Portfolio Theory
Dr. Andrea Rigamonti
andrea.rigamonti@econ.muni.cz
Seminar 7
Content:
• Initial settings and inputs estimation
• Portfolio optimization
Initial settings and inputs estimation
For the inputs estimation we use a rolling window of 120
periods. The portfolio performance will therefore be
computed starting from the 121th period.
In addition to the sample mean and covariance matrix, we
also estimate the shrunk covariance matrix introduced by
Ledoit and Wolf (2004) using the function “linshrink_cov”.
We also compute a naïve 1/N portfolio to be used as
benchmark.
Portfolio optimization
We compute the following optimal portfolios:
• Mean-variance with sample estimates
• Mean-variance with sample mean and shrunk covariance
• Minimum variance with sample covariance
• Minimum variance with shrunk covariance
• Long-only minimum variance with sample covariance
• Long-only minimum variance with shrunk covariance
Portfolio optimization
• Shrinkage portfolio that combines the mean-variance with
the naïve 1/N portfolio, whose weights are given by:
𝒘∗
= 𝛿𝒘 𝑵𝑨𝑰𝑽𝑬 + 1 − 𝛿 𝒘
_
We simply set 𝛿=0.2
• Grouping strategy that optimizes between groups of
assets and uses equal weights within groups. We naively
group assets in groups of 3 by alphabetical order.
_
We do this by computing the average return of each
group, then we estimate the inputs and use them for
optimization. We then repeat each weight 3 times, and
use them for the single assets.