Hephaestus Quant
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Open problems.

No traditional application. Pick a problem, write a proposal. If the thinking is solid, we'll reach out.

Process

How it works

  1. Look through the research problems below.
  2. Pick one that matches what you're capable of and interested in.
  3. Write a structured proposal: how you'd frame the problem, what methodology you'd use, what you'd expect to find, and what could go wrong.
  4. Send it to us (contact info at the bottom).
  5. We review on a rolling basis. If the work is rigorous, we get in touch.

We're not expecting finished research. We want to see how you think about a hard problem: clear framing, honest about limitations, aware of what you don't know.

Research

Open problems

Research Problem 01

Covariance Regularization and Out-of-Sample Risk Stability

Research Question
Does eigenvalue cleaning or shrinkage-based regularization of the sample covariance matrix improve out-of-sample portfolio variance, drawdown, and weight stability relative to the raw sample estimator?
Motivation
In high-dimensional settings, the sample covariance matrix is noisy and poorly conditioned. Optimization based on unstable covariance estimates often leads to extreme weights and fragile diversification.
Objective
Evaluate whether covariance regularization techniques (e.g. shrinkage, eigenvalue filtering, factor-based models) produce more stable and robust portfolios under realistic sampling conditions.
Evaluation Metrics
  • Realized out-of-sample volatility
  • Maximum drawdown
  • Portfolio weight turnover
  • Concentration measures (e.g. Herfindahl index)
  • Condition number / eigenvalue dispersion
Research Problem 02

Optimal Memory in Covariance Estimation Under Regime Shifts

Research Question
What is the optimal memory parameter (lookback horizon or decay rate) for covariance estimation under regime transitions, and how does it impact realized volatility, turnover, and drawdown?
Motivation
Risk models face a structural tradeoff: short memory → reactive but noisy; long memory → stable but slow to adapt. During volatility shocks such as the Global Financial Crisis or the COVID-19 market crash, delayed adaptation can materially increase drawdown.
Objective
Quantify the stability–reactivity tradeoff and determine whether adaptive memory schemes improve out-of-sample risk control relative to static lookback windows.
Evaluation Metrics
  • Realized volatility forecast error
  • Maximum drawdown
  • Ulcer index
  • Turnover and transaction cost impact
  • Time-to-recovery
Evaluation

What we look for in proposals

Problem understanding

Can you explain why this is hard? Where does the naive approach fail? What are the edge cases?

Methodology

Is your approach falsifiable? What does a negative result look like? What are you assuming?

Scope

Is the scope realistic? What's explicitly excluded? Don't try to solve everything at once.

Honesty

Are the limitations stated upfront? A good "I don't know how to handle X yet" beats a hand-wave every time.

Contact

Submit

Send your proposal as a PDF or plain text. Reference the problem (e.g. Research Problem 01) in the subject line.

info@hephaestusquant.org

Rolling review. No deadlines, no cohorts.