Applied Portfolio Optimization 

The following was implemented in Maple by Marcus Davidsson (2009) davidsson_marcus@hotmail.com 

1) Introduction to Permutations 

In this worksheet we assume that we only can take long positions to make things simple. We also assume that all portfolios are equal  

weighted which means that the expected return and covariance are simply additive since we are investing an equal fraction in each stock. 

Our objective is to maximize the Sharpe Ratio for our P stock portfolio.  

We should also note the number of permutations that is required to calculate the "optimal portfolio" where nstock is the total number of stocks

and P is the number of stocks that should be included in the portfolio is given by: 

(1)	(2)	(3)	(4)
(5)	(6)	(7)	(8)

We can also plot the number of permutations required for each amount of nstock and P 

2) Portfolio Optimization for a 2 Stock Portfolio 

We can now run the simulations 

	(9)

3) Portfolio Optimization for a 4 Stock Portfolio 

We can now run the simulations 

	(10)

Legal Notice: ? Maplesoft, a division of Waterloo Maple Inc. 2009. Maplesoft and Maple are trademarks of Waterloo Maple Inc. Neither Maplesoft nor the authors are responsible for any errors contained within and are not liable for any damages resulting from the use of this material.  This application is intended for non-commercial, non-profit use only. Contact the authors for permission if you wish to use this application in for-profit activities.