Finding the mean-variance efficient portfolio
A mean-variance efficient portfolio can be obtained as the solution of minimizing the portfolio variance under the constraint that the portfolio expected return equals a target return. A convenient R function for doing so is the function portfolio.optim() in the R package tseries. Its default implementation finds the mean-variance efficient portfolio weights under the constraint that the portfolio return equals the return on the equally-weighted portfolio. The only argument needed is the monthly return data on the portfolio components for which the weights need to be determined.
The variable returns containing the monthly returns of the DJIA stocks is already loaded in the console.
This is a part of the course
“Introduction to Portfolio Analysis in R”
Exercise instructions
- Load the library
tseries. - Create a mean-variance efficient portfolio of monthly returns using the default of
portfolio.optim()targeting the equally-weighted portfolio return, and assign the output to the variableopt. - Create a vector of weights from your optimized portfolio. Portfolio weights can be found in
opt$pw. Call thispf_weights. - Assign the names to the assets using the provided code.
- Select the optimum weights from
pf_weightsthat are greater than or equal to 1%, call thisopt_weights. - Use barplot() to visualize the distribution of
opt_weights. - Print the expect portfolio return (
opt$pm) and volatility (opt$ps) of the optimized portfolio.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Load tseries
# Create an optimized portfolio of returns
opt <- portfolio.optim(___)
# Create pf_weights
pf_weights <- ___$pw
# Assign asset names
names(pf_weights) <- colnames(returns)
# Select optimum weights opt_weights
opt_weights <- pf_weights[___ >= 0.01]
# Bar plot of opt_weights
# Print expected portfolio return and volatility
___$pm
___$ps
This exercise is part of the course
Introduction to Portfolio Analysis in R
Apply your finance and R skills to backtest, analyze, and optimize financial portfolios.
We have up to now considered the portfolio weights as given. In this chapter, you learn how to determine in R the portfolio weights that are optimal in terms of achieving a target return with minimum variance, while satisfying constraints on the portfolio weights.
Exercise 1: Modern portfolio theory of Harry MarkowitzExercise 2: Mean-variance based investing in DJIA stocksExercise 3: Exploring monthly returns of the 30 DJIA stocksExercise 4: Finding the mean-variance efficient portfolioExercise 5: Effect of the return targetExercise 6: Imposing weight constraintsExercise 7: The efficient frontierExercise 8: Computing the efficient frontier using a grid of target returnsExercise 9: Interpreting the efficient frontierExercise 10: Properties of the efficient frontierExercise 11: The minimum variance and maximum Sharpe ratio portfolioExercise 12: In-sample vs. out-of-sample evaluationExercise 13: Split-sample evaluationExercise 14: Out of sample performance evaluationExercise 15: It ain't overWhat is DataCamp?
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