Mean-variance optimization requires knowledge of the expected returns. In practice, these are rather difficult to know with any certainty. Thus the best we can do is to come up with estimates, for example by extrapolating historical data, This is the main flaw in mean-variance optimization – the optimization procedure is sound, and provides strong mathematical guarantees, given the correct inputs. This is one of the reasons why I have emphasised modularity: users should be able to come up with their own superior models and feed them into the optimizer.
Caution!
Supplying expected returns can do more harm than good. If predicting stock returns were as easy as calculating the mean historical return, we'd all be rich! For most use-cases, I would suggest that you focus your efforts on choosing an appropriate risk model (see :ref:`risk-models`).
As of v0.5.0, you can use :ref:`black-litterman` to significantly improve the quality of your estimate of the expected returns.
.. automodule:: pypfopt.expected_returns
.. note::
For any of these methods, if you would prefer to pass returns (the default is prices),
set the boolean flag ``returns_data=True``
.. autofunction:: mean_historical_return
This is probably the default textbook approach. It is intuitive and easily interpretable,
however the estimates are subject to large uncertainty. This is a problem especially in the
context of a mean-variance optimizer, which will maximise the erroneous inputs.
.. autofunction:: ema_historical_return
The exponential moving average is a simple improvement over the mean historical
return; it gives more credence to recent returns and thus aims to increase the relevance
of the estimates. This is parameterised by the ``span`` parameter, which gives users
the ability to decide exactly how much more weight is given to recent data.
Generally, I would err on the side of a higher span – in the limit, this tends towards
the mean historical return. However, if you plan on rebalancing much more frequently,
there is a case to be made for lowering the span in order to capture recent trends.
.. autofunction:: capm_return
.. autofunction:: returns_from_prices
.. autofunction:: prices_from_returns