Trading, hedging and portfolios in practice

May 9, 2017 — November 18, 2021


Nothing to see here at the moment, apart from snippets I found interesting, as a guy with passable probability theory but weak financial knowledge.

Figure 1

Financial hacker is pragmatic. I can’t tell if it is fun because I can’t even tell if they are joking but numerai’s introduction to secrecy and information in financial markets is a …singular perspective.

1 Fundamental considerations

2 Behavioural considerations

3 Portfolio design

diversity and risk hedging.

Figure 2: Diversity in the portfolio

Bookmarked: Amazing science communication by Jonas Degrave, But why is diversification a free lunch?.

The R package introduction Fast Design of Risk Parity Portfolios by Zé Vinícius and Daniel Palomar is an interesting dummy’s guide to “Modern portfolio” and “risk-parity portfolio” theory.

In 1952, Markowitz proposed in his seminal paper [1] to find a trade-off between the portfolio expected return and its risk measured by the variance:

\[\begin{array}{ll} \underset{\mathbf{w}}{\textsf{maximize}} & \mathbf{w}^{T}\boldsymbol{\mu}-\lambda\mathbf{w}^{T}\boldsymbol{\Sigma}\mathbf{w}\\ \textsf{subject to} & \mathbf{w} \ge \mathbf{0}, \quad\mathbf{1}^T\mathbf{w}=1, \end{array}\]

where \(\lambda\) is a parameter that controls how risk-averse the investor is.

Markowitz’s portfolio has been heavily critized for over half a century and has never been fully embraced by practitioners, among many reasons because:

  • it only considers the risk of the portfolio as a whole and ignores the risk diversification (i.e., concentrates too much risk in few assets, which was observed in the 2008 financial crisis)
  • it is highly sensitive to the estimation errors in the parameters (i.e., small estimation errors in the parameters may change the designed portfolio drastically).

Although portfolio management did not change much during the 40 years after the seminal works of Markowitz and Sharpe, the development of risk budgeting techniques marked an important milestone in deepening the relationship between risk and asset management.…

The alternative risk parity portfolio design has been receiving significant attention from both the theoretical and practical sides because it

  1. diversifies the risk, instead of the capital, among the assets and
  2. is less sensitive to parameter estimation errors.

…Risk parity is an approach to portfolio management that focuses on allocation of risk rather than allocation of capital. … While the minimum variance portfolio tries to minimize the variance (with the disadvantage that a few assets may be the ones contributing most to the risk), the risk parity portfolio tries to constrain each asset (or asset class, such as bonds, stocks, real estate, etc.) to contribute equally to the portfolio overall volatility.

Figure 3: A balanced trading portfolio

Robert Carver has a simple and excellent blog and a couple of books (Carver 2019, 2015) on what I would call “indolent trading”.

4 Betting

See betting.

5 Statistical considerations

How do you learn the parameters of the model? What do estimation errors do to your return?

Figure 5: Diversification and agility in the market

6 Technical considerations

Chris Stucchio’s Notes on setting up a Data Science app on Azure is an excellent learn=by-doing tutorial.

Zorro is a financial algorithm development system:

Zorro is free for private traders because its development was partially donated. Our sponsor believed that all people, especially in developing countries, should learn programming and participate in the financial markets. Small, but regular trading incomes for anyone take liquidity out of the financial system and inject it back into the production cycle. This can boost worldwide demand and reduce the divide between rich and poor.

7 Incoming

In finance, the “Greeks” refer to the partial derivatives of an option pricing model with respect to its inputs. They are important for understanding how an option’s price may change. I discuss the Black—Scholes Greeks in detail.

8 References

Cao, Chen, Hull, et al. 2019. Deep Hedging of Derivatives Using Reinforcement Learning.” SSRN Scholarly Paper ID 3514586.
Carver. 2015. Systematic Trading: A Unique New Method for Designing Trading and Investing Systems.
———. 2019. Leveraged Trading: A Professional Approach to Trading Fx, Stocks on Margin, Cfds, Spread Bets and Futures for All Traders.
Conlon, Cotter, and Kynigakis. 2021. Machine Learning and Factor-Based Portfolio Optimization.” SSRN Scholarly Paper ID 3889459.
Jones, S. L. Peyton, and Eber. n.d. How to Write a Financial Contract.
Jones, SL Peyton, Eber, Seward, et al. 2000. Composing Contracts: An Adventure in Financial Engineering.”
MacKenzie. 2023. Black-Scholes at 50: How a Pricing Model for Options Changed Finance.” Financial Times.
Madan. 2014. Recovering Statistical Theory in the Context of Model Calibrations.” Journal of Financial Econometrics.
Nekrasov. 2014. Kelly Criterion for Multivariate Portfolios: A Model-Free Approach.” SSRN Scholarly Paper ID 2259133.
Taleb. 1996. Dynamic Hedging: Managing Vanilla and Exotic Options: 64.
Thorp. 2006. Chapter 9 The Kelly Criterion in Blackjack Sports Betting, and the Stock Market.” In Handbook of Asset and Liability Management.
Vojtko, and Cisár. 2020. Bitcoin in a Time of Financial Crisis.” SSRN Scholarly Paper ID 3557575.
Zhang, Zohren, and Roberts. 2020. Deep Learning for Portfolio Optimisation.”