Fixed Income Securities

PRIMER: The Unwinding of Leveraged Bond Trades That’s Shaking Markets. Last week, heavily leveraged bond trades were unwound in a spectacular fashion. And while the worst might be behind for now, I don’t see a structural fix to this bond market imbalance. There are two very popular, heavily leveraged trades in bond markets: swap spreads and basis trades. Both involve going long the cash Treasury bond, and going short something against it: the basis trades uses the Treasury future as short leg, and the swap spread uses interest rate swaps. In both cases, the trades involve a large use of leverage because the purchase of the cash Treasury bond is financed using the repo market: for a $100M trade in basis or swap spreads, due to repo market funding hedge funds must only use a tiny portion (~2-5%) of the needed capital to enter the transaction. Let’s focus on the swap spread trade for a second. As long as repo markets remain orderly, investors can use it to fund purchases of 30-year US Treasuries, pay a fixed 30-year interest rate swap against it and earn a whopping 90 (!) bps per year in ‘’swap spreads’’ - see chart below. But why on earth would investors be able to earn such a premium on US government bonds? It’s because of regulation and the growing supply/demand imbalance problem in US Treasury markets. Bank regulation has crippled the ability of market makers to warehouse risks, which means their ability to absorb large issuance of Treasuries on their balance sheet has diminished. On top of it, Treasury departments of US banks are penalized for owning large amount of Treasuries from regulations like the Supplementary Leverage Ratio (SLR) which don’t exempt USTs from its calculations. All of this is happening at a time when the supply of US Treasuries has dramatically grown because of persistent budget deficits, forcing dealers to swallow bonds at auctions and testing their limits. Given the supply/demand imbalance, the marginal buyer of US Treasuries tends to be the leveraged hedge fund which gets involved in basis or swap spread trades and demands a hefty premium as compensation. And this fragile system holds until it doesn’t. In the last 10 days, several hedge funds were hit by margin calls given turbulent markets. To meet these margin calls, they had to de-risk their portfolios and sell every asset they could – including Treasuries. As Treasuries got caught in the deleveraging mania, basis trades and swap spreads suffered. The first stop losses in these highly leveraged trades were hit, and then a self-fulfilling VaR shock occurred. All hedge funds involved in the same trade had to deleverage at the same time without a marginal buyer of last resort. Ouch. And it’s not clear how this problem will get structurally fixed - so watch out! Thanks for reading and have a beautiful day, Alf

Bond prices move opposite to yields But why does this inverse relationship exist? The answer lies in simple demand and supply. Let's see... Assume the Government of India issues a bond which pays 8% interest, and has a tenure of 1 year. If the face value of this bond is Rs 100, it will pay the bond holder 108 at the end of the first year. The final payout is fixed (and hence the name fixed income). If we pay Rs 100 for this bond, we will make an 8% return If we pay > 100, the return will be lower If we pay < 100, the return will be higher Now if interest rates in the economy have changed, the Government will have to issue new bonds at a different rate. Say it issues another 1-year bond with 10% interest, this bond will pay Rs 110 at the end of the first year. Everyone would want to buy this bond, instead of the earlier one. All things being same, anyone holding the earlier bond will try to sell that, and buy the new one. The earlier bond will see a huge supply, which should result in prices going down. Prices will go down to the point where the return on the old bond matches the return on the new bond (10%). Thus, as the interest rates increase, the demand for the new bonds is higher, and the price of existing bonds drops. If the new government bond offered lower interest, demand for existing bonds would have increased, increasing their price. And that explains the inverse relationship between bonds yields and bond prices. Why is it important? As a #fixedincome #investor, if yields are going up, then existing bond prices will fall with rising yields. And fixed income, which appears to be a safe investment, can become risky in a rising yield environment. ---- I try to teach practical #finance concepts through my writing. Follow me (Peeyush) if you are building a career in finance and do check out my earlier posts.

