The portfolio variance
is simply the expected value of the squared deviations of the return on the portfolio from the mean return on the portfolio, that is [mathematical expression not reproducible] (2).
To compute portfolio variance
in a way that solver can update it when it runs, enter the following equation in the portfolio return output cell:
As the weight in each investment is changed, the portfolio return (equation 2) and portfolio variance
(equation 3) change.
However, when supplementing the information on the marginal distributions with information on the portfolio variance
(as a source of dependence information), it turns out that when the variance constraint is "low" enough, our analytical bounds coincide with moment bounds.
We use Black (1972) to find closedform solutions for the optimal portfolio weights, portfolio expected return, and portfolio variance
of the VaR investor.
At their core, robos are based on mean-variance optimization (MVO) the key to which is a portfolio variance
formula that works like this in a two-asset example:
Following the mean-variance model [attributed to Markowitz (1959)], the optimal hedge ratio that maximises expected utility for infinite degree of risk aversion and also minimises portfolio variance
, is: (5)
Alternatively, the MV optimization can be set to minimize the portfolio variance
for a given expected target return.
The change in portfolio variance
is dependent on the size and value of the position holdings.
The second section analytically presents the three key concepts for tracking indices: tracking error variance, excess return, and portfolio variance
. The following section introduces a new criterion, the curvature of the tracking frontier, and discusses the benefits that arise from adding the concept of gradient to the previous ones.
Changes in the Components of the Industry Portfolio Variance
[[sigma].sup.2.sub.p] = the portfolio variance
for the industrial mix of a region