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 Variance
p] = the portfolio variance
for the industrial mix of a region
i], and decreasing in scaled portfolio variance
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.
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.