We are now able to create a function to use fmin() to determine the set of weights that maximize the Sharpe ratio for a given set of returns representing the stocks in our portfolio.

Since fmin() finds a minimum of the applied function, and the efficient portfolio exists at the maximized Sharpe ratio, we need to provide a function that, in essence, returns the negative of the Sharpe ratio, hence allowing fmin() to find a minimum:

In [24]:
   def negative_sharpe_ratio_n_minus_1_stock(weights, 
                                             returns, 
                                             risk_free_rate):
       """
       Given n-1 weights, return a negative sharpe ratio
       """
       weights2 = sp.append(weights, 1-np.sum(weights))
       return -sharpe_ratio(returns, weights2, risk_free_rate)

Our final function is given a DataFrame of returns, and a risk-free rate will run a minimization process on our negative sharpe function. The process is seeded...