How does the minimum variance
frontier change over time?
Refer to the top screen dump. If you click on the Animate button with Block
size left at 50 (months), you will see how the minimum variance frontiers
move around over time. This sequences is computed as follows:
The first 50-month's returns are used to construct
the initial minimum variance frontier from, then the oldest month is dropped
and the 51st month is added. The minimum variance frontier is re-estimated
and re-plotted. This then continues by dropping the current oldest month
and adding the 52nd month, re-estimating and plotting and so on until all
data is used up.
This gives you insight into the dynamics of risk
and return. It also underscores one of the significant problems that arise
when attempting to apply the Markowitz diversification technique. The weights
selected may have been efficient using all realized data assuming that the
minimum variance frontier is stationary. In the real world this is not the
case and so the portfolios identified are likely to fail to be ex ante (i.e.,
in an expected sense) efficient! Backtesting can help you assess the magnitude
of this problem, a tool that we consider next.