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Fixed income has received far less attention than equity portfolio optimisation since Markowitz' original work of 1952, partly as a result of the need to model rates and credit risk. We argue that the shape of the efficient frontier is mainly controlled by linear constraints, with the standard deviation relatively unimportant, and propose a two-factor model for its time evolution.
We discuss a class of risk-sensitive portfolio optimization problems. We consider the portfolio optimization model investigated by Nagai in 2003. The model by its nature can include fixed income securities as well in the portfolio. Under fairly general conditions, we prove the existence of optimal portfolio in both finite and infinite horizon problems.
We present cross and time series analysis of price fluctuations in the U.S. Treasury fixed income market. By means of techniques borrowed from statistical physics we show that the correlation among bonds depends strongly on the maturity and bonds' price increments do not fulfill the random walk hyphoteses.
We present a novel process for generating synthetic datasets tailored to assess asset allocation methods and construct portfolios within the fixed income universe. Our approach begins by enhancing the CorrGAN model to generate synthetic correlation matrices. Subsequently, we propose an Encoder-Decoder model that samples additional data conditioned on a given correlation matrix. The resulting synthetic dataset facilit…
This book, which is in Spanish, provides detailed descriptions, including over 550 mathematical formulas, for over 150 trading strategies across a host of asset classes (and trading styles). This includes stocks, options, fixed income, futures, ETFs, indexes, commodities, foreign exchange, convertibles, structured assets, volatility (as an asset class), real estate, distressed assets, cash, cryptocurrencies, miscella…
This paper analyses the Chinese Sovereign bond yield to find out the principal factors affecting the term structure of interest rate changes. We apply Principal Component Analysis (PCA) on our data consisting of the Chinese Sovereign bond from January 2002 till May 2018 with the different yield to maturity. Then we will discuss the multi-factor immunization model (method on hedging market risk) on a bond portfolio.
We review the main changes in the interbank market after the financial crisis started in August 2007. In particular, we focus on the fixed income market and we analyse the most relevant empirical evidences regarding the divergence of the existing basis between interbank rates with different tenor, such as Libor and OIS. We also discuss a qualitative explanation of these effects based on the consideration of credit an…
We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between Libor and OIS rates, the explosion of Basis Swaps spreads, and the diffusion of collateral agreements and CSA-discounting, in terms of credit and liquidity effects. We also review t…
In decentralized finance (DeFi), designing fixed-income lending automated market makers (AMMs) is extremely challenging due to time-related complexities. Moreover, existing protocols only support single-maturity lending. Building upon the BondMM protocol, this paper argues that its mathematical invariants are sufficiently elegant to be generalized to arbitrary maturities. This paper thus propose an improved design, B…
1. INTRODUCTION During the financial crisis of 2007-09, particularly around the time of the Bear Stearns and Lehman Brothers failures, it became apparent that weaknesses existed in the design of the U.S. tri-party repo market, used by major broker-dealers to finance their inventories of securities. These design weaknesses had the potential to rapidly elevate and propagate systemic risk. Following the crisis, an indus…
The notion of a credit spread curve is fundamental in fixed income investing, but in practice it is not `given' and needs to be constructed from bond prices either for a particular issuer, or for a sector rating-by-rating. Rather than attempting to fit spreads -- and as we discuss here, the Z-spread is unsuitable -- we fit parametrised survival curves. By deriving a valuation formula for a risky bond, we explain and …
We propose an option approach for pricing bond illiquidity that is reminiscent of the celebrated work of Longstaff (1995) on the non-marketability of some non-dividend-paying shares in IPOs. This approach describes a quite common situation in the fixed income market: it is rather usual to find issuers that, besides liquid benchmark bonds, issue some other bonds that either are placed to a small number of investors in…
