Capital Asset Pricing Model

Indices of quadratic programs over reproducing kernel Hilbert spaces for fun and profit ArXiv ID: 2412.18201 “View on arXiv” Authors: Unknown Abstract We give an abstract perspective on quadratic programming with an eye toward long portfolio theory geared toward explaining sparsity via maximum principles. Specifically, in optimal allocation problems, we see that support of an optimal distribution lies in a variety intersect a kind of distinguished boundary of a compact subspace to be allocated over. We demonstrate some of its intelligence by using it to solve mazes and interpret such behavior as the underlying space trying to understand some hypothetical platonic index for which the capital asset pricing model holds. ...

Using Machine Learning to Forecast Market Direction with Efficient Frontier Coefficients ArXiv ID: 2404.00825 “View on arXiv” Authors: Unknown Abstract We propose a novel method to improve estimation of asset returns for portfolio optimization. This approach first performs a monthly directional market forecast using an online decision tree. The decision tree is trained on a novel set of features engineered from portfolio theory: the efficient frontier functional coefficients. Efficient frontiers can be decomposed to their functional form, a square-root second-order polynomial, and the coefficients of this function captures the information of all the constituents that compose the market in the current time period. To make these forecasts actionable, these directional forecasts are integrated to a portfolio optimization framework using expected returns conditional on the market forecast as an estimate for the return vector. This conditional expectation is calculated using the inverse Mills ratio, and the Capital Asset Pricing Model is used to translate the market forecast to individual asset forecasts. This novel method outperforms baseline portfolios, as well as other feature sets including technical indicators and the Fama-French factors. To empirically validate the proposed model, we employ a set of market sector ETFs. ...

Equity Risk Premiums (ERP): Determinants, Estimation, and Implications – The 2021 Edition ArXiv ID: ssrn-3825823 “View on arXiv” Authors: Unknown Abstract The equity risk premium is the price of risk in equity markets, and it is not just a key input in estimating costs of equity and capital in both corporate finan Keywords: equity risk premium, cost of equity, capital asset pricing model, valuation, risk pricing, Equities Complexity vs Empirical Score Math Complexity: 2.5/10 Empirical Rigor: 7.0/10 Quadrant: Street Traders Why: The paper uses foundational finance equations (CAPM, multi-factor models) with minimal advanced derivation, placing math complexity low. However, it heavily relies on historical data, surveys, and real-world market data (default spreads, option prices) to estimate and compare equity risk premiums, making it highly empirical and implementation-focused. flowchart TD A["Research Goal: Determine ERP<br>for Corporate Valuation"] --> B["Key Methodology: Historical Analysis"] B --> C["Data Inputs: Historical<br>Stock Returns vs<br>Risk-Free Rates"] C --> D["Computational Process:<br>Calculate Average Historical ERP<br>& Adjust for Market Conditions"] D --> E["Key Findings: ERP is unstable<br>Context-dependent; Required for<br>accurate Cost of Equity &<br>Valuation models"]

Equity Risk Premiums (ERP): Determinants, Estimation and Implications – The 2017 Edition ArXiv ID: ssrn-2947861 “View on arXiv” Authors: Unknown Abstract The equity risk premium is the price of risk in equity markets and is a key input in estimating costs of equity and capital in both corporate finance and valuat Keywords: equity risk premium, cost of equity, risk and return models, capital asset pricing model, valuation, Equities Complexity vs Empirical Score Math Complexity: 4.0/10 Empirical Rigor: 5.0/10 Quadrant: Street Traders Why: The paper employs established financial mathematics (DCF, option pricing) but focuses on estimation methodologies and practical implications rather than novel derivations. It relies heavily on historical and implied market data, with extensive data appendices and real-world applications for valuation and corporate finance, making it implementation-heavy. flowchart TD A["Research Goal<br>Determine the Equity Risk Premium"] --> B["Methodology<br>Historical Implied & Survey Approaches"] B --> C["Data Inputs<br>Historical Market Returns, Bond Yields, Surveys"] C --> D["Computation<br>Estimate Expected Returns & Risk"] D --> E["Key Findings<br>ERP Varies by Market, Estimation Period, and Method; Critical for Cost of Equity & Valuation"]

Equity Risk Premiums (ERP): Determinants, Estimation and Implications - A Post-Crisis Update ArXiv ID: ssrn-1492717 “View on arXiv” Authors: Unknown Abstract Equity risk premiums are a central component of every risk and return model in finance and are a key input into estimating costs of equity and capital in both c Keywords: equity risk premium, cost of equity, capital asset pricing model, valuation, risk modeling, Equities Complexity vs Empirical Score Math Complexity: 4.0/10 Empirical Rigor: 3.0/10 Quadrant: Philosophers Why: The paper is conceptually oriented, discussing determinants and estimation methods for equity risk premiums without presenting advanced mathematical derivations or rigorous empirical backtesting with specific datasets and performance metrics. flowchart TD A["Research Goal<br>Determine Post-Crisis ERP"] --> B["Methodology<br>Historical & Cross-Sectional Analysis"] B --> C{"Key Inputs<br>Data Sources"} C --> C1["US Equity Returns"] C --> C2["Risk-Free Rates<br>T-Bills/Bonds"] C --> C3["Inflation & Macro Indicators"] C --> D["Computational Processes"] D --> D1["Implied ERP Calculation"] D --> D2["Historical ERP Estimation"] D --> D3["Risk Model Integration<br>CAPE/Dividend Models"] D1 & D2 & D3 --> E["Key Findings<br>Outcomes"] E --> E1["ERP ≈ 4.5-5.5%<br>Post-Crisis Estimate"] E --> E2["ERP is Non-Constant<br>Varies with Market Conditions"] E --> E3["Cost of Equity<br>ERP + Risk-Free Rate"] E --> E4["Valuation Implications<br>Lower Discount Rates"]