Bond Yield Analysis

UK bond yields dropped by 0.09% the other day. Sounds boring but it could cost or save your business thousands. On paper, the fall from 4.61% → 4.52% in 10-year gilts looks like a non-event. A ripple caused by political messaging, investor nerves, or policy noise. But in reality? If you’re running a business especially one that’s growing fast this matters more than you think. Here’s how even small yield shifts hit founders: Loan & Debt Costs → Many SME and scale-up loans track bond-linked swap rates → A 0.1% rate bump on £250K = £250/year → 2-point rise over 3 years = £15K+ in pure interest This isn’t macro theory — it’s your burn rate. Team Pressure: Mortgages → Gilt shifts = fixed mortgage shifts → Higher payments = tighter household budgets → Result? More financial stress, more churn risk You can’t control rates, but you can support your team through them. Investor Confidence & Deal Terms → Higher yields = tighter capital → Valuations adjust, raise timelines stretch → Even strong revenue stories face headwinds It’s not just your deck, it’s the cost of capital landscape behind it. Pricing & Forecasting Strategy → Yields rise when inflation or fiscal doubt creeps in → That filters into: B2B: more negotiation B2C: pricing sensitivity Ops: tighter supplier terms Yield shifts = behaviour shifts Founder Insight: You don’t need to be an economist. But you do need to know what moves your margins. The best operators I know: → Zoom out monthly to check macro signals → Build buffer into every plan from CAC to COGS Even if you never say “gilts” again understanding what shapes the climate around your growth is a real advantage. If you’re planning Q3–Q4 strategy, now’s the time to pressure-test: What if borrowing costs rise 0.5%? What if customers delay payments? Do you have a real buffer or just hope? Macro isn’t the threat. Not adapting is. Are you building a margin-of-safety mindset this half of the year?

Advanced Yield Curve Fitting in Fixed Income Analysis This post explores key yield curve fitting models, their practical applications, and how they support strategic decision-making in fixed income portfolios. 1. Why Yield Curve Fitting Matters in Fixed Income Yield curves reflect the market’s view on interest rates and are used extensively in fixed income analysis. Properly fitting a yield curve is essential for: -> Pricing Bonds Accurately – Provides fair valuation for bonds across different maturities, even when direct market quotes are unavailable. -> Managing Interest Rate Risk – Enables precise calculations of duration, convexity, and risk exposure, critical for hedging strategies. -> Market Forecasting & Rate Expectations – Helps in estimating forward rates, which guide investment and monetary policy decisions. -> Portfolio Optimization – Aligns asset allocation and risk strategies with yield curve movements, improving overall performance. 2. Key Models for Yield Curve Fitting Different models are used to estimate the yield curve, each with its own strengths and trade-offs. The choice of model depends on data availability, market conditions, and the intended application. -> Bootstrapping – A step-by-step method used to extract zero-coupon yields from observed bond prices. This approach is widely used in market environments where accuracy in short-term maturities is crucial. -> Cubic Spline Interpolation – A flexible, non-parametric technique that ensures a smooth yield curve by fitting piecewise polynomials between different maturities. It is useful when a precise, smooth curve is required, but it lacks economic interpretability. -> Nelson-Siegel-Svensson (NSS) Model – One of the most widely used parametric models in fixed income markets, capturing the yield curve’s level, slope, and curvature. This model is particularly effective for forecasting and portfolio risk management. -> Hermite Interpolation – A refinement over cubic splines that provides a smoother transition between maturities, making it useful for yield curve modeling in derivatives pricing. 3. Handling Maturities in Different Models Yield curve models vary in how they treat different maturities: -> Bootstrapping builds the curve sequentially, ensuring accurate short-term estimates but lacking a smooth fit for longer maturities. -> Spline-based models (cubic or Hermite) use observed maturities as key points and apply smooth transitions, making them ideal for market surveillance. -> Parametric models like NSS fit the entire yield curve simultaneously, balancing flexibility with economic interpretability, making them useful for central banks and fixed income investors. As fixed income markets evolve, the ability to apply advanced yield curve models effectively will remain a key differentiator for traders, analysts, and institutional investors. #FixedIncome #YieldCurve #QuantFinance #RiskManagement #PortfolioOptimization #InterestRates #FinancialModeling

