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We study how trading fees and continuous-time arbitrage affect the profitability of liquidity providers (LPs) in Geometric Mean Market Makers (G3Ms). We use stochastic reflected diffusion processes to analyze the dynamics of a G3M model under the arbitrage-driven market. Our research focuses on calculating LP wealth and extends the findings of Tassy and White related to the constant product market maker (Uniswap v2) …
The paper predicts an Efficient Market Property for the equity market, where stocks, when denominated in units of the growth optimal portfolio (GP), have zero instantaneous expected returns. Well-diversified equity portfolios are shown to approximate the GP, which explains the well-observed good performance of equally weighted portfolios. The proposed hierarchically weighted index (HWI) is shown to be an even better …
We propose a novel approach and an empirical procedure to test direct contagion of growth rate in a trade credit network of firms. Our hypotheses are that the use of trade credit contributes to contagion (from many customers to a single supplier - "many to one" contagion) and amplification (through their interaction with the macrocopic variables, such as interest rate) of growth rate. In this paper we test the contag…
This paper studies a portfolio optimization problem in a discrete-time Markovian model of a financial market, in which asset price dynamics depend on an external process of economic factors. There are transaction costs with a structure that covers, in particular, the case of fixed plus proportional costs. We prove that there exists a self-financing trading strategy maximizing the average growth rate of the portfolio …
KellyBoost is a single multi-output XGBoost model whose softmax output is the portfolio: with y the vector of per-asset holding-period returns, the training loss is - log(1 + w y), the negative log growth rate, so the fitted model is the growth-optimal (Kelly) allocation conditioned on the features. The objective is exact rather than a surrogate: we derive the gradient, the analytic diagonal Hessian and the full Hess…
This paper studies a modular cash-overlay rule for allocating between a fixed growth-defensive risky sleeve R and interest-bearing cash C. The risky sleeve is a static 50/50 combination of equal-weight growth/technology and defensive income/value ETF baskets; the target is future R-C return, with the cash leg earning the contemporaneous cash rate. Two independent filters are tested. The slow-tail filter maps continuo…
This paper studies conditional allocation between a growth/technology ETF basket, denoted by $G$, and a defensive income/value-oriented ETF basket, denoted by $D$. The objective is not to discover a new standalone alpha factor, but to examine whether known style exposures can be dynamically allocated using macro-market timing signals. Fama-French five-factor plus momentum attribution shows that the relative portfolio…
This work evaluates the impact of contagious cyber-events, over a finite horizon, on firms' financial health and on a cyber insurance portfolio. Our approach builds on key empirical findings from economics and cybersecurity. In economics, firm size and growth-rate distributions are non-Gaussian and exhibit heavy tails. In cybersecurity, contagion dynamics strongly depend on firm size and environmental conditions. To …
Generating synthetic financial time series that preserve the statistical properties of real market data is essential for stress testing, risk model validation, and scenario design. Existing approaches struggle to simultaneously reproduce heavy-tailed distributions, negligible linear autocorrelation, and persistent volatility clustering. We developed a hybrid hidden Markov framework that discretized excess growth rate…
Drifts of asset returns are notoriously difficult to model accurately and, yet, trading strategies obtained from portfolio optimization are very sensitive to them. To mitigate this well-known phenomenon we study robust growth-optimization in a high-dimensional incomplete market under drift uncertainty of the asset price process $X$, under an additional ergodicity assumption, which constrains but does not fully specif…
This paper describes the Difference-of-Log-Normals (DLN) distribution. A companion paper makes the case that the DLN is a fundamental distribution in nature, and shows how a simple application of the CLT gives rise to the DLN in many disparate phenomena. Here, I characterize its PDF, CDF, moments, and parameter estimators; generalize it to N-dimensions using spherical distribution theory; describe methods to deal wit…
This work analyzes data on all public US firms in the 50 year period 1970-2019, and presents 18 stylized facts of their scale, income, growth, return, investment, and dynamism. Special attention is given to (i) identifying distributional forms; and (ii) scale effects -- systematic difference between firms based on their scale of operations. Notable findings are that the Difference-of-Log-Normals (DLN) distribution ha…
We present a general equilibrium macro-finance model with a positive feedback loop between capital investment and land price. As leverage is relaxed beyond a critical value, through the financial accelerator, a phase transition occurs from balanced growth where land prices reflect fundamentals (present value of rents) to unbalanced growth where land prices grow faster than rents, generating land price bubbles. Unbala…
Purpose: A significant number of the non-financial firms listed at the Nairobi Securities Exchange (NSE) have been experiencing declining financial performance which deters investors from investing in such firms. The lenders are also not willing to lend to such firms. As such, the firms struggle to raise funds for their operations. Prudent financing decisions can lead to financial growth of the firm. The purpose of t…
Ten years ago we presented a modified version of Okun law for the biggest developed economies and reported its excellent predictive power. In this study, we revisit the original models using the estimates of real GDP per capita and unemployment rate between 2010 and 2019. The initial results show that the change in unemployment rate can be accurately predicted by variations in the rate of real economic growth. There …
We consider the problem of maximizing the asymptotic growth rate of an investor under drift uncertainty in the setting of stochastic portfolio theory (SPT). As in the work of Kardaras and Robertson we take as inputs (i) a Markovian volatility matrix $c(x)$ and (ii) an invariant density $p(x)$ for the market weights, but we additionally impose long-only constraints on the investor. Our principal contribution is provin…
Benjamin Graham introduced a very simple formula for valuing a growth stock in 1962. How does it work and why? What is a sensible way to calculate this across many stocks and provide a scoring system to compare stocks amongst each other? We are presenting a methodology here which is put into practice.
