Portfolio optimisation with machine learning

In mean-variance optimisation, what does the covariance matrix primarily capture?

The expected return of each asset individually
How asset returns move in relation to one another
The total market capitalisation of each asset
The Sharpe ratio of the overall portfolio

The covariance matrix records pairwise relationships between asset returns. A high positive covariance means two assets tend to rise and fall together, which reduces diversification benefit. ML methods like shrinkage estimators or factor models help produce more stable covariance estimates from noisy historical data.

Which regularisation technique is most commonly applied to prevent overfitting when training a return-prediction model on financial time series?

Batch normalisation
Principal component analysis
L2 (Ridge) regularisation
Gradient clipping

L2 regularisation penalises large coefficient values, which is especially useful when financial features are noisy or correlated. It shrinks weights toward zero without eliminating them entirely, reducing variance without introducing too much bias - a common trade-off in return-prediction tasks.

Reinforcement learning applied to portfolio rebalancing treats the problem as which type of decision process?

A Markov Decision Process where the agent receives a reward signal after each allocation step
A supervised regression problem where target weights are labelled by a human expert
A clustering problem that groups assets into risk buckets
A generative modelling task that synthesises new price paths

In an MDP framing, the state is the current portfolio and market conditions, the action is the rebalancing decision, and the reward is typically a risk-adjusted return metric. The agent learns a policy by interacting with a market simulator rather than from pre-labelled data.

Walk-forward validation is preferred over standard k-fold cross-validation for financial models primarily because it:

Requires less computational memory
Produces a higher Sharpe ratio automatically
Eliminates the need for feature engineering
Respects the temporal ordering of data and prevents look-ahead bias

Standard k-fold randomly shuffles data, which means the model can train on future observations and test on past ones - a form of look-ahead bias. Walk-forward validation always trains on earlier periods and tests on later ones, mimicking how a model would actually be deployed.

Hierarchical Risk Parity (HRP) differs from classical mean-variance optimisation mainly in that it:

Maximises expected return without any risk constraint
Uses clustering to allocate risk across asset groups rather than inverting the covariance matrix
Requires a minimum of five years of daily price history to function
Is exclusively used for fixed-income portfolios

HRP applies hierarchical clustering to group correlated assets, then distributes risk contributions across those groups. Because it avoids matrix inversion, it is numerically more stable than Markowitz optimisation when the covariance matrix is ill-conditioned or estimated from limited data.

When using an LSTM network to model asset returns, which of the following is a genuine limitation specific to this architecture?

It cannot process sequences of more than 30 time steps
It always requires labelled data from a domain expert
Training is computationally expensive and the model is difficult to interpret
It cannot handle multivariate inputs

LSTMs are powerful for sequential data but require significant compute for training and are notoriously hard to interpret - a real concern in regulated financial contexts where model explainability matters. They also need careful hyperparameter tuning and are prone to overfitting on small financial datasets.

Conditional Value at Risk (CVaR) is preferred over Value at Risk (VaR) as a loss function in ML-based portfolio models because:

CVaR accounts for the magnitude of losses beyond the threshold, not just the probability of exceeding it
CVaR is always a smaller number than VaR for the same confidence level
CVaR is easier to compute with gradient descent
CVaR ignores the tail of the return distribution

VaR only tells you that losses will exceed a threshold with a given probability - it says nothing about how severe those losses might be. CVaR averages the losses in the worst tail scenarios, making it a more informative and coherent risk measure for optimisation objectives.

Transaction cost modelling is important in ML portfolio optimisation because ignoring it tends to:

Reduce the number of assets the model can consider
Increase the model's interpretability
Simplify the covariance estimation problem
Lead to excessive turnover and overestimated live performance

Models that ignore transaction costs tend to rebalance aggressively whenever a small signal appears. In live trading, bid-ask spreads, market impact, and brokerage fees erode returns quickly. Including a realistic cost model in the objective function encourages the model to trade only when the expected gain justifies the friction.

How well do you know ML for portfolios?

Eight questions across core concepts

Concepts tested in this assessment