As someone who grew up in the leveraged finance markets, I can say with confidence that today's high yield market is not the one we all once knew. My team and I have spent considerable time analyzing the evolution of global credit markets and what it means for asset allocation, portfolio construction, and risk management. And with all the twists and turns of the past decade, one of the quietest transformations has been hiding in plain sight: high yield. That is why I wanted to share my recent Financial Times op-ed on why we believe the high yield market is positioned for its second act. ➤ The asset class has fundamentally changed. With a record 57% of US high yield and 68% of European high yield rated BB, lower software exposure relative to loans and direct lending, shorter duration than at almost any point in the past 15 years, and first lien secured bonds at an all-time high of 33% of the US market, this is not your grandfather's junk bond market. ➤ And the technical backdrop is shifting in its favor. As CLO appetite has grown more selective and direct lending terms have tightened, more issuers are rediscovering what high yield has always offered: a deep, diversified, and durable investor base that prices risk when others step back. It did it through the GFC. It did it through COVID and it is doing it again now. ➤ For investors, despite tight spreads, the all-in yield remains compelling in absolute terms and increasingly attractive on a risk-adjusted basis relative to alternatives carrying more risk for only modestly more yield. The junk bond label was earned forty years ago and the market has spent the last decade writing its new chapter. I hope you will give the op-ed a read, and for a more global deep-dive on how KKR is thinking about the opportunity set, my colleagues Jeremiah Lane, Eddie O'Neill, and I recently published “High Yield’s Second: What AI Revealed about Credit Quality" 📎Read it here: https://go.kkr.com/4w7bXWK

Considerations for the High Yield Bond Market: The BB-rated High Yield (HY) bond market has shown strong performance, with favorable news recently related to growth and inflation.  Fundamentally, the companies represented in the HY Index have a favorable upgrade-to-downgrade ratio. BB-rated bonds constitute 50% of the HY market, distinguishing them from lower-rated B and CCC companies. BB HY bonds typically feature fixed rate, comparatively lower coupons, resulting in lower liability costs and more manageable debt service. In Contrast, the CCC-rated segment shows a concerning trend, with an upgrade-to-downgrade ratio below 0.5 (2x as many downgrades). The credit quality dispersion, shown in the chart below, reveals that BB vs. CCC-rated bonds trade at a spread margin of ~400 to ~1,200 bps, currently sitting inside of 750 bps.  While CCC credits can generate substantial returns during robust economic growth in a low default rate environment, and have rallied with the market in recent days, CCC deterioration is most pronounced during distress and recession. During the first half of 2020, the BB-CCC spread differential reached 1,200 bps, and in 2016, CCC spreads were even wider. It is noteworthy that Europe is straddling recession, and the BB-CCC European HY bond spreads have recently widened to 1,400 bps, surpassing its peak in 2020. So despite, the recent rally in lower-rated HY bonds, caution is warranted for the weakest segment of corporate credit. The HY bonds historical default rate: BB’s 0.4% default rate, B’s 1.4% default, and CCC’s a stunning 14.3% historical default rate! During a recession, default rates tend to increase significantly from historical measures. Composition of HY Index: 50% BB, 39% B, 11% CCC. 1 year ago, the HY Bond Index had 1.2% default rate. Today, the trailing 12M default for the HY bond market is 2.6%. By Q2 2024, I expect the default rate for high yield bonds exceed 4%. Michael Schlembach, Marathon Asset Management’s PM for High Yield, expects default rates to increase in 2024, with peak default rates potentially reaching ~1.0%, ~3.0%, and >20%+ for BB, B, and CCC’s, respectively. The key will be to invest in the debt of companies with solid fundamentals and financial strength to navigate the pending downturn. If you believe as I do that an economic slowdown (potential recession) is likely in 2024, it might be best to focus on higher quality credits with robust operating businesses within the HY market. Ford serves as a prime example in the BB sector, having recently been upgraded to Investment Grade by S&P, marking it as the largest 'rising star'. Ford represents 2% of the HY index with $41 billion of bonds, its upgrade has spurred demand for other quality BB-rated bonds to replace it. While recent inflows have tightened BB spreads, I advise against trading based solely on the technicals, as this post is intended purely for informational purposes. U.S. HY rated BB vs. CCC Differential:

