Bangor University Featured PhD Programmes
Xi’an Jiaotong-Liverpool University Featured PhD Programmes
Ulster University Featured PhD Programmes
University of Nottingham Featured PhD Programmes
University of Exeter Featured PhD Programmes

Asset Allocation with Machine Learning and Parameter Uncertainty

Project Description

The University of Bath is inviting applications for the following PhD project based in the School of Management under the supervision of Dr Emmanouil Platanakis ( and Professor David Newton (


The mean-variance portfolio optimization framework of Markowitz (1952) is a highly popular portfolio optimization tool that has been widely used by academics and in the financial services industry. The Markowitz mean-variance portfolio framework is optimal only when asset returns follow a Normal distribution and the input parameters (mean returns and covariance matrix) are known with certainty. However, the prediction of mean returns and covariances can be very challenging and the use of sample (historical) estimates in mean-variance optimization is often subject to significant estimation risk. Furthermore, asset returns do not follow a Normal distribution in practice. As a direct consequence, the mean-variance portfolio construction process as proposed by Markowitz (1952) can be an error maximizer by generating solutions that are very far away from being optimal out-of-sample (when input parameters are uncertain) and this phenomenon has been well-documented in the literature; see, for instance, Ziemba and Mulvey (1998), Levy and Roll (2010) and Levy and Levy (2014.

The main target of this project is to develop robust portfolio optimization techniques that perform well out-of-sample via the novel implementation of machine learning techniques (e.g. supervised, unsupervised, semi-supervised and reinforcement learning) in conjunction with sophisticated portfolio optimization methods (e.g. shrinkage techniques) and advanced statistical methods (e.g. Bayesian inference).


Applicants for a studentship must have obtained, or be about to obtain, a First or Upper Second Class UK Honours degree, or the equivalent qualifications gained outside the UK, in a relevant discipline.

Formal applications should be made via the University of Bath’s online application form:

Please ensure that you quote the supervisor’s name and project title in the ‘Your research interests’ section.

More information about applying for a PhD at Bath may be found here:

Anticipated start date: 28 September 2020.

Funding Notes

Candidates applying for this project will be considered for a University studentship, which will cover UK/EU tuition fees, a training support grant of £1,000 per annum and a tax-free maintenance allowance at the UKRI Doctoral Stipend rate (£15,009 in 2019-20) for a period of up to 4 years. Limited funding opportunities for outstanding Overseas candidates may be available. Some School of Management studentships require recipients to contribute annually up to a maximum of 133 hours of seminar-based teaching and assessment in years 2, 3 and 4 of study (students will not be expected to give lectures).


Levy, H. & Levy, M. (2014). The Benefits of Differential Variance-Based Constraints in Portfolio Optimization. European Journal of Operational Research, 234(2), 372-381.
Levy, M. & Roll, R. (2010). The market portfolio may be mean-variance efficient after all. The Review of Financial Studies, 23(6), 2464-2491.
Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7(1), 77-91.
Ziemba, W. T. & Mulvey, J. M. (1998). Worldwide Asset and Liability Modelling, Cambridge University Press.

How good is research at University of Bath in Business and Management Studies?

FTE Category A staff submitted: 64.90

Research output data provided by the Research Excellence Framework (REF)

Click here to see the results for all UK universities

Email Now

Insert previous message below for editing? 
You haven’t included a message. Providing a specific message means universities will take your enquiry more seriously and helps them provide the information you need.
Why not add a message here
* required field
Send a copy to me for my own records.

Your enquiry has been emailed successfully

FindAPhD. Copyright 2005-2020
All rights reserved.