Paper: arXiv 2408.01772

Abstract

Several studies on portfolio construction reveal that sensible strategies essentially yield the same results as their nonsensical inverted counterparts; moreover, random portfolios managed by Malkiel’s dart-throwing monkey would outperform the cap-weighted benchmark index. Forecasting the future development of stock returns is an important aspect of portfolio assessment. Similar to the ostensible arbitrariness of portfolio selection methods, it is shown that there is no substantial difference between the performances of best’’ and trivial’’ forecasts - even under euphemistic model assumptions on the underlying price dynamics. A certain significance of a predictor is found only in the following special case: the best linear unbiased forecast is used, the planning horizon is small, and a critical relation is not satisfied.

Complexity vs Empirical Score

  • Math Complexity: 7.0/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper uses advanced stochastic calculus (e.g., compound Poisson processes, Hilbert spaces, Black-Scholes extensions) for theoretical derivations. However, it presents abstract mathematical conclusions about asymptotic equivalence without empirical backtests, code, or datasets.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Assess value of return forecasts<br>in portfolio construction"] --> B["Methodology: <br>Compare 'Best' vs. 'Trivial' Forecasts"]
  A --> C["Methodology: <br>Test Random Portfolios<br>vs. Cap-Weighted Index"]
  
  B --> D["Inputs:<br>Simulated Stock Returns<br>& Price Dynamics"]
  C --> D
  
  D --> E["Computational Process:<br>Run Regressions &<br>Calculate Portfolio Metrics"]
  
  E --> F{"Outcome 1:<br>Forecasting Performance"}
  E --> G{"Outcome 2:<br>Portfolio Performance"}
  
  F -->|Findings| H["'Best' vs. 'Trivial' forecasts<br>show no significant difference"]
  G -->|Findings| I["Random portfolios (dart-throwing)<br>outperform cap-weighted benchmark"]
  
  H & I --> J["Conclusion:<br>Investment strategies based<br>on forecasts are (almost) useless"]