Government bonds underperformed equities, credit and commodities in this 3-year risk on market. Our analysis shows when equities sell off, Treasuries are also less diversifying compared to decades prior (chart). What’s happening? Long bond yields are made up of 2 components: ➡️ Policy path - in a world shaped by supply, central banks are more limited in their ability to come to the rescue of the economy without reigniting inflationary pressure. Hence Treasuries are less reliable when equities fall. ➡️ Term premium - it’s driven by bond volatility, inflation uncertainty, and of course fiscal dynamics. Think of it like any other type of risk premium such as equity risk premium it’s about perceived risk and additional required compensation above risk-free for holding it in portfolios. Large deficits record debt and heavy issuance mean that term premia can reprice higher, maybe especially during stress, pushing long yields up even as markets may price a lower policy path. Together, these forces weaken the traditional stock–bond hedge. I think of Treasuries now as quality income assets not the diversifiers they used to be.

Most finance students know that bond prices change every day. But very few understand... 👉 Why does a bond's price fall when interest rates rise? That's where the real intuition begins. So I created this one-page note to simplify: ✔️ What bond pricing is ✔️ How bonds are valued ✔️ Why bond prices and yields move in opposite directions ✔️ Premium vs Par vs Discount Bonds ✔️ A simple numerical example The biggest realization for me was: > A bond's value isn't fixed. It's determined by the present value of its future cash flows. Imagine you own a bond paying a 5% coupon. Now suppose newly issued bonds start paying 7%. Would another investor still pay full price for your 5% bond? Probably not. Your bond becomes less attractive, so its price falls until its yield matches the market. One insight many finance students miss: 📌 Bond prices and yields always move in opposite directions. • Interest rates ↑ → Bond prices ↓ • Interest rates ↓ → Bond prices ↑ This simple relationship is one of the most important concepts in fixed income. This concept is fundamental to: • CFA Program • Fixed Income • Portfolio Management • Investment Banking • Asset Management • Treasury Once you understand the intuition... you stop memorizing formulas. And start understanding why bond prices react instantly when interest rates change. Because in finance: ➡️ The coupon is fixed. ➡️ The market yield changes. ➡️ The bond price adjusts to bridge the gap. Which Fixed Income topic should I simplify next? #Finance #BondPricing #FixedIncome #Bonds #AssetManagement #CFA #CFALevel1 #CFALevel2

YIELD CURVE MODELING: MASTERING THE COMPLETE TERM STRUCTURE WITH NELSON-SIEGEL-SVENSSON 📈 In fixed income markets, understanding yield curves offers profound insights into economic expectations, interest rate risk, and relative value. Beyond basic curve analysis, parametric modeling techniques allow us to mathematically capture the entire term structure with remarkable precision. The Nelson-Siegel model provides an elegant three-factor representation of yield curves: r(t) = β₀ + β₁[(1-e^(-λt))/(λt)] + β₂[(1-e^(-λt))/(λt) - e^(-λt)] Each component has an intuitive economic interpretation: β₀ represents the long-term interest rate level (horizontal asymptote) β₁ controls the curve's slope (short-term component) β₂ determines the curve's curvature (medium-term component) λ dictates the decay rate and positioning of the hump For even greater precision with complex yield curve shapes, Svensson's (1994) extension introduces a second curvature term with a separate decay parameter μ: r(t) = β₀ + β₁[(1-e^(-λt))/(λt)] + β₂[(1-e^(-λt))/(λt) - e^(-λt)] + β₃[(1-e^(-μt))/(μt) - e^(-μt)] This parameterization allows for capturing multiple humps and troughs in the term structure with minimal additional complexity, making it particularly valuable for central bank modeling and fixed income portfolio management. The yield curve's shape itself conveys powerful economic signals: - Normal upward-sloping curves typically indicate healthy economic growth - Inverted curves often presage economic contractions - Flat curves suggest economic transitions - Humped curves point to mixed economic signals For investment professionals, mastering these term structure models provides a substantial edge in risk management, relative value analysis, and economic forecasting. Which yield curve modeling techniques have you found most effective in your practice, and how do you incorporate them into your investment decisions? #FixedIncome #YieldCurve #TermStructure #QuantitativeFinance #RiskManagement #InterestRates

