How to add Risk Contribution/Risk Parity Constraint?

[x829901]

In the following code, I have two questions.

1. How do I add a risk parity constraint where each holding contributes an equal amount of risk?
2. How do I add a risk contribution constraint to, for example, constrain portfolio to no more than 50% of the portfolio's risk can be allocated to growth stocks?

ef = efficient_frontier.EfficientFrontier(mu, S)
ef.add_constraint(lambda w: w @ growth == w @ value)
ef.add_constraint(lambda w: w @ largecap >= w @ midcap)
ef.add_constraint(lambda w: w @ midcap >= w @ smallcap)
ef.add_sector_constraints(region_mapper, region_lower, region_upper)
ef.add_sector_constraints(size_mapper, size_lower, size_upper)
ef.add_sector_constraints(style_mapper, style_lower, style_upper)
ef.add_sector_constraints(type_mapper, type_lower, type_upper)
ef.add_sector_constraints(asset_mapper, asset_lower, asset_upper)
ef.add_sector_constraints(sector_mapper, sector_lower, sector_upper)
ef.min_volatility()
weights = ef.clean_weights(0.005)

For reference, here is how I am calculating risk contribution from each asset in a portfolio.

p = prices
S = risk_models.risk_matrix(p, 'sample_cov')
pvar = np.dot(w.T, np.dot(S, w))
pvol = np.sqrt(np.dot(w.T, np.dot(S, w)))
pvolw = ((np.dot(w, S)) / pvar) * w

w is the portfolio's % weighting for each ticker as a pandas Series, (screenshot below).

pvolw is the pandas Series of each holding's risk contribution as a percentage of total portfolio risk (screenshot below). For example, you'll see that stock ticker AB US Equity is contributing 1.6546% to the portfolio risk volatility.

[robertmartin8]

Hi @x829901,

Unfortunately that isn't currently possible. Risk contribution / risk parity is not a convex problem in general, though for simple constraints there is an equivalent convex problem (see page 46 here).

There is a python library called riskparity.py that can solve these problems, and I recently got permission from the authors to build it into PyPortfolioOpt, but that won't happen for several months.

Best, Robert

[x829901]

Ok thanks. Yes, it would very useful to constrain risk weightings. Cash weightings can be deceptive in terms of how much risk exposure there actually within the portfolio.