i

Monday, 6 January 2014

Resampling the Efficient Frontier - With How Many Observations?

Since optimizer inputs are stochastic variables, it follows that any efficient frontier must be a stochastic object. The efficient frontier we usually plot in mean/variance space is the expected efficient frontier. The realized efficient frontier will almost always deviate from the expected frontier and will lie within certain confidence bands.
Several attempts have been made to illustrate the stochastic nature of the efficient frontier, the most famous one probably being the so-called "Resampled Efficient Frontier" (tm) by Michaud/Michaud(1998).
Resampling involves setting the number of simulations as well as setting the number of observations to generate in each simulation. The importance of the latter decision is typically underestimated.
The chart below plots the resampled portfolios of 16 portfolios on a particular mean/variance efficient frontier...


The larger density of points at the bottom left end of the frontier is a result from the fact that there exist two very similar corner portfolios in this area of the curve.
The chart below plots the same frontier with the same number of simulations, but a much larger number of generated observations...

 

As the confidence bands, average weights or any risk and return characteristics are largely determined by the choice of number of simulations and number of observations in each simulation, it is worth keeping an eye on these modelling decisions when using relying on a resampling approach for investment purposes.

No comments:

Post a Comment