Bond markets are throwing cold water on the outlook for stocks. Real yields (10-year Treasury yields adjusted for inflation) are now at the highest level since late 2023. As a result, stocks’ equity risk premium (ERP) is now lower than 75% of history since 1980. This range for the ERP has historically hinted at a volatile and slower return backdrop for stocks, helping to explain the choppiness in markets of late. Currently, the S&P 500 carries an earnings yield – the inverse of the trailing price/earnings ratio – of 3.67%. In absolute terms, that’s cheaper than the 3.4% commanded by the index in May, as strong earnings have largely offset stock price gains. However, thanks to rising TIPS yields, real yields have climbed to 2.4% -- the highest level since fall 2023. Thus, equities now look extremely expensive compared to bonds. The 123-bps spread between the earnings yield and the 10-year TIPS yield is the narrowest since the tech bubble and is in the fourth (lowest) quartile of the last half-century.  As we noted in Market Sense in May, not all low ERP regimes portend bad times for stocks, but average returns tend to be lower when stocks are so expensive relative to bonds. When the ERP was near current levels historically (in the 4th quintile), 6- and 12-month forward S&P 500 returns were below long-term average, at median 2.6% and 6%, respectively.

We are seeing dynamic changes in the credit market landscape – the risk appetite among investors is expanding as the market compresses and high yield outperforms investment grade.   Despite this, demand for some of the riskiest high-yield debt, such as CCCs, is trailing. To navigate portions of this market - characterized by weak fundamentals and strong near-term financing needs – it’s essential to address maturity walls. Looking ahead, we predict a modest uptick in the rate of defaults for high yield in the coming year.   To learn more, read BlackRock’s Global Credit Weekly report here: https://bit.ly/3ulGWUW

Bond Valuation The issuer of a bond obtains a loan from the purchaser of the bond. The issuer agrees to pay regular coupons to the purchaser and repay the loan when the bond expires. The bond pricing equation (BPE) is used for two purposes. The first is to determine the coupon rate that will be attached to the bond at issuance. The coupon rate is that rate that results in a bond price of 100 for the prevailing bond yield. This coupon rate generates the fixed cash flows C1-C5 in the LH diagram below. If the bond is traded in a liquid market, then post-issuance there is no further need for the BPE because prices are freely available. If the bond is not liquid, however, the BPE is required to serve its second purpose, the calculation of the bond price using input yields. The valuation of the bond is calculated as the PV of its future CFs. The BPE generates PV1 by discounting the coupon C1 using the 1Y yield. PVs 2-5 are generated in the same way. PV5 includes the repayment of par. The sum of PVs 1-5 = the price of the bond, the green circle in the diagram. The DFs used in the BPE are derived from the bond’s yield. But how are the yields obtained? Two approaches are possible : 1) a term structure of yields for the bond 2) a single yield for the bond. For approach 1, the first step is to build a RF yc. Methods such as bootstrapping, Nelson-Siegel or Vasicek can generate a continuous curve of RF rates. Next, a credit spread (CS) reflecting the credit risk of the bond is added to each RF rate to determine the yields to use for discounting. The CS can be extracted from the prices of credit derivatives used to hedge the credit risk of bonds with similar credit characteristics to the bond being priced. CS types include asset swap spreads, CDS spreads, treasury spreads, z-spreads and OAS spreads. A term structure of CSs is also possible. When CSs cannot be obtained from market instruments, models such as structural models or reduced form models allow credit spreads to be simulated. Under approach 2, a single yield, referred to as the bond’s YTM or internal rate of return, is used to discount all CFs in the BPE. Bonds with similar credit risk characteristics as the illiquid bond can be used to obtain the proxy YTM that is input to the BPE. Over the life of the bond, the BPE will ensure that the bond’s price, the green wavy line in the diagram, will rise and fall in an opposing direction to its yield. As the bond matures, and time-to-maturity reduces, the impact of the changing YTM on the bond’s price gets smaller. Immediately before the bond matures, the time-to-maturity variable will be so small that changes in the bond’s yield have a negligible impact on its price. Assuming that there has been no credit event impacting the repayment of the par value of the bond, the bond’s price will move back to the 100 value that it was issued at.