Market-Based "Actual" Returns of Investors

Paper: arXiv 2304.06466

Authors: Victor Olkhov

Abstract

We describe how the market-based average and volatility of the “actual” return, which the investors gain within their market sales, depend on the statistical moments, volatilities, and correlations of the current and past market trade values. We describe three successive approximations. First, we derive the dependence of the market-based average and volatility of a single sale return on market trade statistical moments determined by multiple purchases in the past. Then, we describe the dependence of average and volatility of return that a single investor gains during the “trading day.” Finally, we derive the market-based average and volatility of return of different investors during the “trading day” as a function of volatilities and correlations of market trade values. That highlights the distribution of the “actual” return of market trade and can serve as a benchmark for “purchasing” investors.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a detailed theoretical derivation of investor actual returns based on statistical moments, correlations, and multi-period trade values. However, it lacks empirical validation, backtesting on real market data, and code for implementation.

Research Flowchart

  flowchart TD
    A[Goal: Derive Market-Based 'Actual' Returns & Volatility] --> B[Inputs: Current & Past Market Trade Values]
    B --> C[Step 1: Single Sale Return Model]
    C --> D[Step 2: Single Investor Daily Return Model]
    D --> E[Step 3: Multi-Investor Market-Wide Model]
    E --> F[Analysis: Calculate Statistical Moments, Volatilities & Correlations]
    F --> G[Outcome: Actual Return Distribution & Benchmark for Purchasing Investors]