The 𝗬𝗶𝗲𝗹𝗱 𝗦𝘂𝗽𝗲𝗿𝗰𝘆𝗰𝗹𝗲: A Perfect Storm Pushing G7 Bond Yields to 20-Year Highs 📉 Last week, we witnessed a continuation of a powerful trend: the global bond selloff. This isn't just a blip; G7 government bond yields (10-year maturity and higher) have surged to their highest levels since 2004. (see charts from Bloomberg) Here are the four key catalysts creating this "perfect storm" for bond investors: 1️⃣ 𝗧𝗵𝗲 𝗨𝗻𝗱𝘆𝗶𝗻𝗴 𝗜𝗻𝗳𝗹𝗮𝘁𝗶𝗼𝗻𝗮𝗿𝘆 𝗦𝗽𝗮𝗿𝗸 The primary culprit is inflation. While the headlines might not reflect immediate runaway inflation, the underlying pressures remain stubbornly elevated.  The primary driver? "𝗘𝗻𝗲𝗿𝗴𝘆 𝗽𝗿𝗶𝗰𝗲𝘀". 2️⃣ 𝗧𝗵𝗲 𝗗𝗲𝗯𝘁 𝗔𝘃𝗮𝗹𝗮𝗻𝗰𝗵𝗲: 𝗔 𝗙𝗹𝗼𝗼𝗱 𝗼𝗳 𝗡𝗲𝘄 𝗦𝘂𝗽𝗽𝗹𝘆 Governments worldwide are running persistently large deficits. To fund this spending, they are issuing an ever-increasing mountain of bonds. The sheer volume of new bond issuance creates an oversupply, which pushes prices down (and yields, which move in the opposite direction, up). 3️⃣ 𝗧𝗵𝗲 𝗘𝗻𝗱 𝗼𝗳 𝗤𝘂𝗮𝗻𝘁𝗶𝘁𝗮𝘁𝗶𝘃𝗲 𝗘𝗮𝘀𝗶𝗻𝗴 For years, central banks, led by the US Federal Reserve, were the biggest buyers of bonds. This policy, known as 𝗾𝘂𝗮𝗻𝘁𝗶𝘁𝗮𝘁𝗶𝘃𝗲 𝗲𝗮𝘀𝗶𝗻𝗴 (𝗤𝗘), artificially inflated bond prices and suppressed yields. Those days are over. The Fed's balance sheet is now potentially shrinking, meaning they are moving from being a major net buyer to a potential net seller. This 𝗾𝘂𝗮𝗻𝘁𝗶𝘁𝗮𝘁𝗶𝘃𝗲 𝘁𝗶𝗴𝗵𝘁𝗲𝗻𝗶𝗻𝗴 removes a massive source of demand from the market, allowing yields to rise to a more natural, market-determined level. 4️⃣ 𝗧𝗵𝗲 𝗦𝗵𝗶𝗳𝘁 𝗶𝗻 𝗥𝗶𝘀𝗸 𝗦𝗲𝗻𝘁𝗶𝗺𝗲𝗻𝘁 Amidst a landscape defined by deglobalization and increased geopolitical fragmentation, the risk premium investors demand has risen significantly. Investors are now requiring: • 𝗔 𝗵𝗶𝗴𝗵𝗲𝗿 𝘁𝗲𝗿𝗺 𝗽𝗿𝗲𝗺𝗶𝘂𝗺 - the extra yield they demand for holding a longer-term bond and tying up their capital for longer. • 𝗔 𝗹𝗮𝗿𝗴𝗲𝗿 𝗶𝗻𝗳𝗹𝗮𝘁𝗶𝗼𝗻 𝗽𝗿𝗲𝗺𝗶𝘂𝗺 - the compensation they require for the risk that inflation will erode the purchasing power of their returns. 💡The clear message for investors is that 𝗿𝗮𝘁𝗲𝘀 𝘄𝗶𝗹𝗹 𝘀𝘁𝗮𝘆 𝗵𝗶𝗴𝗵𝗲𝗿 𝗳𝗼𝗿 𝗹𝗼𝗻𝗴𝗲𝗿.  This isn't just a temporary phase; it's a structural shift in the global financial landscape. #GlobalBonds #CentralBanks #InterestRates #Inflation

