112 Optimizing Optimization
optimization. It is especially suitable for assets with nonnormal return distri-
butions, which is common for assets such as hedge funds, private equity, and
commodities.
Portfolio attributes
Efficient surface
The WPA shows a three-dimensional plot of the current portfolio, the bench-
mark portfolio, and 10 optimal portfolios that lie on the efficient surface. The
vertical axis is expected return, and the other two dimensions are expected risk
(standard deviation) and tracking error.
The user can identify portfolios that have:
- The same expected return with lower standard deviation
- The same risk (standard deviation) with higher expected return
Higher moments
The WPA shows a variety of portfolio attributes for the various portfolios,
including skewness, kurtosis, and probability of breaching a user-specified thresh-
old. These results are particularly useful for comparing an existing portfolio to a
full-scale optimal portfolio.
Probability of loss
The WPA allows the user to evaluate probability of loss in a variety of ways.
It shows probability of loss both at the end of the horizon and throughout the
horizon. The user has the flexibility to vary the length of the horizon, the per-
centage loss threshold, and the portfolio value.
The WPA allows the user to estimate probability of loss analytically, by
Monte Carlo simulation or by bootstrap simulation.
Value at risk
The WPA shows value at risk measured both at the end of the horizon and
throughout the horizon. The user has the flexibility to vary the length of the
horizon, the VaR threshold, and the portfolio value.
The WPA allows the user to estimate value at risk analytically, by Monte
Carlo simulation or by bootstrap simulation.
Joint probability of loss
Many investors care about both absolute and relative performance. The WPA
shows the joint probability of failing to achieve an absolute target and simulta-
neously underperforming the benchmark.