My Research

Understanding the CAPM Equation

2025-01-16

The CAPM's relative pricing mechanism based on the market portfolio has been mistakenly interpreted as that only the systematic risk is priced, while non-systematic risk can be diversified away and is not rewarded.

An Analytic Solution to the Mean-Variance Equilibrium: Is the Market Beta a Valuable Tool?

• If the tangent portfolio is equal to the market portfolio, is the market in equilibrium? No!
• Can we using the beta pricing formula to price derivatives in the market? No!
• In the CAPM equation, can the market beta of a stock take infinitely many values? Yes!
• Is the market beta a redundant variable or a valuable tool? a redundant variable

The Arbitrage Pricing Theory (APT) with Arbitrage Opportunities

We design a numerical example of APT that incorporates arbitrage opportunities

Countably Infinite Market: Completeness and Pricing Function

We prove the standard form of the second fundamental theorem of asset pricing, where there are an infinite number of assets, and the pricing functions are continuous.

Arbitrage Opportunities and the First Fundamental Theorem of Asset Pricing in an Infinite Market

We prove the standard Fundamental Theorem of Asset Pricing (FTAP) with the no-arbitrage condition, not the sophisticated concept such as NFLVR (No Free Lunch with Vanishing Risk) or else. We illustrate the FTAP in the infinite market by numerical examples.

Book Draft: Analysis of Pure Finance

Abad's View of Asset Pricing: A new framework (axiomatic system) of financial theory Which Starts to answer the following questions

1. Can financial assets be priced? If so, can it be represented by a functional?
2. Are there any value creations during the construction of an asset portfolio?
3. What is the relationship between limited liability and no arbitrage?
4. How can the above questions be stated mathematically?