Market narratives are dangerous when they get too far ahead of themselves. It's easy to look at historically low implied yields for equities and think that bond yields look positively juicy. The price we pay for equities has risen relative to expected earnings, driving down the implied yield. At the same time, bond yields have risen dramatically. For investors who have lived through the post-GFC yield dearth (negative yields, anyone?), bond yields are appealing. The appeal increases when market narratives compare yields across asset spaces without mentioning the key differences in the metrics. All yields are not created equal. Here is the observation: Yields of Treasuries, Cash, Corporate bonds and Equities are tightly clustered together (08/29 data). - Treasury bonds (Bloomberg Treasury Index) = 3.97%  - Corporate bonds (Bloomberg Corporate Index) = 4.91% - Cash (1-3 month bills) = 4.21% - Equities (S&P 500 12 mo forward earnings yield) = 4.11% This might lead one to conclude that bonds are cheap versus riskier assets like equities. Here are the problems with that simple narrative: - Comparing equity yields to bond yields is flawed. Bond yields are highly predictive of bond returns and implied equity yields say little about future equity returns. - The level of yield convergence is likewise unpredictive of future equity returns: We created a convergence indicator (essentially a cointegration residual) to look at 1) the relationships of yield convergence to forward equity returns and 2) the relationship of convergence to relative forward equity returns (forward equity return versus forward bond returns). Conclusion: Since 1995 there is no correlation between yield convergence and 3-month, 6-month or 12-month S&P500 forward returns or those returns relative to forward bond returns. There are countless discrete examples that illustrate high convergence of yields does not translate into poor forward equity returns and vice versa. Here are a couple: - In 1997, average Cash yield 5%, Treasuries 6% and Equities 5% - high convergence: Avg. 12-month forward S&P 500 return was 27% - In 2008, average Cash 1.2%, Treasuries 2.8% and Equities 7.2% – low convergence: Avg. 12-month forward S&P 500 return was -16.5% Some observations: - The earnings yield of equities is remarkably stable relative to fixed income’s yield volatility. Does this observation help with allocation decisions? Maybe. Maybe not. - Historical context matters. The brutal suppression of bond yields by the Fed from 2009 to 2021 contributed massively to the wide spread in asset yields and our perception of the ‘fair value’ of those relationships. The bottom line: The last 5 years have been a reality check for bonds. The Aggregate bond index is annualizing negative 80 bps. Long treasuries come in close to negative 9% a year. Bonds might be useful going forward, but just because they’ve been coming up tails for the last 5 years does not mean they are going to start coming up heads.

We're Having One of The Worst 10-Year Runs for Treasuries This Century The 10-year annualized return for the iShares 20+ Year Treasury ETF (TLT) currently sits at -0.94% (per year). That means investors in long-term government bonds have lost nearly 1% per year for a decade, even after accounting for income. That’s a dramatic departure from the long-term average of 5.34%—and it’s left many wondering: Do bonds still make sense in a diversified portfolio? Here’s what’s often overlooked: Bonds are one of the few asset classes where we can reasonably forecast future returns. Unlike equities—where even long-term outcomes can be highly unpredictable—bond math gives us a powerful tool: the current yield. While current yield doesn’t tell us much about what will happen over the next 12–24 months, it does a surprisingly accurate job of predicting average annual returns over the next 10 years. So what’s the yield on 20-year Treasuries today? ➡️ 4.93% That suggests long-term bond investors buying today could see returns near 5% annually over the next decade—a strong reversal from the last 10 years. Yes, recent returns have been dismal. But for long-term investors, that pain may have set the stage for much better outcomes ahead. This is your reminder: Don’t abandon any investment based on backward-looking results. Focus on where we are today—and what the math says about the road ahead.

EndGame Macro: The 30-year TIPS yield just crossed 2.72% a level we haven’t seen in decades. It means investors are demanding 2.72% above inflation to hold that bond for the next three decades. That’s a seismic move. Here’s what it’s telling us: 1. Investors Want Real Compensation: Markets are demanding a much higher return after inflation to hold long-duration government debt. That implies fading trust in both inflation stability and fiscal prudence. 2. A Crack in Long-Term Confidence: When real yields rise sharply, it often means the market is starting to price in risk either from uncontrolled inflation, weakening Fed credibility, or excess debt issuance that’s swamping demand. 3. Policy Has Lost Its Anchoring Effect: Historically, the Fed’s forward guidance kept long-end real yields contained. That’s breaking down. Today’s surge is not due to optimism it’s a stress signal. 4. Structural, Not Cyclical: This isn’t a one-off blip from CPI volatility or a Fed hike surprise. It reflects long-term structural stress: debt saturation, shrinking foreign demand, and a shrinking pool of natural buyers for 30-year bonds. Why It Matters to You? Rising TIPS yields can reshape the entire investment landscape. It affects: •Long-term mortgage rates •Corporate borrowing costs •Valuations for equities and real assets •Portfolio hedging decisions It’s also a warning sign. When the market demands this much compensation for holding “safe” U.S. debt over 30 years, it means the system is pricing in uncertainty, not stability. Bottom Line: The 30-year TIPS is flashing red not because inflation is rising now, but because long-term belief in the system’s ability to contain it is breaking down. It’s not a blip it’s a barometer of structural fragility.

