Quant Strategies Off-cycle Internship

Il y a 5 mois

Paris, France Millennium Temps plein

Quant Strategies Off-Cycle Internship
- We are looking for a 5-6 months off-cycle intern.
- You should bring a strong theoretical background and be fluent in python and pandas.
- All necessary computational infrastructure and technical support will be at your disposal.
- You will be based in the Millennium offices in Paris.

**Analysis and Applications of Alternative Portfolio Optimization Approaches**

**Background**

Over 70 years ago Harry Markowitz launched finance into a new era by inventing modern portfolio theory [1].

Markowitz approach is to choose the right portfolio as the one that maximizes expected returns and controls the risk (modelled as the variance of the portfolio).

One of the (possibly undesired) consequences of the above approach is that the resulting allocation distributes large parts of the risk to the small modes of, the correlation matrix of returns of the different securities.

There are many alternative approaches that lead to portfolios that are optimal in a different sense [2,3,4] and that redistribute risk differently. Their respective derivations are typically very different and yet the resulting allocations can often be brought into similar forms.

**Objective(s)**

(a) Unify the theoretical foundations that lead to the different portfolio optimization strategies.

Exemplary directions:

- Are there some shared first principles that can unify the different approaches? - The following approaches are typically derived from different principles and yet ( are expected returns):

- Markowitz approach [1] 1
- Max. entropy approach [2] 0
- Agnostic Risk Parity approach [3] 1 2
- What are the practical limitations and possible/necessary extensions in realistic settings?
- How does the structure of impact the results?
- How should the methods be adapted in a dynamic setting under cost constraints?
- References _
- [1] Markowitz, H., Portfolio selection. Journal of Finance. 7(1):77-91, (1952) _
- [2] Windcliff, H. & Boyle P., The 1/n pension plan puzzle, North American Actuarial Journal. 8. 32-45, (2004) _
- [3] Benichou, R., Lemperiere, Y., Sérié,E., Kockelkoren, J., Seager, P., Bouchaud, J.P. & Potters, M. Agnostic Risk Parity: Taming Known and Unknown-Unknowns. The Journal of Investment Strategies. 6. 10.21314, (2016)_

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