The purpose of this paper is to introduce a new growth adjusted price-earnings measure (GA-P/E) and assess its efficacy as measure of value and predictor of future stock returns. Taking inspiration from the interpretation of the traditional price-earnings ratio as a period of time, the new measure computes the requisite payback period whilst accounting for earnings growth. Having derived the measure, we outline a num…
Copper price is widely used as a proxy for industrial activity, manufacturing demand, and global growth expectations.
A CTA that trades futures on economic data, not only price — growth, inflation, positioning, and nowcasts as the signal set.
Behind the curve means policy (or a book) is too easy or too slow relative to incoming inflation, growth, or a Taylor-type benchmark — the market is already pricing a catch-up.
A bull flattener is the curve flattening as yields fall, usually because the front end rallies more than the long end into easier policy or a growth scare.
Okun’s law is the empirical link between unemployment changes and GDP growth — a rule of thumb, not a structural identity.
China credit impulse measures the change in new credit growth relative to GDP and is widely used as a leading indicator for Chinese demand and global cyclical momentum.
GDP Nowcast — High-frequency aggregation of activity data to estimate current-quarter growth in real time.
Output Gap — Estimated distance of GDP from potential output, informing policy reaction functions.
A recession is a significant, persistent, broad decline in activity — in the US, an NBER call, not the two-negative-quarters rule.
Retail Sales Growth — Nominal and real consumption momentum, critical for growth and inflation nowcasts.
Stagflation is high inflation with stagnant growth and a soft labor market — the 1970s regime that breaks the simple Phillips cartoon.
Wage Growth — Nominal pay momentum that feeds services inflation persistence and Fed reaction functions.
China Property Cycle — Developer stress and land sales impacting global commodities and EM growth.
A growth stock is priced for high expected earnings or sales growth — a duration asset dressed as an equity.
The PEG ratio is P/E divided by expected earnings growth — a back-of-the-envelope adjustment of the multiple for growth.
Sector Rotation Signals — Cyclical versus defensive leadership indicating growth and rates regime.
The 1973–74 OPEC embargo quadrupled oil prices, fused inflation with a growth shock (stagflation), and ended the last illusions of the post-war energy-cheap regime.
Steepener Flattener Trade — Curve trades expressing views on growth, inflation, and term premium independently of level.
Terms of Trade Shock — Relative export-import price shifts altering growth and currency paths.
A Financial Conditions Index aggregates variables such as rates, credit spreads, equities, and the dollar to measure how supportive or restrictive the market environment is for growth and risk assets.
The term structure of interest rates across maturities, used to read growth, liquidity, and stress expectations.
Kelly is the stake that maximizes the expected log of wealth — an aggressive sizing rule that needs a true edge and a stomach.
The 2s10s Treasury curve measures the spread between 10-year and 2-year Treasury yields and is a key indicator of growth expectations, policy path, and term structure dynamics.
Short high asset-growth firms and long low/negative growth — the investment/empire-building anomaly.
Time equity beta with oil’s recent move or level — a macro overlay that treats crude as a growth/inflation signal.
Intersect 12-1 momentum with low asset growth — keep winners that are not empire-building.
Rotate among style sleeves (value, growth, quality, size) using the momentum of the styles themselves.
The 2s10s Treasury curve measures the spread between 10-year and 2-year Treasury yields and is a key indicator of growth expectations, policy path, and term structure dynamics.
Short high asset-growth firms and long low/negative growth — the investment/empire-building anomaly.
Behind the curve means policy (or a book) is too easy or too slow relative to incoming inflation, growth, or a Taylor-type benchmark — the market is already pricing a catch-up.
A bull flattener is the curve flattening as yields fall, usually because the front end rallies more than the long end into easier policy or a growth scare.
China credit impulse measures the change in new credit growth relative to GDP and is widely used as a leading indicator for Chinese demand and global cyclical momentum.
China Property Cycle — Developer stress and land sales impacting global commodities and EM growth.
Copper price is widely used as a proxy for industrial activity, manufacturing demand, and global growth expectations.
Time equity beta with oil’s recent move or level — a macro overlay that treats crude as a growth/inflation signal.
A Financial Conditions Index aggregates variables such as rates, credit spreads, equities, and the dollar to measure how supportive or restrictive the market environment is for growth and risk assets.
GDP Nowcast — High-frequency aggregation of activity data to estimate current-quarter growth in real time.
A growth stock is priced for high expected earnings or sales growth — a duration asset dressed as an equity.
Intersect 12-1 momentum with low asset growth — keep winners that are not empire-building.
Rotate among style sleeves (value, growth, quality, size) using the momentum of the styles themselves.
The 1973–74 OPEC embargo quadrupled oil prices, fused inflation with a growth shock (stagflation), and ended the last illusions of the post-war energy-cheap regime.
Okun’s law is the empirical link between unemployment changes and GDP growth — a rule of thumb, not a structural identity.
The PEG ratio is P/E divided by expected earnings growth — a back-of-the-envelope adjustment of the multiple for growth.
Retail Sales Growth — Nominal and real consumption momentum, critical for growth and inflation nowcasts.
Sector Rotation Signals — Cyclical versus defensive leadership indicating growth and rates regime.
Stagflation is high inflation with stagnant growth and a soft labor market — the 1970s regime that breaks the simple Phillips cartoon.
Steepener Flattener Trade — Curve trades expressing views on growth, inflation, and term premium independently of level.
A CTA that trades futures on economic data, not only price — growth, inflation, positioning, and nowcasts as the signal set.
Terms of Trade Shock — Relative export-import price shifts altering growth and currency paths.
Wage Growth — Nominal pay momentum that feeds services inflation persistence and Fed reaction functions.
The term structure of interest rates across maturities, used to read growth, liquidity, and stress expectations.