Day 21: Key Measures in Fixed-Income Analysis for Interest Rate Sensitivity In fixed-income analysis, investors and risk managers use several key measures to quantify a bond's or portfolio's sensitivity to changes in interest rates. These measures help understand the risk and behavior of fixed-income securities in response to interest rate fluctuations. 🏦 💲 🚀 1. Duration ⌛ ⏲️ Duration measures the sensitivity of a bond's price to changes in interest rates. It is expressed in years and represents the weighted average time to receive all cash flows (coupon and principal). Types of Duration: 1. Macaulay Duration:⌛ ⏲️ The weighted average time to receive cash flows. Useful for understanding a bond's time profile but less common in market risk analysis. 2. Modified Duration:⌛ ⏲️ Measures the percentage change in a bond's price for a 1% change in yield. Use Case: Assesses price sensitivity to small interest rate changes. 3. Effective Duration:⌛ ⏲️ Used for bonds with embedded options (e.g., callable bonds). Reflects price sensitivity to interest rate changes, accounting for option-like features. 2. Convexity 📊 ✈️ Convexity measures the curvature in the relationship between a bond's price and yield. It captures the second-order sensitivity of a bond's price to changes in interest rates. 3. Yield Measures Yield to Maturity (YTM): 🎢 🏦 The annualized rate of return earned if the bond is held to maturity. Helps in comparing bonds with different coupons and maturities. Current Yield: 🎢 🏦 Annual coupon payment divided by the current bond price. Yield Spread:🎢 🏦 The difference between the yields of two bonds is often used to measure credit or liquidity risk. Duration and convexity are foundational tools in fixed-income analysis. They provide insights into price sensitivity and help investors and risk managers assess and mitigate interest rate risk. By combining these metrics with other measures like PVBP and key rate duration, professionals can manage bond portfolios more effectively. Let me know if you'd like further calculations or examples! 💸 🗝️ 💲 #Quant #Finance #QuantitativeFinance #Derivatives #MarketRisk #RiskManagement #Trading #Risk #InterestRates #StressTesting

Why have bond yields risen so much since the Fed cut by 50bp? 1 The data have been firm, so there’s a fear that the Fed did too much 2 Breakeven inflation rates have risen significantly. However, you have to ask why the 10-year b/e , and the nominal, fell so much previously. It looks like the market yield undershot. If we buy the Fed’s long run estimate of 2% inflation and 2.9% Fed funds, a 10s to 3month rate spread of 125bp would give us roughly 4.2% on the 10- year, or where we are now. So a decent chunk of the rise in yields looks like s correction from an overly-bullish view. 3 The market priced in fed funds lower than the Fed’s Survey of Economic Projections (SEP) and now prices in a bit higher. It got ahead of itself (and the Fed). 4 Consistent with this overshooting, the market was willing to accept a negative term premium on the two year. That’s now gone. It’s stopped fighting the Fed. 5 The market may be increasing its odds of a Trump victory. An expanded budget deficit from already engorged levels, and import controls, will boost inflation and increase bond issuance. Threats to change @federalreserve leadership increase future inflation risks. 6 Higher oil prices since September may reflect higher odds of an Israel/Iran escalation, though the oil price dipped recently. 7 Geek alert: in many macro models, easier monetary policy today delivers expectations of tougher policy down the track. This suggests the market thinks the Fed overdid the first cut. Overall assessment: A The market got ahead of itself by pricing in a more aggressive Fed, encouraged by the 50bp cut. This has corrected. B In the light of subsequent data, the market sees the 50bp cut as too aggressive. C Firmer data have boosted long run growth and inflation expectations, and therefore market views of where future Fed policy needs to be D There are concerns over future fiscal prospects The Fed will be concerned by the market’s reaction. It won’t want to see a tightening of policy coming through a further bond sell off if it cuts further, so it will cite “data dependency” to soft pedal.