forecasting.

Data Sources

The analysis uses U.S. Treasury zero-coupon yields derived from actively traded Treasury securities, along with Federal Reserve policy rate data for regime identification. Yield data is updated daily. The model re-estimates parameters daily but only stores month-end values. There may be some lag depending on when source data arrives, particularly for Fed Funds policy rate data.

Technical Documentation

For detailed model specifications and methodology, visit the Fixed Income section under the documentation link in the main navigation bar.

Was this section helpful?
Common Questions
Why are the confidence bands so wide?

Bands represent the 5th to 95th percentile range from 1000 Monte Carlo simulations. They widen at longer horizons as uncertainty compounds. The GJR-GARCH volatility model means bands expand during volatile periods. This reflects genuine uncertainty, not model error. If bands seem too wide, try a shorter forecast horizon.

Why does the forecast show an unusual curve shape?

The ESR model can produce non-standard shapes when historical patterns suggest unusual dynamics, such as forecasting an inversion based on current regime conditions. Unusual shapes often reflect genuine model predictions rather than errors. Interpret them in context of current monetary policy.

How do I download the forecast data?

Click the download button in the header toolbar next to the date selector. You must be logged in to download data. Data exports as CSV including point forecasts and confidence band boundaries for the selected month.

What do the diamond marker colors mean?

Green solid diamonds indicate the actual realized rate fell within the 90% confidence band (between the 5th and 95th percentile forecasts). Red hollow diamonds indicate the actual rate fell outside this range. The accuracy badge in the chart header summarizes how many maturities fell within the bands.

Why is the accuracy percentage low for some forecasts?

Low accuracy often occurs during regime transitions or unexpected Fed policy shifts. The model's 90% confidence bands are designed to capture 90% of outcomes on average. During volatile periods or structural breaks, more actualizations may fall outside the bands. This indicates genuine forecast difficulty rather than model failure.

Why don't I see any diamond markers or the orange actualization line?

Actualizations only appear for forecast horizons that have already passed. By default, the page displays the most recent available forecast date, which means the entire forecast period is still in the future and no actual rates exist yet. To see actualizations, use the date selector to choose a date far enough in the past that some or all of the forecast horizon has elapsed. For example, if you want to see how a 1-year forecast performed, select a date at least one year ago.

Understanding the Model

Common questions about interpreting ESR model outputs:

Why are there large forecast errors during Fed policy changes?

Policy transitions create regime changes that are difficult to predict in advance. The ESR model identifies regimes (Upward, Downward, Status-quo) based on recent history. When the Fed unexpectedly shifts policy, the model may initially continue forecasting based on the prior regime until enough data confirms the new regime.

Can I use these forecasts for corporate bonds?

These are government bond (risk-free rate) forecasts. For corporate bonds, you'll need to add a credit spread estimate based on the issuer's credit quality, sector, and economic conditions. The Treasury forecasts provide the base rate; credit spreads move semi-independently.

What does a forecasted inversion mean?

An inverted yield curve (short rates above long rates) has historically preceded recessions. If the ESR model forecasts inversion, it's projecting that near-term rates will exceed long-term rates, often reflecting expectations of Fed tightening followed by eventual cuts. This is a signal worth noting for risk management.

Was this section helpful?

Use these workflows to efficiently analyze interest rate forecasts:

Working with Forecast Uncertainty

Interest rate forecasts are probability-weighted estimates, not predictions. The confidence bands show the range where rates could reasonably fall. For risk management, consider the full band range, not just the point forecast. Band width reflects forecast uncertainty and is one input some investors use when evaluating position sizing.

Regime-Aware Analysis

The ESR model's regime structure is key to interpretation. In an Upward regime, the model expects rates to trend higher, and forecasts will reflect this bias. In a Downward regime, expect declining rate forecasts. During regime transitions (often around major Fed meetings), forecast uncertainty increases. Check the model documentation for current regime classification.

Using Actualizations for Model Assessment

The diamond markers and orange actualization line show how past forecasts compared to actual outcomes. A high accuracy percentage suggests the model's uncertainty bands are well-calibrated. Look for patterns in missed forecasts: consistent misses at certain maturities may indicate systematic bias. Use actualization data to calibrate your confidence in current forecasts.

Was this section helpful?

Was this page helpful?