As part of an assignment in a course called Asset Pricing, we were tasked to plot a minimum-variance frontier of 10 industry portfolios with tangency portfolio & determine the weights of the industry portfolios at tangency portfolio.
Industry_Portfolios.xlsx contains monthly nominal (net) returns for ten industry portfolios, expresssed as a percentage. i. These returns cover the ten-year period from Jan 2004 through Dec 2013.
- Calculate the vector of mean returns and covariance matrix of returns for the ten industry portfolios.
- Use this to plot the minimum-variance frontier generated by the ten industry portfolios, with mean return on the y axis and standard deviation of return on the x axis. The plot should cover the range from 0% to 2% per month on the y axis.
- Now suppose that the riskless asset offers risk-free return of 0.13% per month. Plot the efficient frontier (with the riskless asset) on the same plot as the minimum-variance frontier generated by the ten industry portfolios.
- Calculate the weights of the ten industry portfolios at the tangency portfolio.
Minimum-variance frontier: the minimum-variance frontier consists of portfolios with lowest risk for given mean return. Hence no portfolio can lie outside (i.e. to the left) of the minimum-variance frontier.
Efficient frontier: the efficient frontier consists of portfolios with highest mean return for given risk. Hence rational risk-averse investors will choose to hold optimal portfolio that lies on the efficient frontier.
Tangency portfolio: Tangency portfolio is risky portfolio with highest Sharpe ratio. Hence if all investors are rational and risk-averse, then the tangency portfolio will be the market portfolio.
The code is carried out on Jupyter Notebook using Python 3.6. Most libraries imported in this code comes together with Anaconda.
- Parsing the excel file of the 10 Industry portfolios
- Calculate vector of mean returns & covariance matrix of returns
- Determine Lagrange multipliers e.g. alpha, delta, zeta
- Provide evenly-spaced values for plot of Minimum-Variance portfolio
- Determine mean, variance and weights of Minimum-Variance portfolio
- Determine expected return, variance and weights of Tangency portfolio
- Plot the Minimum Frontier portfolio with Tangency portfolio