  We adopt deep learning models to directly optimise the portfolio Sharpe
ratio. The framework we present circumvents the requirements for forecasting
expected returns and allows us to directly optimise portfolio weights by
updating model parameters. Instead of selecting individual assets, we trade
Exchange-Traded Funds (ETFs) of market indices to form a portfolio. Indices of
different asset classes show robust correlations and trading them substantially
reduces the spectrum of available assets to choose from. We compare our method
with a wide range of algorithms with results showing that our model obtains the
best performance over the testing period, from 2011 to the end of April 2020,
including the financial instabilities of the first quarter of 2020. A
sensitivity analysis is included to understand the relevance of input features
and we further study the performance of our approach under different cost rates
and different risk levels via volatility scaling.
