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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.
This paper explores several types of income which have not been explored so far by authors who tackled income and wealth distribution using Statistical Physics. The main types of income we plan to analyze are income before redistribution (or gross income), income of retired people (or pensions), and income of active people (mostly wages). The distributions used to analyze income distributions are Fermi-Dirac distribu…
Polynomial distribution can be applied to dynamical systems in certain situations. Macroeconomic systems characterized by economic variables such as income and wealth can be modelled similarly using polynomials. We extend our previous work to data regarding income from a more diversified pool of countries, which contains developed countries with high income, developed countries with middle income, developing and unde…
In an incomplete continuous-time securities market with uncertainty generated by Brownian motions, we derive closed-form solutions for the equilibrium interest rate and market price of risk processes. The economy has a finite number of heterogeneous exponential utility investors, who receive partially unspanned income and can trade continuously on a finite time-interval in a money market account and a single risky se…
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…
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…
The distribution of income and wealth in developed economies exhibits a robust two-class structure: an exponential (Boltzmann--Gibbs) bulk covering $\sim\!97\%$ of the population, and a power-law (Pareto) tail in the upper $\sim\!3\%$. We derive this structure from first principles via an explicit mechanistic chain: Gibrat's law for firm growth implies a Zipf firm-size distribution; maximum entropy applied to within-…
We consider the problem of optimal annuitization with labour income, where an agent aims to maximize utility from consumption and labour income under age-dependent force of mortality. Using a dynamic programming approach, we derive closed-form solutions for the value function and the optimal consumption, portfolio, and labor supply strategies. Our results show that before retirement, investment behavior increases wit…
We propose a framework for transfer learning of discount curves across different fixed-income product classes. Motivated by challenges in estimating discount curves from sparse or noisy data, we extend kernel ridge regression (KR) to a vector-valued setting, formulating a convex optimization problem in a vector-valued reproducing kernel Hilbert space (RKHS). Each component of the solution corresponds to the discount …
We consider an infinite horizon portfolio problem with borrowing constraints, in which an agent receives labor income which adjusts to financial market shocks in a path dependent way. This path-dependency is the novelty of the model, and leads to an infinite dimensional stochastic optimal control problem. We solve the problem completely, and find explicitly the optimal controls in feedback form. This is possible beca…
This paper explores a real-world fundamental theme under a data science perspective. It specifically discusses whether fraud or manipulation can be observed in and from municipality income tax size distributions, through their aggregation from citizen fiscal reports. The study case pertains to official data obtained from the Italian Ministry of Economics and Finance over the period 2007-2011. All Italian (20) regions…
Income tax systems with pass-through entities transfer a firm's incomes to the shareholders, which are taxed individually. In 2014, a Chilean tax reform introduced this type of entity and changed to an accrual basis that distributes incomes (but not losses) to shareholders. A crucial step for the Chilean taxation authority is to compute the final income of each individual, given the complex network of corporations an…
Intra-household inequality continues to remain a neglected corner despite renewed focus on income and wealth inequality. Using the LIS micro data, we present evidence that this neglect is equivalent to ignoring up to a third of total inequality. For a wide range of countries and over four decades, we show that at least 30 per cent of total inequality is attributable to inequality within the household. Using a simple …
Accounting frameworks follow stipulations of existing Accounting Theories. This exploratory research sets out to trace the evolution of accounting theories of Charge and Discharge Syndrome and the Corollary of Double Entry. Furthermore, it dives into the theories of Income Determination, garnishing it with areas of diversities in the use of Accounting Information while review of theories of recent growths and develop…
Recent research has documented a significant rise in the volatility (e.g., expected squared change) of individual incomes in the U.S. since the 1970s. Existing measures of this trend abstract from individual heterogeneity, effectively estimating an increase in average volatility. We decompose this increase in average volatility and find that it is far from representative of the experience of most people: there has be…
Constant product markets with concentrated liquidity (CL) are the most popular type of automated market makers. In this paper, we characterise the continuous-time wealth dynamics of strategic LPs who dynamically adjust their range of liquidity provision in CL pools. Their wealth results from fee income, the value of their holdings in the pool, and rebalancing costs. Next, we derive a self-financing and closed-form op…
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.
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…
TU through ultra-long bond futures, bunds, gilts, JGBs — duration trend, the sleeve that made 2022 a CTA year.
Steepeners, flatteners, and butterflies on the bond/STIR strip — duration-neutral-ish curve trades as a CTA RV sleeve.
A covered call is long the stock and short a call — you sell upside for premium and keep the downside.
Iron Condor Structure — Short vol range trade expressing view of subdued movement between strikes.
The quantity theory is MV = PY: money times velocity equals nominal income. In the strong form, a one-off money increase raises prices one-for-one if V and Y are stable.
A dividend is a cash (or stock) distribution of residual earnings to shareholders, declared by the board and not a contractual coupon.
Dividend yield is annual dividends per share divided by price — the income run-rate the market is capitalizing, not a promised return.
Earnings per share is net income attributable to common, divided by weighted-average shares — basic or diluted.
EBIT is earnings before interest and tax — operating profit after depreciation, before capital structure and the tax man.
The income statement is the period’s revenues minus expenses — accrual earnings, not cash.
Return on assets is net income (or EBIT) divided by total assets — how much profit the whole sheet produces before you celebrate leverage.
Return on equity is net income divided by book equity — the accounting yield on residual capital, levered.
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.
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.
Dividend yield is annual dividends per share divided by price — the income run-rate the market is capitalizing, not a promised return.
Duration Risk — Interest-rate sensitivity of bond portfolios, amplified in low-yield high-duration regimes.
Earnings per share is net income attributable to common, divided by weighted-average shares — basic or diluted.
Fallen Angels — Investment-grade downgrades into high yield, creating forced selling and index rebalancing flows.
TU through ultra-long bond futures, bunds, gilts, JGBs — duration trend, the sleeve that made 2022 a CTA year.
The income statement is the period’s revenues minus expenses — accrual earnings, not cash.
Indirect bidder allotment tracks the share of Treasury auctions awarded to indirect bidders, often used as a proxy for foreign and institutional demand.
Steepeners, flatteners, and butterflies on the bond/STIR strip — duration-neutral-ish curve trades as a CTA RV sleeve.
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.