# Hedging and portfolios in practice

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

## Portfolio design

The R package introduction Fast Design of Risk Parity Portfolios by ZĂ© VinĂ­cius and Daniel Palomar is an interesting dummyâ€™s guide to â€śModern portfolioâ€ť and â€śrisk-parity portfolioâ€ť 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.

Markowitzâ€™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.â€¦

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.

â€¦Risk parity is an approach to portfolio management that focuses on allocation of risk rather than allocation of capital. â€¦ 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.

## Betting

In the special case of all-or-nothing bets, things are different than variable return instruments.

Introductory: Zvi Mowshowitz on Kelly bets.

## Statistical considerations

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

Jonathan Kinlay, on market timing strategies via Machine Learning.

## Technical considerations

I suppose the Bitstamp api is a model of the kind of system retail or casual traders must interface with.

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

Jones, S. L. Peyton, and J.-M. Eber. n.d. How to Write a Financial Contract.

Jones, SL Peyton, J.-M. Eber, J. Seward, and Simon Peyton Jones. 2000. â€śComposing Contracts: An Adventure in Financial Engineering,â€ť September. https://www.microsoft.com/en-us/research/publication/composing-contracts-an-adventure-in-financial-engineering/.

Madan, Dilip B. 2014. â€śRecovering Statistical Theory in the Context of Model Calibrations.â€ť Journal of Financial Econometrics, July, nbu020. https://doi.org/10.1093/jjfinec/nbu020.

Nekrasov, Vasily. 2014. â€śKelly Criterion for Multivariate Portfolios: A Model-Free Approach.â€ť SSRN Scholarly Paper ID 2259133. Rochester, NY: Social Science Research Network. https://papers.ssrn.com/abstract=2259133.

Thorp, Edward O. 2006. â€śChapter 9 the Kelly Criterion in Blackjack Sports Betting, and the Stock Market.â€ť In Handbook of Asset and Liability Management, 1:385â€“428. Elsevier. https://doi.org/10.1016/S1872-0978(06)01009-X.

Zhang, Zihao, Stefan Zohren, and Stephen Roberts. 2020. â€śDeep Learning for Portfolio Optimisation,â€ť May. https://arxiv.org/abs/2005.13665v2.