Maximize quadratic utility function
In the video on challenges of portfolio optimization, you saw how to solve a quadratic utility optimization problem with the package quadprog. This exercise will show you how to solve a quadratic utility problem using the PortfolioAnalytics
package. Recall the quadratic utility formulation has two terms, one for portfolio mean return and another for portfolio variance with a risk aversion parameter, lambda.
This exercise is part of the course
Intermediate Portfolio Analysis in R
Exercise instructions
- Create a portfolio specification object using asset names from the
index_returns
dataset and name the portfolio specification objectport_spec
. - Add a full investment constraint such that the weights sum to 1 to the
port_spec
object. - Add a long only constraint such that the weight of an asset is between 0 and 1 to the
port_spec
object. - Add an objective to maximize portfolio mean return to the
port_spec
object. - Add an objective to minimize portfolio variance to the
port_spec
object. Risk aversion should be set to 10. - Run the optimization. This problem can be solved by a quadratic programming solver so we specify
optimize_method = "ROI"
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Create the portfolio specification
port_spec <- portfolio.spec(assets = ___)
# Add a full investment constraint such that the weights sum to 1
port_spec <- add.constraint(portfolio = ___, type = ___)
# Add a long only constraint such that the weight of an asset is between 0 and 1
port_spec <- add.constraint(portfolio = ___, type = ___)
# Add an objective to maximize portfolio mean return
port_spec <- add.objective(portfolio = ___, type = ___, name = ___)
# Add an objective to minimize portfolio variance
port_spec <- add.objective(portfolio = port_spec, type = ___, name = ___, risk_aversion = ___)
# Solve the optimization problem
opt <- optimize.portfolio(R = ___, portfolio = ___, optimize_method = "ROI")