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