For the last two decades, most financial markets have undergone an evolution toward electronification. The market for corporate bonds is one of the last major financial markets to follow this unavoidable path. Traditionally quote-driven i.e., dealer-driven) rather than order-driven, the market for corporate bonds is still mainly dominated by voice trading, but a lot of electronic platforms have emerged. These electro…
We consider the problem of concurrent portfolio losses in two non-overlapping credit portfolios. In order to explore the full statistical dependence structure of such portfolio losses, we estimate their empirical pairwise copulas. Instead of a Gaussian dependence, we typically find a strong asymmetry in the copulas. Concurrent large portfolio losses are much more likely than small ones. Studying the dependences of th…
This study examines the effects of macroeconomic policies on financial markets using a novel approach that combines Machine Learning (ML) techniques and causal inference. It focuses on the effect of interest rate changes made by the US Federal Reserve System (FRS) on the returns of fixed income and equity funds between January 1986 and December 2021. The analysis makes a distinction between actively and passively man…
We adopt Deep Reinforcement Learning algorithms to design trading strategies for continuous futures contracts. Both discrete and continuous action spaces are considered and volatility scaling is incorporated to create reward functions which scale trade positions based on market volatility. We test our algorithms on the 50 most liquid futures contracts from 2011 to 2019, and investigate how performance varies across d…
In fixed income sector, the yield curve is probably the most observed indicator by the market for trading and fifinancing purposes. A yield curve plots interest rates across different contract maturities from short end to as long as 30 years. For each currency, the corresponding curve shows the relation between the level of the interest rates (or cost of borrowing) and the time to maturity. For example, the U.S. doll…
In the last years, increasing efforts have been put into the development of effective stress tests to quantify the resilience of financial institutions. Here we propose a stress test methodology for central counterparties based on a network characterization of clearing members, whose links correspond to direct credits and debits. This network constitutes the ground for the propagation of financial distress: equity lo…
Asset Swap Spread — Spread between bond yield and floating leg, linking credit and funding markets.
A callable bond lets the issuer redeem early at a schedule of prices — you sold a call to the issuer and should be paid for it.
Carry and Roll Down — Expected return from holding higher-yielding tenor as it rolls down a positively sloped curve.
CDS Basis Trade — Arbitrage between cash bonds and CDS contracts revealing funding and counterparty frictions.
Cheapest-to-deliver is the bond a futures (or CDS) seller will deliver because it minimizes their cost — the option that sits inside the contract.
CLO Issuance — Structured credit supply that absorbs leveraged loans and shapes spread regimes.
Commercial Mortgage Delinquency — Office and retail stress feeding through CRE credit and regional bank risk.
Convexity Risk — Non-linear price response to yield changes, especially relevant in MBS and long bonds.
A coupon is the contractual interest payment on a bond — usually a fixed percent of par, sometimes floating, sometimes zero.
Credit Default Swap Spread — Market-implied default risk premium for single names and indices.
Distressed Debt Ratio — Share of debt trading at deep discounts — early warning for credit cycle turns.
Duration Risk — Interest-rate sensitivity of bond portfolios, amplified in low-yield high-duration regimes.
Fallen Angels — Investment-grade downgrades into high yield, creating forced selling and index rebalancing flows.
Indirect bidder allotment tracks the share of Treasury auctions awarded to indirect bidders, often used as a proxy for foreign and institutional demand.
An inverted curve is short rates above long rates — a market statement about expected cuts, term premium, and sometimes recession risk.
Key Rate Duration — Bucketed rate sensitivity across curve points for relative-value and hedge construction.
Leveraged Loan Index — Floating-rate corporate credit sensitive to defaults, spreads, and CLO demand.
Macaulay duration is the present-value-weighted average time to receive a bond’s cash flows — duration in years, before the modified-duration hedge ratio.
MBS Prepayment Speed — Refinancing and turnover driven cash-flow uncertainty in agency mortgages.
Modified duration is the percent price change for a 1% (100bp) parallel yield move — the first-order hedge ratio from the yield function.
A municipal bond is debt of a US state, city, or related authority — often tax-exempt, with credit that is not a Treasury.
