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.
Changes in the Components of the Industry
Portfolio Variancep] = the
portfolio variance for the industrial mix of a region
i], and decreasing in scaled
portfolio variance (risk), [[sigma].
The objective of MV model is to find the weight of assets that will minimize the
portfolio variance at a level of required rate of return.
Portfolio variance depends on the variance of each asset and also the correlations among themselves.
To create the efficient frontier we specified a return and had solver minimize the
portfolio variance by changing the weight invested in each stock.
