Technical working papers and research notes on quantitative finance, capital allocation, and decision frameworks. Rigorous analysis for practitioners and researchers.
WORKING PAPER
Terminal Value Sensitivity in DCF Models: A Quantitative Framework
From Equations to Capital Research
January 2025
Terminal value often represents 60-80% of total DCF valuation, yet receives proportionally less analytical attention than explicit forecast periods. This paper develops a systematic framework for terminal value sensitivity analysis, proposing a "terminal value confidence interval" that accounts for uncertainty in growth rates, cost of capital, and capital intensity assumptions simultaneously.
TECHNICAL NOTE
Black-Litterman Implementation: Confidence Calibration and Prior Selection
From Equations to Capital Research
November 2024
The Black-Litterman model's practical value depends critically on two under-specified elements: the uncertainty parameter (τ) and the view confidence matrix (Ω). This note provides calibration procedures for both, with empirical tests across multiple asset classes and market regimes.
WORKING PAPER
Correlation Breakdown Under Stress: Implications for Portfolio VaR
From Equations to Capital Research
September 2024
Standard VaR models use unconditional correlations that systematically underestimate tail risk. We document correlation behavior across 1987, 1998, 2008, and 2020 market stress events, finding average correlation increases of 40-60% at the 1% tail. We propose a regime-switching covariance estimator for stress-adjusted VaR.
CASE STUDY
Hedging Discontinuous Risk: The EUR/CHF Floor Removal
From Equations to Capital Research
July 2024
The Swiss National Bank's abandonment of the 1.20 EUR/CHF floor on January 15, 2015 provides a natural experiment in hedging discontinuous risk. We compare stop-loss orders (which failed catastrophically due to gapping) with put options (which provided full protection at known cost), quantifying the economic difference.
Single-period Brinson attribution is well-defined, but linking across periods introduces residuals. We compare arithmetic, geometric, and Carino smoothing approaches, testing each against realistic portfolio scenarios with high turnover and volatile markets.
WORKING PAPER
Execution Shortfall and Market Impact: An Empirical Analysis of Order Types
From Equations to Capital Research
March 2024
Market orders guarantee execution but expose traders to adverse selection and market impact. We analyze execution quality across order types using a proprietary dataset, quantifying the trade-off between execution certainty and execution cost as a function of order size, volatility, and spread.
DISCLAIMER
These papers are working drafts shared for educational and research purposes. They do not constitute investment advice. All quantitative examples are illustrative. Past performance is not indicative of future results. Please consult qualified professionals for specific investment decisions.