Option-Adjusted Spread — Spread adjusted for embedded prepayment options in callable bonds and MBS.
Par value is the face amount the issuer promises to repay at maturity — 100 cents on the dollar in bond language.
Primary Dealer Survey — Desk-level policy expectations that front-run official communications.
Rising Stars — High-yield upgrades into investment grade, often supporting spread tightening episodes.
Steepener Flattener Trade — Curve trades expressing views on growth, inflation, and term premium independently of level.
TBA Roll Specialness — Delivery-option value in TBA markets signaling collateral scarcity or abundance.
Treasury auction bid-to-cover ratio measures the amount of demand relative to supply at an auction and is used to assess investor appetite for government debt.
Treasury auction tail measures how much the auction clears above or below the expected market yield, providing a sensitive signal of auction quality and investor demand.
TIPS are US Treasuries whose principal adjusts with CPI — a real-rate instrument, not a magic inflation hedge for every horizon.
Yield to maturity is the constant discount rate that sets the bond’s dirty price equal to its remaining cash flows if held to maturity and coupons are reinvested at that same rate.
Yield to worst is the lowest yield among the plausible call, put, and maturity paths — the conservative quote on an embedded-option bond.
Z Spread — Static spread over the government curve capturing credit and liquidity premium.
A zero-coupon bond pays no coupon and one cash flow at maturity — duration equals maturity, and the whole return is pull-to-par plus yield change.
Asset Swap Spread — Spread between bond yield and floating leg, linking credit and funding markets.
A callable bond lets the issuer redeem early at a schedule of prices — you sold a call to the issuer and should be paid for it.
Carry and Roll Down — Expected return from holding higher-yielding tenor as it rolls down a positively sloped curve.
CDS Basis Trade — Arbitrage between cash bonds and CDS contracts revealing funding and counterparty frictions.
Cheapest-to-deliver is the bond a futures (or CDS) seller will deliver because it minimizes their cost — the option that sits inside the contract.
CLO Issuance — Structured credit supply that absorbs leveraged loans and shapes spread regimes.
Commercial Mortgage Delinquency — Office and retail stress feeding through CRE credit and regional bank risk.
Convexity Risk — Non-linear price response to yield changes, especially relevant in MBS and long bonds.
A coupon is the contractual interest payment on a bond — usually a fixed percent of par, sometimes floating, sometimes zero.
Credit Default Swap Spread — Market-implied default risk premium for single names and indices.
Distressed Debt Ratio — Share of debt trading at deep discounts — early warning for credit cycle turns.
Duration Risk — Interest-rate sensitivity of bond portfolios, amplified in low-yield high-duration regimes.
Fallen Angels — Investment-grade downgrades into high yield, creating forced selling and index rebalancing flows.
Indirect bidder allotment tracks the share of Treasury auctions awarded to indirect bidders, often used as a proxy for foreign and institutional demand.
An inverted curve is short rates above long rates — a market statement about expected cuts, term premium, and sometimes recession risk.
Key Rate Duration — Bucketed rate sensitivity across curve points for relative-value and hedge construction.
Leveraged Loan Index — Floating-rate corporate credit sensitive to defaults, spreads, and CLO demand.
Macaulay duration is the present-value-weighted average time to receive a bond’s cash flows — duration in years, before the modified-duration hedge ratio.
MBS Prepayment Speed — Refinancing and turnover driven cash-flow uncertainty in agency mortgages.
Modified duration is the percent price change for a 1% (100bp) parallel yield move — the first-order hedge ratio from the yield function.
A municipal bond is debt of a US state, city, or related authority — often tax-exempt, with credit that is not a Treasury.
Option-Adjusted Spread — Spread adjusted for embedded prepayment options in callable bonds and MBS.
Par value is the face amount the issuer promises to repay at maturity — 100 cents on the dollar in bond language.
Primary Dealer Survey — Desk-level policy expectations that front-run official communications.