I am having trouble coming up with a function to optimize the weights to be as equal as possible.
It is a long-short portfolio with 6 positions weights is a cvx variable: [long, long, short, short, long/short, long/short]
There are some constraints such as gross exposure cannot exceed 2, gross long cannot exceed 1.5.
To get portfolio weights as close to equal weight as possible, one way is to minimize the variance of the absolute value of weights.
cvxpy.Minimize(cvx.sum_squares(cvx.sum(cvx.abs(weights)) - cvx.abs(weights)/6))
But this throws "does not follow DCP rules".
What's the problem in this line that causes the violation of DCP rules?
More importantly, any thoughts on how to write an objective function to push weights to as equal weight as possible?
Clarification on my question:
Here's the problem I need to solve:
I have a portfolio with 6 stocks, with the following beta: [0.7, 1.5, 0.4, 0.8, 0.5, 1]
the first two must be long, the second two must be short, the 5th and 6th stock can be long and short.
gross exposure cannot exceed 2
leveraged long exposure cannot exceed 1.5
beta adjusted net long or short exposure cannot exceed 0.5
Objective: portfolio as close to equal weight as possible.
betas = [0.7, 1.5, 0.4, 0.8, 0.5, 1] weight_longs = cvx.Variable(2) weight_shorts = cvx.Variable(2) weight_longorshort = cvx.Variable(2) weights = cvx.hstack([weight_longs, weight_shorts, weight_longorshort]) # Constraints: bounds = [w_longs>=0.0, w_shorts<=-0.0] gross_exp = [cvx.sum(cvx.abs(weights)) <=2] lev_long = [cvx.sum(w_longs) + cvx.sum(cvx.pos(w_longorshort)) <= 1.5] beta_net_exp = [cvx.abs(cvx.sum(np.array(betas) * weights)) <= 0.5] constraints = bounds + gross_exp + lev_long + beta_net_exp # Minimize the variance of absolute value of weights to achieve close to equal weight obj_func = cvx.sum_squares(cvx.abs(weights) - cvs.abs(weights/6)) cvx.Problem(obj_func, constraints)